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+ "The [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) is a class that allows you to arbitarily combine multiple states, potentially of different types, into a new state that can be used with the navlie framework.\n", + "\n", + "Let's consider the previous example where we used the following $SE(2)$ pose transformation matrix to represent the state:\n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab} & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2).\n", + "$$\n", + "\n", + "Suppose we now also want to estimate a wheel odometry bias $\\mathbf{b} \\in \\mathbb{R}^2$ in addition to the robot's pose. Our state is now \n", + "\n", + "$$\n", + "\\mathbf{x} = (\\mathbf{T}, \\mathbf{b}) \\in SE(2) \\times \\mathbb{R}^2.\n", + "$$\n", + "\n", + "This can be implemented easily using the [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) class in one of two ways: either directly or by inheritance. We'll show the former approach first." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [0.1 2. ]\n" + ] + } + ], + "source": [ + "import navlie as nav \n", + "import numpy as np\n", + "\n", + "# Define the pose and bias as their own states\n", + "T = nav.lib.SE2State(value = [0.1, 2.0, 3.0], stamp = 0.0, state_id=\"pose\")\n", + "b = nav.lib.VectorState(value = [0.1, 2.0], stamp = 0.0, state_id=\"bias\")\n", + "\n", + "# Combine into a composite state, and its ready to use!\n", + "x = nav.CompositeState([T, b], stamp=0.0)\n", + "\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``CompositeState`` class is a subclass of the ``State`` class, but who's ``value`` is a list of states, referred to as the *substates*. A convenience of this class is that the composite state's ``plus``, ``minus``, and ``copy`` methods have already been implemented for you based on the implementations in the substates. Note that the order in which the states are listed is important, and will correspond to the order of the components in the vectors involved in the ``plus`` and ``minus`` operations. This can be demonstrated with the following example." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Result after plus():\n", + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.45359612 -0.89120736 1.80531705]\n", + " [ 0.89120736 0.45359612 6.55185711]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [4.1 7. ]\n", + "\n", + "Result after minus():\n", + "[[1.]\n", + " [2.]\n", + " [3.]\n", + " [4.]\n", + " [5.]]\n" + ] + } + ], + "source": [ + "# plus() and minus() have been defined for you. Here, the first three elements\n", + "# of the vector to be added correspond to the pose (since it has 3 DOF), and the\n", + "# last two to the bias.\n", + "x_temp = x.plus(np.array([1,2,3,4,5]))\n", + "print(\"\\nResult after plus():\")\n", + "print(x_temp)\n", + "\n", + "dx = x_temp.minus(x)\n", + "print(\"\\nResult after minus():\")\n", + "print(dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we must write a process model that works with this state. We'll use the same process model as before, but now we'll also include the wheel odometry bias in the state. The bias process model will be modelled as a random walk of the form \n", + "\n", + "$$\n", + "\\mathbf{b}_{k+1} = \\mathbf{b}_k + \\Delta t \\mathbf{w}^\\mathrm{bias}_k,\n", + "$$\n", + "\n", + "where $\\mathbf{w}^{\\mathrm{bias}}_k \\sim \\mathcal{N}(0, \\mathbf{Q}^{\\mathrm{bias}})$ represents random error associated with this otherwise constant process model, which allows the bias to slowly vary. The process model for the composite state is then" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.linalg import expm\n", + "\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "class WheeledRobotWithBias(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " pose = x.value[0]\n", + " bias = x.value[1]\n", + " vel = np.array([u.value[0] - bias.value[0], u.value[1] - bias.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value[0].value = pose.value @ expm(wedge_se2(vel * dt))\n", + "\n", + " # Largely data generation and jacobian purposes, we also update the bias\n", + " # state with an input, even if the input here is always zero in the\n", + " # nominal case.\n", + " x_next.value[1].value = bias.value + u.value[2:4]*dt\n", + " return x_next\n", + " \n", + " def input_covariance(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(4) * 0.1**2\n", + "process_model = WheeledRobotWithBias(Q)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'd like to use the same measurement model as before, which was just a series of range measurements to known landmarks:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: nav.lib.SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: nav.lib.SE2State):\n", + " return self.R\n", + " \n", + "R = 0.1**2\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The problem is that this was made for an ``SE2State`` instead of our new composite state, and specifically the line `pos = x.value[0:2, 2]` is going to throw an error when we feed in a composite state. This is easy to change, but then that means we have to make a similar change for all sorts of different state definitions. An alternative is to use the [CompositeMeasurementModel](../_autosummary/navlie.composite.CompositeMeasurementModel.rst), which is just a lightweight wrapper around one measurement model that \"assigns\" the model to a specific substate, referenced to by its `state_id` field. It is used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RangeToLandmarkSE2(of substate pose)\n", + "Jacobian:\n", + "[[0. 0.46544123 0.88507893 0. 0. ]]\n" + ] + } + ], + "source": [ + "meas_models = []\n", + "for lm in landmarks:\n", + " meas_models.append(\n", + " nav.CompositeMeasurementModel(RangeToLandmarkSE2(lm, R), \"pose\")\n", + " )\n", + "\n", + "print(meas_models[0])\n", + "print(\"Jacobian:\")\n", + "print(meas_models[0].jacobian(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This does mean that the `state_id` of each substate must be unique, but this is a good practice anyway. The `CompositeMeasurementModel` will then automatically handle the extraction of the relevant substate from the composite state and pass it to the measurement model, as well as handle the corresponding Jacobian accordingly. This is a good way to avoid having to write a lot of boilerplate code for different state definitions. Notice in the above example that the Jacobian has two extra zeros at the end, which correspond to the bias state that has no effect on the measurement. This is automatically handled by the `CompositeMeasurementModel`.\n", + "\n", + "With our problem now set up, we can run a filter on it with the same snippet as usual!" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, \n", + " input_func=lambda t, x: np.array([0.5, 0.3, 0.0, 0.0]), \n", + " input_covariance= Q, \n", + " input_freq=50, \n", + " meas_model_list=meas_models, \n", + " meas_freq_list=[10, 10, 10, 10] \n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2, 0.1**2, 0.1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0,0].set_title(\"Pose Estimation Errors\")\n", + "axs[0,0].set_ylabel(\"theta (rad)\")\n", + "axs[1,0].set_ylabel(\"x (m)\")\n", + "axs[2,0].set_ylabel(\"y (m)\")\n", + "axs[2,0].set_xlabel(\"Time (s)\")\n", + "axs[0, 1].set_title(\"Bias Estimation Errors\")\n", + "axs[0, 1].set_ylabel(\"ang. vel. (rad/s)\")\n", + "axs[1, 1].set_ylabel(\"forward vel. (m/s)\")\n", + "axs[1, 1].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Inheriting from `CompositeState`\n", + "\n", + "The previous example showed how to use the `CompositeState` class directly, but it's also possible to inherit from it. This is useful if you want to add some extra methods or attributes to the composite state, or if you are going to frequently be using the same composite state. Here's an example of how you would do it:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "WheeledRobotState(stamp=0.1, state_id=None) with substates:\n", + " SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.1, dof=2, state_id=bias)\n", + " [0.1 2. ]\n", + "SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n" + ] + } + ], + "source": [ + "class WheeledRobotState(nav.CompositeState):\n", + " def __init__(self, pose_values: np.ndarray, bias_values: np.ndarray, stamp: float):\n", + " pose = nav.lib.SE2State(pose_values, stamp=stamp, state_id=\"pose\")\n", + " bias = nav.lib.VectorState(bias_values, stamp=stamp, state_id=\"bias\")\n", + " super().__init__([pose, bias], stamp=stamp)\n", + "\n", + " # Define any getter that you want for convenience! \n", + " @property\n", + " def pose(self):\n", + " return self.value[0]\n", + "\n", + " @property\n", + " def bias(self):\n", + " return self.value[1]\n", + "\n", + " def copy(self):\n", + " return WheeledRobotState(self.pose.copy(), self.bias.copy())\n", + " \n", + "x = WheeledRobotState([0.1, 2.0, 3.0], [0.1, 2.0], stamp = 0.1)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can end up looking a lot cleaner, and is potentially more flexible to work with since you can add methods and attributes to the composite state. For example, because of the getters we defined above, we can access the pose and bias more ergonomically with `x.pose` and `x.bias`." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/doctrees/nbsphinx/tutorial/jacobians.ipynb b/_build/doctrees/nbsphinx/tutorial/jacobians.ipynb new file mode 100644 index 00000000..49b93bd8 --- /dev/null +++ b/_build/doctrees/nbsphinx/tutorial/jacobians.ipynb @@ -0,0 +1,340 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Jacobians in navlie\n", + "\n", + "As you may know, many state estimation algorithm require access to process model and measurement model Jacobians, with respect to the state and sometimes other inputs. For states belonging to Lie groups, algorithms will require _Lie Jacobians_, which differ from traditional derivatives as they conform to the constraints of the group. The abstraction provided by the $\\oplus$ and $\\ominus$ operators (implemented with `State.plus` and `State.minus` respectively) allow for a generic definition of a derivative:\n", + "\n", + "$$\n", + "\\left.\\frac{D f(\\mathcal{X})}{D \\mathcal{X}}\\right|_{\\bar{\\mathcal{X}} }\\triangleq \\left.\\frac{\\partial f(\\bar{\\mathcal{X}} \\oplus \\delta \\mathbf{x}) \\ominus f(\\bar{\\mathcal{X}})}{\\partial \\delta \\mathbf{x}}\\right|_{\\delta \\mathbf{x} = \\mathbf{0}},\n", + "$$\n", + "\n", + "which can be shown to fall back to a traditional derivatives when $\\oplus$ and $\\ominus$ are defined to be regular addition/subtraction. This derivative definition is used universally throughout navlie, and roughly follows what is done in the [Micro Lie Theory paper](https://arxiv.org/pdf/1812.01537.pdf). In that reference, seperate definitions are given for \"left\" and \"right\" derivatives, whereas we have aggregated them into a single definition, with left and right derivatives naturally arising from the choice of $\\oplus$ and $\\ominus$ operators.\n", + "\n", + "If you dont want to worry about this, the good news is that navlie computes Lie Jacobians for you by default using finite difference. However, finite difference can have some drawbacks, such as being computationally expensive and less accurate than analytic derivatives. In this notebook, we will show you how to use analytic derivatives in navlie, which offer the maximum accuracy and speed.\n", + "\n", + "## Jacobians - Traditional Approach\n", + "Recall the traditional approach to the previous example. We had defined the state to be $\\mathbf{x} = [\\theta, x, y]^T$ and the process model to be\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t \\\\\n", + "x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t \\\\\n", + "y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where $\\omega_k$ is the angular velocity and $v_k$ is the linear velocity. Since the state is just a regular vector, Lie Jacobians fall back to regular Jacobians, and standard derivative techniques lead to the following expressions for the process model Jacobian with respect to the state\n", + "\n", + "$$\n", + "\\mathbf{F} := \\frac{\\partial f(\\mathbf{x}_k, \\mathbf{u}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 1 & 0 & 0 \\\\ -v_k \\sin(\\theta_k) \\Delta t & 1 & 0 \\\\ v_k \\cos(\\theta_k) \\Delta t & 0 & 1 \\end{bmatrix}\n", + "$$\n", + "\n", + "To implement this Jacobian in navlie, all we need to do is override the `jacobian()` method in our process model, and it will get used automatically by the estimation algorithms. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import navlie as nav\n", + "import numpy as np\n", + "\n", + "from navlie.lib import VectorInput, VectorState\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + " def jacobian(self, x:VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " F = np.eye(3)\n", + " F[1, 0] = -u.value[1] * dt * np.sin(x.value[0])\n", + " F[2, 0] = u.value[1] * dt * np.cos(x.value[0])\n", + " return F\n", + "\n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, lets just double check that we did everything correctly by comparing with finite difference. All process models inherit the `jacobian_fd()` method, which computes the Jacobian using finite difference. We can use this to compare with our analytic Jacobian." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682942 1. 0. ]\n", + " [ 0.01080605 0. 1. ]]\n", + "\n", + "Finite difference:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682943 1. 0. ]\n", + " [ 0.01080604 0. 1. ]]\n" + ] + } + ], + "source": [ + "x = VectorState([1,2,3]) \n", + "u = VectorInput([0.1, 0.2]) \n", + "dt = 0.1 \n", + "\n", + "print(\"Analyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Jacobians match almost perfectly, but differ slightly due to errors in finite difference. This is expected, as finite difference is only an approximation. Nevertheless, finite difference is generally sufficiently accurate for most applications.\n", + "\n", + "
\n", + "Note: The `jacobian` methods must *always* return a 2D array.\n", + "
\n", + "\n", + "\n", + "\n", + "Moving on to the measurement model, which was previously defined to be \n", + "\n", + "$$\n", + "\\mathbf{y}_k = || \\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)} || \n", + "$$ \n", + "\n", + "where $\\mathbf{r}_k$ is the robot's position and $\\boldsymbol{\\ell}^{(i)}$ is the $i$th landmark. The measurement model Jacobian with respect to the state is\n", + "\n", + "$$ \n", + "\\mathbf{G} := \\frac{\\partial g(\\mathbf{x}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 0 & \\frac{(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})^T}{||(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})||} \\end{bmatrix},\n", + "$$\n", + "\n", + "and we can implement this in navlie by again overriding the `jacobian()` method in our measurement model. Adding this to our measurement model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[0. 0.70710678 0.70710678]]\n", + "\n", + "Finite difference:\n", + "[[0. 0.70710696 0.70710696]]\n" + ] + } + ], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + " def jacobian(self, x: VectorState) -> np.ndarray:\n", + " G = np.zeros((1, 3))\n", + " r = x.value[1:]\n", + " G[0,1:] = (r - self.landmark_position) / np.linalg.norm(r - self.landmark_position)\n", + " return G\n", + " \n", + "meas_model = RangeToLandmark(np.array([1, 2]))\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(meas_model.jacobian(x))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(meas_model.jacobian_fd(x))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can again see that the results match nicely." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jacobians - Lie Group Approach \n", + "\n", + "Now, lets see how to implement analytical Jacobians when states belong to Lie groups. In the previous example the state was $\\mathbf{T} \\in SE(2)$ and the process model was\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t).\n", + "$$\n", + "\n", + "To derive the Jacobian, we can \"perturb\" both sides of the equation and manipulate. This is a common technique for deriving Lie Jacobians, and for computing matrix-vector derivatives in general. For more details, we recommend reading [State Estimation for Robotics by Tim Barfoot](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf).\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\mathbf{T}_{k+1} &= \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + "\\bar{\\mathbf{T}}_{k+1} \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\bar{\\mathbf{T}}_{k} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\underbrace{\\bar{\\mathbf{T}}_{k+1}^{-1} \\bar{\\mathbf{T}}_{k}}_{\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\exp((\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}) \\delta \\boldsymbol{\\xi}_{k})^\\wedge) \\\\\n", + " \\delta \\boldsymbol{\\xi}_{k+1} &= \\underbrace{\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1})}_{\\mathbf{F}} \\delta \\boldsymbol{\\xi}_{k}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "There, we used the _adjoint matrix_ $\\mathbf{Ad}(\\cdot)$, to invoke the identity $\\mathbf{X}^{-1} \\exp(\\boldsymbol{\\xi}^\\wedge) \\mathbf{X} = \\exp(\\mathbf{Ad}(\\mathbf{X}) \\boldsymbol{\\xi}^\\wedge)$, which is true for any $\\mathbf{X} \\in SE(2)$. The adjoint matrix for $SE(2)$ is given by \n", + "\n", + "$$ \n", + "\\mathbf{Ad}(\\mathbf{T}) = \\begin{bmatrix} 1 & \\mathbf{0} \\\\ - \\boldsymbol{\\Omega} \\mathbf{r} & \\mathbf{C} \\end{bmatrix}\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\Omega} = \\begin{bmatrix} 0 & -1 \\\\ 1 \n", + "&0 \\end{bmatrix}$.\n", + "\n", + "
\n", + "Note: in this Jacobian derivation, we perturbed the state $\\mathbf{T} = \\bar{\\mathbf{T}} \\exp(\\delta \\boldsymbol{\\xi}^\\wedge)$ \"on the right\" because that corresponds to what was implemented in the `plus()` method of our `SE2State` class. It is important to be consistent here for everything to work.\n", + "
\n", + "\n", + "Now, we can implement this Jacobian in navlie by overriding the `jacobian()` method in our process model. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [ 0.0394695 0.92106099 0.38941834]\n", + " [ 0.19470917 -0.38941834 0.92106099]]\n", + "\n", + "Finite difference:\n", + "[[ 1.00000000e+00 -1.10747782e-11 -1.10747782e-11]\n", + " [ 3.94695038e-02 9.21060995e-01 3.89418343e-01]\n", + " [ 1.94709171e-01 -3.89418342e-01 9.21060994e-01]]\n" + ] + } + ], + "source": [ + "from navlie.lib import SE2State, VectorInput\n", + "from scipy.linalg import expm\n", + "\n", + "\n", + "def wedge_se2(x:np):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def adjoint_se2(T:np.ndarray):\n", + " C = T[:2, :2]\n", + " r = T[:2, 2]\n", + " Omega = np.array([[0, -1], [1, 0]])\n", + " Ad = np.zeros((3,3))\n", + " Ad[0,0] = 1\n", + " Ad[1:,1:] = C\n", + " Ad[1:,0] = - Omega @ r\n", + " return Ad\n", + "\n", + "\n", + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(u * dt))\n", + " return x_next\n", + " def input_covariance(self, x:SE2State, u:VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + " def jacobian(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " return adjoint_se2(expm(-wedge_se2(u * dt)))\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)\n", + "x = SE2State(expm(wedge_se2(np.array([1,2,3]))))\n", + "u = VectorInput([4, 2])\n", + "dt = 0.1\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that when using Lie groups, our Jacobian no longer has dependence on the state itself. This can be a tangible advantage when the state estimate has high uncertainty, where using a traditional approach can result in excessive linearization errors when the state estimate is far from the true value." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/doctrees/nbsphinx/tutorial/lie_groups.ipynb b/_build/doctrees/nbsphinx/tutorial/lie_groups.ipynb new file mode 100644 index 00000000..75ce7373 --- /dev/null +++ b/_build/doctrees/nbsphinx/tutorial/lie_groups.ipynb @@ -0,0 +1,424 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Lie group approach\n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "Another way we could approach the same state estimation task is to instead use Lie group theory, which is becoming increasingly common practice in state estimation. Lie group theory can be very abstract, and the main references that navlie refer to are the following:\n", + "\n", + "1. [A micro Lie theory for state estimation in robotics](https://arxiv.org/abs/1812.01537)\n", + "2. [T.Barfoot, State Estimation for Robotics](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf)\n", + "\n", + "\n", + "## Define the State\n", + "Instead of representing the state using a vector, we will represent the state using an element of the *special Euclidean group* $SE(2)$, sometimes called *pose transformation matrices*. Elements of this group are 3x3 matrices of the form \n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab}(\\theta) & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2)\n", + "$$\n", + "\n", + "where $\\mathbf{r}_a = [x,y]^T$ again denotes the position of the robot and $\\mathbf{C}_{ab}(\\theta) \\in SO(2)$ is a rotation matrix (sometimes called a direction cosine matrix) with the form \n", + "\n", + "$$ \n", + "\\mathbf{C}_{ab}(\\theta) = \\begin{bmatrix} \\cos \\theta & - \\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{bmatrix}.\n", + "$$\n", + "\n", + "The rotation matrix transforms vectors resolved in one frame to another frame, i.e. $\\mathbf{r}_a = \\mathbf{C}_{ab} \\mathbf{r}_b$. Unlike vectors, elements of $SO(2)$ or $SE(2)$ cannot be added together to produce another valid element of $SE(2)$, but they can be multiplied together with the result still having the same form.\n", + "\n", + "$$\n", + "\\mathbf{T}_1 \\mathbf{T}_2 \\in SE(2)\n", + "$$\n", + "\n", + " To proceed further with our mathematical setup, we need to define a few very common operators seen in Lie group theory. The first two are the \"wedge\" $(\\cdot)^\\wedge$ and \"vee\" $(\\cdot)^\\vee$ operators, which for this specific group has the form\n", + "\n", + "$$ \n", + "\\begin{bmatrix} \\theta \\\\ x \\\\ y \\end{bmatrix}^\\wedge = \\begin{bmatrix} 0 & -\\theta & x \\\\ \\theta & 0 & y \\\\ 0 & 0 & 0 \\end{bmatrix}\n", + "$$\n", + "\n", + "and the $(\\cdot)^\\vee$ operator simply does the exact inverse of $(\\cdot)^\\wedge$. We can implement them as follows.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "%reset -f\n", + "import numpy as np\n", + "\n", + "# Helper functions for SE(2)\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def vee_se2(X):\n", + " return np.array([X[1, 0], X[0, 2], X[1, 2]])\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Two other fundamental relationships appearing in Lie group theory are the exponential (denoted $\\exp$) and logarithmic (denoted $\\log$) maps. While these have a deeper definition, for our case it suffices to think of them as simply the [matrix exponential](https://en.wikipedia.org/wiki/Matrix_exponential) and [matrix logarithm](https://en.wikipedia.org/wiki/Logarithm_of_a_matrix). Using the wedge and vee operators for $SE(2)$ defined above, we can convert a 3x1 vector to an $SE(2)$ element and back as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "An element of SE2:\n", + "[[ 0.99500417 -0.09983342 0.18467933]\n", + " [ 0.09983342 0.99500417 0.30949192]\n", + " [ 0. 0. 1. ]]\n", + "\n", + "The original vector 'representing' it:\n", + "[0.1 0.2 0.3]\n" + ] + } + ], + "source": [ + "from scipy.linalg import expm, logm\n", + "\n", + "T = expm(wedge_se2(np.array([0.1, 0.2, 0.3])))\n", + "print(\"An element of SE2:\")\n", + "print(T)\n", + "\n", + "x = vee_se2(logm(T))\n", + "print(\"\\nThe original vector 'representing' it:\")\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have the tools we need to abstract-ify our problem a little bit. As commonly seen in the literature, we can define the so-called \"oplus\" and \"ominus\" operators as follows (sometimes called \"boxplus\" $\\boxplus$ and \"boxminus\" $\\boxminus$):\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbf{T}_2 &= \\mathbf{T}_1 \\oplus \\boldsymbol{\\xi} := \\mathbf{T}_1 \\exp(\\boldsymbol{\\xi}^\\wedge) \\\\\n", + "\\boldsymbol{\\varepsilon} &= \\mathbf{T}_2 \\ominus \\mathbf{T}_1 := \\log(\\mathbf{T}_2^{-1} \\mathbf{T}_1)^\\vee\n", + "\\end{aligned}\n", + "$$ \n", + "\n", + "Here, both $\\boldsymbol{\\varepsilon}, \\boldsymbol{\\xi} \\in \\mathbb{R}^3$ are 3x1 vectors. The $\\oplus: SE(2) \\times \\mathbb{R}^3 \\to SE(2)$ operator \"adds\" a vector to an $SE(2)$ element to produce another $SE(2)$ element, and the $\\ominus:SE(2) \\times SE(2) \\to \\mathbb{R}^3$ operator \"subtracts\" two $SE(2)$ elements to produce a vector that represents the \"difference\" between them. \n", + "\n", + "\n", + "With this context, lets implement an $SE(2)$ state inside navlie's framework. To define a custom state, you must subclass the `nav.State` abstract class and you *must* implement the `plus`, `minus`, and `copy` methods. These methods play exactly the role of $\\oplus$ and $\\ominus$ described above, while the `copy` method is used to create a deep copy of that state object. In addition, state objects must hold an integer property named `dof` that specifies the *degrees of freedom* associated with that state. For $SE(2)$, this is 3." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.0, dof=3, state_id=None)\n", + " [[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n" + ] + } + ], + "source": [ + "import navlie as nav\n", + "\n", + "class SE2State(nav.State):\n", + " def __init__(self, value :np.ndarray, stamp: float):\n", + " super().__init__(value=value, dof=3, stamp=stamp)\n", + "\n", + " def plus(self, dx: np.ndarray):\n", + " new_value = self.value @ expm(wedge_se2(dx))\n", + " return SE2State(new_value, self.stamp)\n", + "\n", + " def minus(self, other: \"SE2State\"):\n", + " other_inv = np.linalg.inv(other.value)\n", + " return vee_se2(logm(other_inv @ self.value))\n", + " \n", + " def copy(self):\n", + " return SE2State(self.value.copy(), self.stamp)\n", + "\n", + "x = SE2State(np.eye(3), 0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Process Model\n", + "\n", + "Now, we must adapt the process model to work with our new `SE2State`. It is well known that the rotational kinematics can be written directly in terms of rotation matrices using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{C}}_{ab} = \\mathbf{C}_{ab}\\begin{bmatrix}0 & -\\omega \\\\ \\omega & 0 \\end{bmatrix} \n", + "$$\n", + "\n", + "and that the translational kinematics can be written in vector form using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{r}}_a = \\mathbf{C}_{ab} \\begin{bmatrix} v \\\\ 0 \\end{bmatrix} .\n", + "$$\n", + "\n", + "By stacking these into matrices it follows that \n", + "$$ \n", + "\\dot{\\mathbf{T}} = \\mathbf{T} \\boldsymbol{\\varpi}^\\wedge\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\varpi} = [\\omega, v, 0]^T$. This equation is now a linear, matrix-valued ODE, and can be integrated exactly over a short duration $\\Delta t = t_{k+1} - t_k$ using the matrix exponential. This gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}_k^\\wedge \\Delta t)\n", + "$$\n", + "\n", + "which we can implement as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " vel = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(vel * dt))\n", + " return x_next\n", + " \n", + " def input_covariance(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Measurement Model\n", + "\n", + "Finally, our measurement model remains largely unchanged. We just need to extract the position from an `SE2State` object now, as done below." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: SE2State):\n", + " return self.R\n", + " \n", + "\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmarkSE2(landmark, 0.1**2) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run the Filter!\n", + "\n", + "And that's it! All remaining snippets are now _literally_ copy-pasted from our previous approach with zero modifications. Using the abstraction framework in navlie, we can easily switch between different state representations and process/measurement models without having to change any of data generation or filtering code. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.02, dof=3, state_id=None)\n", + " [[ 9.99950000e-01 -9.99983333e-03 5.99990000e-03]\n", + " [ 9.99983333e-03 9.99950000e-01 2.99997500e-05]\n", + " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00]]\n", + "VectorInput(stamp=0.04, state_id=None)\n", + " [0.52438924 0.40056502]\n", + "Measurement(stamp=0.0, state_id=None) of PoseRangeToLandMark\n", + " 2.299276237837416\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.5, 0.3]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[1])\n", + "print(input_data[2])\n", + "print(meas_data[3])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Built-in Lie group states \n", + "While we implemented our own `SE2State` from scratch here for pedagogical purposes, navlie comes with many built-in Lie group states that you can use out of the box. Some of the built-in Lie group states include:\n", + "\n", + "- `nav.lib.SO2State`: representing 2D rotations using, beloning to the group $SO(2)$\n", + "- `nav.lib.SO3State`: representing 3D rotations using, beloning to the group $SO(3)$\n", + "- `nav.lib.SE2State`: representing 2D poses using, beloning to the group $SE(2)$\n", + "- `nav.lib.SE3State`: representing 3D poses using, beloning to the group $SE(3)$\n", + "- `nav.lib.SE23State`: representing \"extended\" poses that also contain velocity information, belonging to the group $SE_2(3)$\n", + "- `nav.lib.SL3State`: representing 3D homographies, belonging to the group $SL(3)$\n", + "\n", + "Each of these classes stores the value as a square numpy array in the `x.value` property. Moreover, closed-form formulas for the exponential and logarithmic maps have been implemented for each of these states, which is faster than using `scipy.linalg.expm` and `scipy.linalg.logm`. These underlying operations have even been implemented in C++ for maximum speed. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/doctrees/nbsphinx/tutorial/traditional.ipynb b/_build/doctrees/nbsphinx/tutorial/traditional.ipynb new file mode 100644 index 00000000..4db74a60 --- /dev/null +++ b/_build/doctrees/nbsphinx/tutorial/traditional.ipynb @@ -0,0 +1,392 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Traditional Approach\n", + "\n", + "In this tutorial, we'll simulate a simple 2D localization problem as per the figure below. We'll assume that we have a robot following a simple body-frame-velocity model, which has access to noisy measurements of its forward velocity $v$ and angular velocity $\\omega$. In addition, this robot will have a time-of-flight sensor that gives it range measurements to a few known landmarks in the environment. \n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "\n", + "## Define the State\n", + "The first step is to define the state of the robot. We'll start with a more traditional approach and define the state of the robot to be a vector of the form $\\mathbf{x} = [\\theta, x, y ]^T$, where $x$ and $y$ are the robot's position in the world and $\\theta$ is its orientation. We'll also define the control inputs to be $\\mathbf{u} = [\\omega, v]^T$, the robot's forward and angular velocity. The process (motion) model of the robot is then given by:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\dot{\\theta} &= \\omega,\\\\\n", + " \\dot{x} &= v \\cos(\\theta), \\\\\n", + " \\dot{y} &= v \\sin(\\theta). \n", + "\\end{aligned}\n", + "$$\n", + "\n", + "However, this is in continuous time, and we need to discretize it to use it in a filter. For now, we'll use the simple Euler discretization method, which gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t, \\\\\n", + " x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t, \\\\\n", + " y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t.\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Lets now code up our state and process model using navlie's framework. Since our state is just a regular 3x1 vector, we can use a standard type from the built-in library: [navlie.lib.VectorState](../_autosummary/navlie.lib.states.VectorState.rst)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "np.random.seed(0)\n", + "import navlie as nav\n", + "from navlie.lib import VectorState\n", + "\n", + "x = VectorState([0, 0, 0], stamp=0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `VectorState` is a subclass of the abstract [State](../_autosummary/navlie.types.State.rst) class in navlie, which is one of the core primitive types. The value of the state is stored as a numpy array, and can be accessed directly through `x.value`. \n", + "\n", + "\n", + "## Define the Process Model\n", + "For the process model, we'll choose to define our own from scratch here. Process models in navlie *must* inherit from the abstract [navlie.ProcessModel](../_autosummary/navlie.types.ProcessModel.rst) class and implement the `evaluate` and either the `input_covariance` or `covariance` methods." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "from navlie.lib import VectorInput\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The methods in navlie process models must always accept the arguments shown above: a `State` object, an `Input` object, and a float `dt`. The `evaluate` method must always return a valid (i.e. subclass of a) `State` object, and the `input_covariance` method must always return a square numpy array. There are more optional methods that can be implemented for performance reasons, but we will cover those later.\n", + "\n", + "## Define the Measurement Model(s)\n", + "Moving on to the measurement model, if $\\mathbf{r}_a = [x,y]^T$ denotes the position vector of the robot resolved in the world frame, and $\\mathbf{\\ell}^{(i)}_{a} \\in \\mathbb{R}^2$ is the 2 x 1 position vector of landmark $i$, then the measurement model for each landmark is simply \n", + "\n", + "$$ \n", + "y_i = ||\\mathbf{r}_a - \\mathbf{\\ell}^{(i)}_{a}||\n", + "$$\n", + "\n", + "In navlie, measurement models must be implemented in a similar way to process models: inherit from the [navlie.MeasurementModel](../_autosummary/navlie.types.MeasurementModel.rst) abstract class, and then implement the `evaluate` and `covariance` methods. Here's an example for this problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmark(landmark) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## (Simulation only) Generate fake data\n", + "\n", + "The next step is to generate some fake data for our simulation (although navlie is also compatible with real data). To do this, we will use the [DataGenerator](../_autosummary/navlie.datagen.DataGenerator.rst) class which is used as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n", + "VectorInput(stamp=0.0, state_id=None)\n", + " [0.4867558 0.40227221]\n", + "Measurement(stamp=0.0, state_id=None) of RangeToLandmark\n", + " 1.5906187969698615\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.3, 0.5]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[0])\n", + "print(input_data[0])\n", + "print(meas_data[0])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output of the `DataGenerator.generate` method is three lists: a list of ground-truth `State` objects, a list of `Input` objects, and a list of [Measurement](../_autosummary/navlie.types.Measurement.rst) objects, with the input/measurement lists possibly being corrupted by random noise if the `noise=True` flag is set. Each item in these lists correspond to different points in time. We can plot the trajectory as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Plot the state trajectory\n", + "pos = np.array([state.value[1:] for state in state_data])\n", + "plt.plot(pos[:, 0], pos[:, 1])\n", + "plt.scatter(landmarks[:, 0], landmarks[:, 1])\n", + "# add labels\n", + "for i, landmark in enumerate(landmarks):\n", + " plt.annotate(f\"Landmark {i}\", landmark)\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "plt.title(\"Simulated Trajectory\")\n", + "plt.axis(\"equal\")\n", + "\n", + "\n", + "# Plot the input data\n", + "plt.figure()\n", + "u_array = np.array([u.value for u in input_data])\n", + "u_stamps = np.array([u.stamp for u in input_data])\n", + "plt.plot(u_stamps, u_array[:, 0], label=\"omega\")\n", + "plt.plot(u_stamps, u_array[:, 1], label=\"v\")\n", + "plt.xlabel(\"Time (s)\")\n", + "plt.ylabel(\"Input\")\n", + "plt.title(\"Input Data\")\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run a filter!\n", + "\n", + "Finally, lets run an extended Kalman filter on this data to get a state estimate that uses only the noisy measurements. In the below filter, we instantiate the [ExtendedKalmanFilter](../_autosummary/navlie.filters.ExtendedKalmanFilter.rst) to use on our data, and looping over the input measurements while also calling the correction step whenever a measurement occurs." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "\n", + "# You can try other filters too!\n", + "# kalman_filter = nav.UnscentedKalmanFilter(process_model)\n", + "# kalman_filter = nav.IteratedKalmanFIlter(process_model)\n", + "\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filters in navlie are all designed to be *stateless*: this means that the actual state estimate is stored externally to the filter objects, in this case in a container called [StateWithCovariance](../_autosummary/navlie.types.StateWithCovariance.rst). Although this adds a slight burden on the user, it has the advantage of being more transparent, and also providing the ability to combine different filters in the same loop! For example, you could use an EKF for the prediction, but a UKF for the correction, or even to use different filters for different measurement models!\n", + "\n", + "\n", + "Once estimates have been obtained, we will often be interested in evaluating the performance. The [GaussianResultList](../_autosummary/navlie.utils.GaussianResultList.rst) object is a useful container for evaluating the quality of the state estimates when ground truth data is available. It calculates useful metrics such as raw error, Mahalanobis distance, and normalized estimation error squared (NEES). " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "# results.nees \n", + "# results.three_sigma\n", + "# results.error\n", + "# results.md # mahalanobis distance\n", + "# # and more...\n", + "\n", + "# Some plotting functions that work directly with GaussianResultList\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a final note, `GaussianResultList` will invoke the `State.minus` method of the state objects to calculate the error. As we will see next, this allows us to implement a custom measure of error, when it might not make sense to directly subtract two of our state objects." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/doctrees/nbsphinx/tutorial_composite_11_0.png b/_build/doctrees/nbsphinx/tutorial_composite_11_0.png new file mode 100644 index 00000000..5975d2dc Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_composite_11_0.png differ diff --git a/_build/doctrees/nbsphinx/tutorial_composite_11_1.png b/_build/doctrees/nbsphinx/tutorial_composite_11_1.png new file mode 100644 index 00000000..9138fd24 Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_composite_11_1.png differ diff --git a/_build/doctrees/nbsphinx/tutorial_lie_groups_12_0.png b/_build/doctrees/nbsphinx/tutorial_lie_groups_12_0.png new file mode 100644 index 00000000..7028588e Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_lie_groups_12_0.png differ diff --git a/_build/doctrees/nbsphinx/tutorial_lie_groups_12_1.png b/_build/doctrees/nbsphinx/tutorial_lie_groups_12_1.png new file mode 100644 index 00000000..0dc7ed62 Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_lie_groups_12_1.png differ diff --git a/_build/doctrees/nbsphinx/tutorial_traditional_13_0.png b/_build/doctrees/nbsphinx/tutorial_traditional_13_0.png new file mode 100644 index 00000000..3dbc3f21 Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_traditional_13_0.png differ diff --git a/_build/doctrees/nbsphinx/tutorial_traditional_13_1.png b/_build/doctrees/nbsphinx/tutorial_traditional_13_1.png new file mode 100644 index 00000000..5b75a622 Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_traditional_13_1.png differ diff --git a/_build/doctrees/nbsphinx/tutorial_traditional_9_0.png b/_build/doctrees/nbsphinx/tutorial_traditional_9_0.png new file mode 100644 index 00000000..f3d0d162 Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_traditional_9_0.png differ diff --git a/_build/doctrees/nbsphinx/tutorial_traditional_9_1.png b/_build/doctrees/nbsphinx/tutorial_traditional_9_1.png new file mode 100644 index 00000000..53322f71 Binary files /dev/null and b/_build/doctrees/nbsphinx/tutorial_traditional_9_1.png differ diff --git a/_build/doctrees/tutorial.doctree b/_build/doctrees/tutorial.doctree new file mode 100644 index 00000000..57db71cb Binary files /dev/null and b/_build/doctrees/tutorial.doctree differ diff --git a/_build/doctrees/tutorial/composite.doctree b/_build/doctrees/tutorial/composite.doctree new file mode 100644 index 00000000..b34c4f10 Binary files /dev/null and b/_build/doctrees/tutorial/composite.doctree differ diff --git a/_build/doctrees/tutorial/jacobians.doctree b/_build/doctrees/tutorial/jacobians.doctree new file mode 100644 index 00000000..9962eb15 Binary files /dev/null and b/_build/doctrees/tutorial/jacobians.doctree differ diff --git a/_build/doctrees/tutorial/lie_groups.doctree b/_build/doctrees/tutorial/lie_groups.doctree new file mode 100644 index 00000000..3303024d Binary files /dev/null and b/_build/doctrees/tutorial/lie_groups.doctree differ diff --git a/_build/doctrees/tutorial/traditional.doctree b/_build/doctrees/tutorial/traditional.doctree new file mode 100644 index 00000000..20d627fc Binary files /dev/null and b/_build/doctrees/tutorial/traditional.doctree differ diff --git a/_build/html/.buildinfo b/_build/html/.buildinfo new file mode 100644 index 00000000..fc813a60 --- /dev/null +++ b/_build/html/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file hashes the configuration used when building these files. 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navlie.batch.estimator

+

Batch estimator to construct batch problems composed of prior residuals, process residuals, and +measurement residuals.

+

The BatchEstimator.solve() method constructs and solves a batch problem over a sequence +of input and measurement data. Process and measurement residuals are automatically created +and added to the problem, using the generic definitions of process and measurement residuals +defined in the module navlie.batch.residuals.

+

Classes

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BatchEstimator([solver_type, max_iters, ...])

Main class for the batch estimator.

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.batch.gaussian_mixtures.html b/_build/html/_autosummary/navlie.batch.gaussian_mixtures.html new file mode 100644 index 00000000..7925b761 --- /dev/null +++ b/_build/html/_autosummary/navlie.batch.gaussian_mixtures.html @@ -0,0 +1,1100 @@ + + + + + + + + navlie.batch.gaussian_mixtures — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.batch.gaussian_mixtures

+

Classes

+ + + + + + + + + + + + + + + + + + +

GaussianMixtureResidual(errors, weights)

A Gaussian mixture residual.

HessianSumMixtureResidual(errors, weights[, ...])

The Hessian-Sum-Mixture method patched for compatibility with nonlinear least squares solvers.

MaxMixtureResidual(errors, weights)

Based on the following reference, @article{olson2013inference, title={Inference on networks of mixtures for robust robot mapping}, author={Olson, Edwin and Agarwal, Pratik}, journal={The International Journal of Robotics Research}, volume={32}, number={7}, pages={826--840}, year={2013}, publisher={SAGE Publications Sage UK: London, England} }

MaxSumMixtureResidual(errors, weights[, ...])

Based on the following reference: @ARTICLE{9381625, author={Pfeifer, Tim and Lange, Sven and Protzel, Peter}, journal={IEEE Robotics and Automation Letters}, title={Advancing Mixture Models for Least Squares Optimization}, year={2021}, volume={6}, number={2}, pages={3941-3948}, doi={10.1109/LRA.2021.3067307}}

SumMixtureResidual(errors, weights)

For details see the reference @ARTICLE{9381625, author={Pfeifer, Tim and Lange, Sven and Protzel, Peter}, journal={IEEE Robotics and Automation Letters}, title={Advancing Mixture Models for Least Squares Optimization}, year={2021}, volume={6}, number={2}, pages={3941-3948}, doi={10.1109/LRA.2021.3067307}}

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navlie.batch

+

A subpackage for batch least-squares estimation.

+

Modules

+ + + + + + + + + + + + + + + + + + +

navlie.batch.estimator

Batch estimator to construct batch problems composed of prior residuals, process residuals, and measurement residuals.

navlie.batch.gaussian_mixtures

navlie.batch.losses

Robust loss functions to be used in nonlinear least squares problems.

navlie.batch.problem

Main interface for nonlinear least squares problems.

navlie.batch.residuals

A set of commonly-used residuals in batch estimation.

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.batch.losses.CauchyLoss.html b/_build/html/_autosummary/navlie.batch.losses.CauchyLoss.html new file mode 100644 index 00000000..36de81b9 --- /dev/null +++ b/_build/html/_autosummary/navlie.batch.losses.CauchyLoss.html @@ -0,0 +1,1155 @@ + + + + + + + + navlie.batch.losses.CauchyLoss — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.batch.losses

+

Robust loss functions to be used in nonlinear least squares problems.

+

Robust loss functions here must inherit from the LossFunction interface, +which defines a loss and a weight.

+

Classes

+ + + + + + + + + + + + +

CauchyLoss([c])

L2Loss()

Standard L2 loss.

LossFunction()

Abstract base class for any loss function.

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navlie.batch.problem

+

Main interface for nonlinear least squares problems.

+

Allows for the construction of nonlinear least squares problem by adding +arbitrary residual terms, and allows for solving these using either Gauss-Newton +or Levenberg Marquardt.

+

This code is inspired by utiasSTARTS pySLAM repo (https://github.com/utiasSTARS/pyslam), +as well as Ceres.

+

Classes

+ + + + + + + + + +

OptimizationSummary(size_state, size_error, ...)

Class to store a summary of the optimization problem.

Problem([solver, max_iters, step_tol, ftol, ...])

Main class for building nonlinear least squares problems.

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.batch.residuals.ProcessResidual.html b/_build/html/_autosummary/navlie.batch.residuals.ProcessResidual.html new file mode 100644 index 00000000..edf153a2 --- /dev/null +++ b/_build/html/_autosummary/navlie.batch.residuals.ProcessResidual.html @@ -0,0 +1,1175 @@ + + + + + + + + navlie.batch.residuals.ProcessResidual — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.batch.residuals.html b/_build/html/_autosummary/navlie.batch.residuals.html new file mode 100644 index 00000000..06a7ecd3 --- /dev/null +++ b/_build/html/_autosummary/navlie.batch.residuals.html @@ -0,0 +1,1108 @@ + + + + + + + + navlie.batch.residuals — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.batch.residuals

+

A set of commonly-used residuals in batch estimation.

+
+
These residuals are
    +

  • the PriorResidual, to assign a prior estimate on the state,

    • +

  • the ProcessResidual, which uses a navlie ProcessModel to compute an error between +a predicted state and the actual state,

    • +

  • a MeasurementResidual, which uses a navlie Measurement to compare +a true measurement to the measurement predicted by the MeasurementModel.

    • +
+
+
+

Classes

+ + + + + + + + + + + + + + + +

MeasurementResidual(keys, measurement)

A generic measurement residual.

PriorResidual(keys, prior_state, ...)

A generic prior error.

ProcessResidual(keys, process_model, u)

A generic process residual.

Residual(keys)

Abstract class for a residual to be used in batch estimation.

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.composite.CompositeInput.html b/_build/html/_autosummary/navlie.composite.CompositeInput.html new file mode 100644 index 00000000..9eaf45ab --- /dev/null +++ b/_build/html/_autosummary/navlie.composite.CompositeInput.html @@ -0,0 +1,1364 @@ + + + + + + + + navlie.composite.CompositeInput — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.composite.CompositeMeasurementModel.html b/_build/html/_autosummary/navlie.composite.CompositeMeasurementModel.html new file mode 100644 index 00000000..37ee10b6 --- /dev/null +++ b/_build/html/_autosummary/navlie.composite.CompositeMeasurementModel.html @@ -0,0 +1,1215 @@ + + + + + + + + navlie.composite.CompositeMeasurementModel — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.composite.CompositeProcessModel

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.composite.CompositeProcessModel.html b/_build/html/_autosummary/navlie.composite.CompositeProcessModel.html new file mode 100644 index 00000000..08438a3b --- /dev/null +++ b/_build/html/_autosummary/navlie.composite.CompositeProcessModel.html @@ -0,0 +1,1297 @@ + + + + + + + + navlie.composite.CompositeProcessModel — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.composite.CompositeState

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.composite.CompositeState.html b/_build/html/_autosummary/navlie.composite.CompositeState.html new file mode 100644 index 00000000..99fc261e --- /dev/null +++ b/_build/html/_autosummary/navlie.composite.CompositeState.html @@ -0,0 +1,1622 @@ + + + + + + + + navlie.composite.CompositeState — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.composite.html b/_build/html/_autosummary/navlie.composite.html new file mode 100644 index 00000000..2d820806 --- /dev/null +++ b/_build/html/_autosummary/navlie.composite.html @@ -0,0 +1,1100 @@ + + + + + + + + navlie.composite — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.composite

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Classes

+ + + + + + + + + + + + + + + + + + +

CompositeInput(input_list)

<under development>

CompositeMeasurement(y, state_id)

Converts a standard Measurement into a CompositeMeasurement, which simply replaces the model with a CompositeMeasurementModel.

CompositeMeasurementModel(model, state_id)

Wrapper for a standard measurement model that assigns the model to a specific substate (referenced by state_id) inside a CompositeState.

CompositeProcessModel(model_list[, shared_input])

<under development> Should this be called a StackedProcessModel? # TODO: Add documentation and tests

CompositeState(state_list[, stamp, state_id])

A "composite" state object intended to hold a list of State objects as a single conceptual "state".

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+Created using Sphinx 7.1.2.
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.datagen.DataGenerator.html b/_build/html/_autosummary/navlie.datagen.DataGenerator.html new file mode 100644 index 00000000..48f9b1ad --- /dev/null +++ b/_build/html/_autosummary/navlie.datagen.DataGenerator.html @@ -0,0 +1,1182 @@ + + + + + + + + navlie.datagen.DataGenerator — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.datagen.generate_measurement.html b/_build/html/_autosummary/navlie.datagen.generate_measurement.html new file mode 100644 index 00000000..2eaabe24 --- /dev/null +++ b/_build/html/_autosummary/navlie.datagen.generate_measurement.html @@ -0,0 +1,1118 @@ + + + + + + + + navlie.datagen.generate_measurement — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.datagen.html b/_build/html/_autosummary/navlie.datagen.html new file mode 100644 index 00000000..ff32d9db --- /dev/null +++ b/_build/html/_autosummary/navlie.datagen.html @@ -0,0 +1,1097 @@ + + + + + + + + navlie.datagen — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.datagen

+

Tools for data generation.

+

Functions

+ + + + + + +

generate_measurement(state, model[, noise, ...])

Generates a Measurement object given a measurement model and corresponding ground truth State objects.

+

Classes

+ + + + + + +

DataGenerator(process_model, input_func, ...)

A class used for data generation given a process model, and as many measurement models as you want.

+
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navlie.datagen.generate_measurement

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.filters.generate_sigmapoints.html b/_build/html/_autosummary/navlie.filters.generate_sigmapoints.html new file mode 100644 index 00000000..fcdac9ce --- /dev/null +++ b/_build/html/_autosummary/navlie.filters.generate_sigmapoints.html @@ -0,0 +1,1118 @@ + + + + + + + + navlie.filters.generate_sigmapoints — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.filters

+

Module containing many predict-correct style filters.

+

Functions

+ + + + + + + + + + + + + + + +

check_outlier(error, covariance)

Performs the Normalized-Innovation-Squared (NIS) test to identify an outlier.

generate_sigmapoints(dof, method)

Generates unit sigma points from three available methods.

mean_state(x_array, weights)

Computes a weighted mean of a list of State instances in an iterated manner, until reaching a maximun number of iterations or a small update.

run_filter(filter, x0, P0, input_data, meas_data)

Executes a predict-correct-style filter given lists of input and measurement data.

+

Classes

+ + + + + + + + + + + + + + + + + + + + + +

CubatureKalmanFilter(process_model[, ...])

+
param process_model:
+

process model to be used in the prediction step

+
+
+

ExtendedKalmanFilter(process_model[, ...])

On-manifold nonlinear Kalman filter.

GaussHermiteKalmanFilter(process_model[, ...])

+
param process_model:
+

process model to be used in the prediction step

+
+
+

IteratedKalmanFilter(process_model[, ...])

On-manifold iterated extended Kalman filter.

SigmaPointKalmanFilter(process_model[, ...])

On-manifold nonlinear Sigma Point Kalman filter.

UnscentedKalmanFilter(process_model[, ...])

+
param process_model:
+

process model to be used in the prediction step

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navlie.imm

+

Module for the Interacting Multiple Model (IMM) filter.

+

Functions

+ + + + + + + + + + + + + + + + + + +

gaussian_mixing(weights, x_list)

A Gaussian mixing method that handles both vectorspace Gaussians

gaussian_mixing_vectorspace(weights, means, ...)

Calculate the mean and covariance of a Gaussian mixture on a vectorspace.

reparametrize_gaussians_about_X_par(X_par, ...)

Reparametrize each Lie group Gaussian in X_list about X_par.

run_imm_filter(filter, x0, P0, input_data, ...)

Executes an InteractingMultipleModel filter

update_X(X, mu, P)

Given a Lie group Gaussian with mean mu and covariance P, expressed in the tangent space of X, compute Lie group StateAndCovariance X_hat such that the Lie algebra Gaussian around X_hat has zero mean.

+

Classes

+ + + + + + + + + + + + + + + +

IMMResult(imm_estimate, state_true)

+
param estimate:
+

Estimated state and corresponding covariance.

+
+
+

IMMResultList(result_list)

+
param result_list:
+

A list of GaussianResult, intended such that each element corresponds

+
+
+

IMMState(model_states, model_probabilities)

InteractingModelFilter(kf_list, ...)

On-manifold Interacting Multiple Model Filter (IMM).

+
+ + +
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navlie.filters.UnscentedKalmanFilter

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navlie.lib.camera

+

Module containing a basic pinhole camera model.

+

See the CameraProjection measurement model for an example of how this can be +used with navlie’s MeasurementModel class.

+

Classes

+ + + + + + + + + +

PinholeCamera(fu, fv, cu, cv, image_width, ...)

Class for a pinhole camera model.

PoseMatrix(T)

A convenient class to store SE(3) poses.

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navlie.lib.datasets.SimulatedInertialLandmarkDataset

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.html b/_build/html/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.html new file mode 100644 index 00000000..12d09b3a --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.html @@ -0,0 +1,1161 @@ + + + + + + + + navlie.lib.datasets.SimulatedInertialLandmarkDataset — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.imu

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.datasets.generate_landmark_positions.html b/_build/html/_autosummary/navlie.lib.datasets.generate_landmark_positions.html new file mode 100644 index 00000000..8ab09b4d --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.datasets.generate_landmark_positions.html @@ -0,0 +1,1116 @@ + + + + + + + + navlie.lib.datasets.generate_landmark_positions — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.datasets.SimulatedInertialGPSDataset

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navlie.lib.datasets

+

A collection of simulated dataset examples.

+

Functions

+ + + + + + +

generate_landmark_positions(cylinder_radius, ...)

Generates landmarks arranged in a cylinder.

+

Classes

+ + + + + + + + + + + + +

SimulatedInertialGPSDataset([x0, Q, R, ...])

SimulatedInertialLandmarkDataset([x0, Q, R, ...])

SimulatedPoseRangingDataset([x0, Q, R, ...])

Simulated dataset of a simple rigid robot moving in 3D space with range measurements to anchors.

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navlie.lib.camera.PoseMatrix

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navlie.lib.datasets.generate_landmark_positions

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navlie.lib

+

The built-in library of common state, process model, and measurement model implementations.

+

Modules

+ + + + + + + + + + + + + + + + + + + + + +

navlie.lib.camera

Module containing a basic pinhole camera model.

navlie.lib.datasets

A collection of simulated dataset examples.

navlie.lib.imu

A module for IMU data and kinematics.

navlie.lib.models

navlie.lib.preintegration

navlie.lib.states

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navlie.lib.imu.adjoint_IE3

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navlie.lib.imu

+

A module for IMU data and kinematics.

+

Note that the treatment of IMU kinematics in this module is different from +typical treatments in the sense that it is done directly on \(SE_2(3)\). A +PDF describing the detailed derivations can be found at the +following link.

+

Functions

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

G_matrix(gravity, dt)

G_matrix_inv(gravity, dt)

L_matrix(unbiased_gyro, unbiased_accel, dt)

Computes the jacobian of the nav state with respect to the input.

M_matrix(phi_vec)

The M matrix from the derivation document.

N_matrix(phi_vec)

The N matrix from Barfoot 2nd edition, equation 9.211

U_matrix(omega, accel, dt)

U_matrix_inv(omega, accel, dt)

U_tilde_matrix(omega, accel, dt)

adjoint_IE3(X)

Adjoint matrix of the "Incremental Euclidean Group".

delta_matrix(dt)

get_unbiased_imu(x, u)

Removes bias from the measurement.

inverse_IE3(X)

Inverse matrix on the "Incremental Euclidean Group".

+

Classes

+ + + + + + + + + + + + +

IMU(gyro, accel, stamp[, bias_gyro_walk, ...])

Data container for an IMU reading.

IMUKinematics(Q[, gravity])

The IMU Kinematics refer to the following continuous time model:

IMUState(nav_state, bias_gyro, bias_accel[, ...])

The IMU state is a composite state that contains the navigation state (attitude, velocity, position), and the gyro and accelerometer biases.

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.models.RangePointToAnchor.html b/_build/html/_autosummary/navlie.lib.models.RangePointToAnchor.html new file mode 100644 index 00000000..cb0f9de8 --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.models.RangePointToAnchor.html @@ -0,0 +1,1214 @@ + + + + + + + + navlie.lib.models.RangePointToAnchor — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.models.RangePoseToAnchor

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+Created using Sphinx 7.1.2.
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.models.RangeRelativePose.html b/_build/html/_autosummary/navlie.lib.models.RangeRelativePose.html new file mode 100644 index 00000000..34145aaf --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.models.RangeRelativePose.html @@ -0,0 +1,1213 @@ + + + + + + + + navlie.lib.models.RangeRelativePose — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.models.RelativeBodyFrameVelocity

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navlie.lib.models.SingleIntegrator

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.models.SingleIntegrator.html b/_build/html/_autosummary/navlie.lib.models.SingleIntegrator.html new file mode 100644 index 00000000..d571970a --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.models.SingleIntegrator.html @@ -0,0 +1,1310 @@ + + + + + + + + navlie.lib.models.SingleIntegrator — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.preintegration

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.models.html b/_build/html/_autosummary/navlie.lib.models.html new file mode 100644 index 00000000..f49f6411 --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.models.html @@ -0,0 +1,1151 @@ + + + + + + + + navlie.lib.models — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.models

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Classes

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AbsolutePosition(R)

World-frame, or "absolute" position measurement.

AbsoluteVelocity(R)

World-frame, or "absolute" velocity measurement.

Altitude(R[, minimum, bias])

A model that returns the z component of a position vector.

BodyFrameVelocity(Q)

The body-frame velocity process model assumes that the input contains both translational and angular velocity measurements, both relative to a local reference frame, but resolved in the robot body frame.

CameraProjection(pose_state_id, ...)

Measurement model describing the projection of a landmark into a camera.

DoubleIntegrator(Q)

The double-integrator process model is a second-order point kinematic model given in continuous time by

DoubleIntegratorWithBias(Q)

The double-integrator process model, but with an additional bias on the input.

GlobalPosition(R)

This class is deprecated.

Gravitometer(R[, gravity_vector])

Gravitometer model of the form

InvariantMeasurement(meas[, direction, model])

Given a Measurement object, the class will construct a left- or right-invariant innovation ready to be fused into a state estimator.

InvariantPointRelativePosition(y, model)

LinearMeasurement(C, R)

A generic linear measurement model of the form

Magnetometer(R[, magnetic_vector])

Magnetometer model of the form

OneDimensionalPositionVelocityRange(R)

PointRelativePosition(landmark_position, R)

Measurement model describing the position of a known landmark relative to the robot, resolved in the body frame.

PointRelativePositionSLAM(pose_state_id, ...)

Measurement model describing the position of an unknown landmark relative to the robot, resolved in the body frame.

RangePointToAnchor(anchor_position, R)

Range measurement from a point state to an anchor (which is also another point).

RangePoseToAnchor(anchor_position, ...)

Range measurement from a pose state to an anchor.

RangePoseToPose(tag_body_position1, ...)

Range model given two absolute poses of rigid bodies, each containing a ranging tag.

RangeRelativePose(tag_body_position, ...)

Range model given a pose of another body relative to current pose.

RelativeBodyFrameVelocity(Q1, Q2)

The relative body-frame velocity process model is of the form

SingleIntegrator(Q)

The single-integrator process model is a process model of the form

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navlie.lib.imu.IMUState

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navlie.lib.models.AbsolutePosition

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.html b/_build/html/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.html new file mode 100644 index 00000000..892f6515 --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.html @@ -0,0 +1,1345 @@ + + + + + + + + navlie.lib.preintegration.AngularVelocityIncrement — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.html b/_build/html/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.html new file mode 100644 index 00000000..5af2f45b --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.html @@ -0,0 +1,1345 @@ + + + + + + + + navlie.lib.preintegration.BodyVelocityIncrement — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.preintegration.LinearIncrement.html b/_build/html/_autosummary/navlie.lib.preintegration.LinearIncrement.html new file mode 100644 index 00000000..c2f58c67 --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.preintegration.LinearIncrement.html @@ -0,0 +1,1450 @@ + + + + + + + + navlie.lib.preintegration.LinearIncrement — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.preintegration.PreintegratedBodyVelocity

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.html b/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.html new file mode 100644 index 00000000..e8a874f6 --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.html @@ -0,0 +1,1299 @@ + + + + + + + + navlie.lib.preintegration.PreintegratedBodyVelocity — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.preintegration.PreintegratedIMUKinematics

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navlie.lib.preintegration.PreintegratedLinearModel

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.html b/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.html new file mode 100644 index 00000000..c1267fd9 --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.html @@ -0,0 +1,1298 @@ + + + + + + + + navlie.lib.preintegration.PreintegratedLinearModel — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.preintegration.PreintegratedWheelOdometry

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+ © Copyright 2022.
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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.html b/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.html new file mode 100644 index 00000000..b1d4f764 --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.html @@ -0,0 +1,1294 @@ + + + + + + + + navlie.lib.preintegration.PreintegratedWheelOdometry — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.preintegration.PreintegratedLinearModel

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navlie.lib.preintegration.RelativeMotionIncrement

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navlie.lib.preintegration.WheelOdometryIncrement

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.html b/_build/html/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.html new file mode 100644 index 00000000..47b21d6f --- /dev/null +++ b/_build/html/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.html @@ -0,0 +1,1360 @@ + + + + + + + + navlie.lib.preintegration.WheelOdometryIncrement — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.lib.states

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navlie.lib.preintegration

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Classes

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AngularVelocityIncrement(Q[, bias, state_id])

This is a preintegration class for angular velocity measurements, on only attitude.

BodyVelocityIncrement(group, Q[, bias, state_id])

This is a general preintegration class for any process model of the form

IMUIncrement(input_covariance, gyro_bias, ...)

Initializes an "identity" IMU RMI.

LinearIncrement(input_covariance, ...[, ...])

This class preintegrates any process model of the form

PreintegratedAngularVelocity()

PreintegratedBodyVelocity()

Process model that performs prediction of the state given an RMI \(\Delta \mathbf{U}_{ij}\) according to the equation

PreintegratedIMUKinematics([gravity])

PreintegratedLinearModel()

Process model that applies a preintegrated LinearIncrement to predict a state forward in time using the equation

PreintegratedWheelOdometry()

RelativeMotionIncrement(dof)

WheelOdometryIncrement(Q[, bias, state_id])

This is a preintegration class for wheel odometry measurements on SE(n).

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navlie.lib.states

+

Classes

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

MatrixLieGroupState(value, group[, stamp, ...])

The MatrixLieGroupState class.

SE23State(value[, stamp, state_id, direction])

A state object for 2D rigid body transformations with velocity.

SE2State(value[, stamp, state_id, direction])

A state object for 2D rigid body transformations.

SE3State(value[, stamp, state_id, direction])

A state object for 3D rigid body transformations.

SL3State(value[, stamp, state_id, direction])

A state object representing the special linear group in 3D.

SO2State(value[, stamp, state_id, direction])

A state object for rotations in 2D.

SO3State(value[, stamp, state_id, direction])

A state object for rotations in 3D.

StampedValue(value[, stamp, state_id, ...])

+
param value:
+

Value of of the input.

+
+
+

VectorInput(value[, stamp, state_id, covariance])

A standard vector-based input, with value represented by a 1D numpy array.

VectorState(value[, stamp, state_id])

A standard vector-based state, with value represented by a 1D numpy array.

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navlie.types

+

This module contains the core primitive types used throughout navlie.

+

Classes

+ + + + + + + + + + + + + + + + + + + + + + + + +

Dataset()

A container to store a dataset.

Input(dof[, stamp, state_id, covariance])

Measurement(value[, stamp, model, state_id])

A simple data container containing a generic measurement's value, timestamp, and corresponding model stored as a MeasurementModel object.

MeasurementModel()

Abstract measurement model base class, used to implement measurement models of the form

ProcessModel()

Abstract process model base class for process models of the form

State(value, dof[, stamp, state_id])

An abstract state \(\mathcal{X}\) is an object containing the following attributes:

StateWithCovariance(state, covariance)

A data container containing a State object and a covariance array.

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navlie.types.Dataset

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.utils.GaussianResult.html b/_build/html/_autosummary/navlie.utils.GaussianResult.html new file mode 100644 index 00000000..73e19d3f --- /dev/null +++ b/_build/html/_autosummary/navlie.utils.GaussianResult.html @@ -0,0 +1,1313 @@ + + + + + + + + navlie.utils.GaussianResult — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.utils.jacobian

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navlie.utils

+

Collection of miscellaneous utility functions and classes.

+

Functions

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

associate_stamps(first_stamps, second_stamps)

Associate timestamps.

find_nearest_stamp_idx(stamps_list, stamp)

Find the index of the nearest stamp in stamps_list to stamp.

jacobian(fun, x[, step_size, method])

Compute the Jacobian of a function.

monte_carlo(trial, num_trials[, num_jobs, ...])

Monte-Carlo experiment executor.

plot_error(results[, axs, label, sharey, ...])

A generic three-sigma bound plotter.

plot_meas(meas_list, state_list[, axs, sharey])

Given measurement data, make time-domain plots of the measurement values and their ground-truth model-based values.

plot_meas_by_model(meas_list, state_list[, ...])

Given measurement data, make time-domain plots of the measurement values and their ground-truth model-based values.

plot_nees(results[, ax, label, color, ...])

Makes a plot of the NEES, showing the actual NEES values, the expected NEES, and the bounds of the specified confidence interval.

plot_poses(poses[, ax, line_color, ...])

Plots a pose trajectory, representing the attitudes by triads plotted along the trajectory.

randvec(cov[, num_samples])

Produces a random zero-mean column vector with covariance given by cov

schedule_sequential_measurements(model_list, ...)

Schedules sequential measurements from a list of MeasurementModels that cannot generate measurements at the same time.

set_axes_equal(ax)

Sets the axes of a 3D plot to have equal scale.

state_interp(query_stamps, state_list[, method])

Performs "linear" (geodesic) interpolation between State objects.

van_loans(A_c, L_c, Q_c, dt)

Van Loan's method for computing the discrete-time A and Q matrices.

+

Classes

+ + + + + + + + + + + + +

GaussianResult(estimate, state_true)

A data container that simultaneously computes various interesting metrics about a Gaussian filter's state estimate, given the ground-truth value of the state.

GaussianResultList(result_list)

A data container that accepts a list of GaussianResult objects and stacks the attributes in numpy arrays.

MonteCarloResult(trial_results)

A data container which computes various interesting metrics associated with Monte Carlo experiments, such as the average estimation error squared (EES) and the average normalized EES.

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navlie.types.StateWithCovariance

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navlie.utils.associate_stamps

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+ + \ No newline at end of file diff --git a/_build/html/_autosummary/navlie.utils.jacobian.html b/_build/html/_autosummary/navlie.utils.jacobian.html new file mode 100644 index 00000000..5280000e --- /dev/null +++ b/_build/html/_autosummary/navlie.utils.jacobian.html @@ -0,0 +1,1148 @@ + + + + + + + + navlie.utils.jacobian — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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navlie.utils.plot_meas

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navlie.utils.randvec

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a/_build/html/_sources/_autosummary/navlie.batch.estimator.BatchEstimator.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.estimator.BatchEstimator.rst.txt new file mode 100644 index 00000000..b4222adc --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.estimator.BatchEstimator.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.estimator.BatchEstimator +===================================== + +.. currentmodule:: navlie.batch.estimator + +.. autoclass:: BatchEstimator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.estimator.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.estimator.rst.txt new file mode 100644 index 00000000..29b2582d --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.estimator.rst.txt @@ -0,0 +1,31 @@ +navlie.batch.estimator +====================== + +.. automodule:: navlie.batch.estimator + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + BatchEstimator + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.GaussianMixtureResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.GaussianMixtureResidual.rst.txt new file mode 100644 index 00000000..4cf8538f --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.GaussianMixtureResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.GaussianMixtureResidual +======================================================= + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: GaussianMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.HessianSumMixtureResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.HessianSumMixtureResidual.rst.txt new file mode 100644 index 00000000..dacea608 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.HessianSumMixtureResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.HessianSumMixtureResidual +========================================================= + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: HessianSumMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.MaxMixtureResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.MaxMixtureResidual.rst.txt new file mode 100644 index 00000000..feb7ccc0 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.MaxMixtureResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.MaxMixtureResidual +================================================== + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: MaxMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.MaxSumMixtureResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.MaxSumMixtureResidual.rst.txt new file mode 100644 index 00000000..49b7a8d7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.MaxSumMixtureResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.MaxSumMixtureResidual +===================================================== + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: MaxSumMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.SumMixtureResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.SumMixtureResidual.rst.txt new file mode 100644 index 00000000..be782443 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.SumMixtureResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.SumMixtureResidual +================================================== + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: SumMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.rst.txt new file mode 100644 index 00000000..91df23dd --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.gaussian_mixtures.rst.txt @@ -0,0 +1,35 @@ +navlie.batch.gaussian\_mixtures +=============================== + +.. automodule:: navlie.batch.gaussian_mixtures + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + GaussianMixtureResidual + HessianSumMixtureResidual + MaxMixtureResidual + MaxSumMixtureResidual + SumMixtureResidual + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.batch.losses.CauchyLoss.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.losses.CauchyLoss.rst.txt new file mode 100644 index 00000000..8a2b1e42 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.losses.CauchyLoss.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.losses.CauchyLoss +============================== + +.. currentmodule:: navlie.batch.losses + +.. autoclass:: CauchyLoss + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.losses.L2Loss.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.losses.L2Loss.rst.txt new file mode 100644 index 00000000..dbe005c2 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.losses.L2Loss.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.losses.L2Loss +========================== + +.. currentmodule:: navlie.batch.losses + +.. autoclass:: L2Loss + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.losses.LossFunction.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.losses.LossFunction.rst.txt new file mode 100644 index 00000000..b275f496 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.losses.LossFunction.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.losses.LossFunction +================================ + +.. currentmodule:: navlie.batch.losses + +.. autoclass:: LossFunction + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.losses.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.losses.rst.txt new file mode 100644 index 00000000..fc889ee2 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.losses.rst.txt @@ -0,0 +1,33 @@ +navlie.batch.losses +=================== + +.. automodule:: navlie.batch.losses + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + CauchyLoss + L2Loss + LossFunction + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.batch.problem.OptimizationSummary.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.problem.OptimizationSummary.rst.txt new file mode 100644 index 00000000..bcb8ee19 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.problem.OptimizationSummary.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.problem.OptimizationSummary +======================================== + +.. currentmodule:: navlie.batch.problem + +.. autoclass:: OptimizationSummary + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.problem.Problem.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.problem.Problem.rst.txt new file mode 100644 index 00000000..40846284 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.problem.Problem.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.problem.Problem +============================ + +.. currentmodule:: navlie.batch.problem + +.. autoclass:: Problem + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.problem.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.problem.rst.txt new file mode 100644 index 00000000..c85847bb --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.problem.rst.txt @@ -0,0 +1,32 @@ +navlie.batch.problem +==================== + +.. automodule:: navlie.batch.problem + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + OptimizationSummary + Problem + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.batch.residuals.MeasurementResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.residuals.MeasurementResidual.rst.txt new file mode 100644 index 00000000..b288b24c --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.residuals.MeasurementResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.residuals.MeasurementResidual +========================================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: MeasurementResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.residuals.PriorResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.residuals.PriorResidual.rst.txt new file mode 100644 index 00000000..4976a042 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.residuals.PriorResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.residuals.PriorResidual +==================================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: PriorResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.residuals.ProcessResidual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.residuals.ProcessResidual.rst.txt new file mode 100644 index 00000000..33b29685 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.residuals.ProcessResidual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.residuals.ProcessResidual +====================================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: ProcessResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.residuals.Residual.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.residuals.Residual.rst.txt new file mode 100644 index 00000000..2752872c --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.residuals.Residual.rst.txt @@ -0,0 +1,10 @@ +navlie.batch.residuals.Residual +=============================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: Residual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.batch.residuals.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.residuals.rst.txt new file mode 100644 index 00000000..d9198a9f --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.residuals.rst.txt @@ -0,0 +1,34 @@ +navlie.batch.residuals +====================== + +.. automodule:: navlie.batch.residuals + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + MeasurementResidual + PriorResidual + ProcessResidual + Residual + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.batch.rst.txt b/_build/html/_sources/_autosummary/navlie.batch.rst.txt new file mode 100644 index 00000000..d327bc0e --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.batch.rst.txt @@ -0,0 +1,36 @@ +navlie.batch +============ + +.. automodule:: navlie.batch + + + + + + + + + + + + + + + + + + + +.. rubric:: Modules + +.. autosummary:: + :toctree: + :template: custom-module-template.rst + :recursive: + + navlie.batch.estimator + navlie.batch.gaussian_mixtures + navlie.batch.losses + navlie.batch.problem + navlie.batch.residuals + diff --git a/_build/html/_sources/_autosummary/navlie.composite.CompositeInput.rst.txt b/_build/html/_sources/_autosummary/navlie.composite.CompositeInput.rst.txt new file mode 100644 index 00000000..49444858 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.composite.CompositeInput.rst.txt @@ -0,0 +1,10 @@ +navlie.composite.CompositeInput +=============================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeInput + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.composite.CompositeMeasurement.rst.txt b/_build/html/_sources/_autosummary/navlie.composite.CompositeMeasurement.rst.txt new file mode 100644 index 00000000..3aa7b2c7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.composite.CompositeMeasurement.rst.txt @@ -0,0 +1,10 @@ +navlie.composite.CompositeMeasurement +===================================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeMeasurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.composite.CompositeMeasurementModel.rst.txt b/_build/html/_sources/_autosummary/navlie.composite.CompositeMeasurementModel.rst.txt new file mode 100644 index 00000000..3d086bbb --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.composite.CompositeMeasurementModel.rst.txt @@ -0,0 +1,10 @@ +navlie.composite.CompositeMeasurementModel +========================================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeMeasurementModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.composite.CompositeProcessModel.rst.txt b/_build/html/_sources/_autosummary/navlie.composite.CompositeProcessModel.rst.txt new file mode 100644 index 00000000..8ba205b7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.composite.CompositeProcessModel.rst.txt @@ -0,0 +1,10 @@ +navlie.composite.CompositeProcessModel +====================================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeProcessModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.composite.CompositeState.rst.txt b/_build/html/_sources/_autosummary/navlie.composite.CompositeState.rst.txt new file mode 100644 index 00000000..a2124b82 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.composite.CompositeState.rst.txt @@ -0,0 +1,10 @@ +navlie.composite.CompositeState +=============================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.composite.rst.txt b/_build/html/_sources/_autosummary/navlie.composite.rst.txt new file mode 100644 index 00000000..6d49c4aa --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.composite.rst.txt @@ -0,0 +1,35 @@ +navlie.composite +================ + +.. automodule:: navlie.composite + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + CompositeInput + CompositeMeasurement + CompositeMeasurementModel + CompositeProcessModel + CompositeState + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.datagen.DataGenerator.rst.txt b/_build/html/_sources/_autosummary/navlie.datagen.DataGenerator.rst.txt new file mode 100644 index 00000000..0d12bc00 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.datagen.DataGenerator.rst.txt @@ -0,0 +1,10 @@ +navlie.datagen.DataGenerator +============================ + +.. currentmodule:: navlie.datagen + +.. autoclass:: DataGenerator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.datagen.generate_measurement.rst.txt b/_build/html/_sources/_autosummary/navlie.datagen.generate_measurement.rst.txt new file mode 100644 index 00000000..ed9151b3 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.datagen.generate_measurement.rst.txt @@ -0,0 +1,6 @@ +navlie.datagen.generate\_measurement +==================================== + +.. currentmodule:: navlie.datagen + +.. autofunction:: generate_measurement \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.datagen.rst.txt b/_build/html/_sources/_autosummary/navlie.datagen.rst.txt new file mode 100644 index 00000000..0fadd626 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.datagen.rst.txt @@ -0,0 +1,38 @@ +navlie.datagen +============== + +.. automodule:: navlie.datagen + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + generate_measurement + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + DataGenerator + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.filters.CubatureKalmanFilter.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.CubatureKalmanFilter.rst.txt new file mode 100644 index 00000000..0e4deac2 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.CubatureKalmanFilter.rst.txt @@ -0,0 +1,10 @@ +navlie.filters.CubatureKalmanFilter +=================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: CubatureKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.ExtendedKalmanFilter.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.ExtendedKalmanFilter.rst.txt new file mode 100644 index 00000000..04abc897 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.ExtendedKalmanFilter.rst.txt @@ -0,0 +1,10 @@ +navlie.filters.ExtendedKalmanFilter +=================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: ExtendedKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.GaussHermiteKalmanFilter.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.GaussHermiteKalmanFilter.rst.txt new file mode 100644 index 00000000..5a7fbbb5 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.GaussHermiteKalmanFilter.rst.txt @@ -0,0 +1,10 @@ +navlie.filters.GaussHermiteKalmanFilter +======================================= + +.. currentmodule:: navlie.filters + +.. autoclass:: GaussHermiteKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.IteratedKalmanFilter.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.IteratedKalmanFilter.rst.txt new file mode 100644 index 00000000..7f5c0fae --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.IteratedKalmanFilter.rst.txt @@ -0,0 +1,10 @@ +navlie.filters.IteratedKalmanFilter +=================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: IteratedKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.SigmaPointKalmanFilter.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.SigmaPointKalmanFilter.rst.txt new file mode 100644 index 00000000..b5561363 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.SigmaPointKalmanFilter.rst.txt @@ -0,0 +1,10 @@ +navlie.filters.SigmaPointKalmanFilter +===================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: SigmaPointKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.UnscentedKalmanFilter.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.UnscentedKalmanFilter.rst.txt new file mode 100644 index 00000000..48cfcfd7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.UnscentedKalmanFilter.rst.txt @@ -0,0 +1,10 @@ +navlie.filters.UnscentedKalmanFilter +==================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: UnscentedKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.check_outlier.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.check_outlier.rst.txt new file mode 100644 index 00000000..8c57017a --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.check_outlier.rst.txt @@ -0,0 +1,6 @@ +navlie.filters.check\_outlier +============================= + +.. currentmodule:: navlie.filters + +.. autofunction:: check_outlier \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.generate_sigmapoints.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.generate_sigmapoints.rst.txt new file mode 100644 index 00000000..0e3d73b3 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.generate_sigmapoints.rst.txt @@ -0,0 +1,6 @@ +navlie.filters.generate\_sigmapoints +==================================== + +.. currentmodule:: navlie.filters + +.. autofunction:: generate_sigmapoints \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.mean_state.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.mean_state.rst.txt new file mode 100644 index 00000000..768de0f1 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.mean_state.rst.txt @@ -0,0 +1,6 @@ +navlie.filters.mean\_state +========================== + +.. currentmodule:: navlie.filters + +.. autofunction:: mean_state \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.filters.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.rst.txt new file mode 100644 index 00000000..31deba7f --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.rst.txt @@ -0,0 +1,46 @@ +navlie.filters +============== + +.. automodule:: navlie.filters + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + check_outlier + generate_sigmapoints + mean_state + run_filter + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + CubatureKalmanFilter + ExtendedKalmanFilter + GaussHermiteKalmanFilter + IteratedKalmanFilter + SigmaPointKalmanFilter + UnscentedKalmanFilter + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.filters.run_filter.rst.txt b/_build/html/_sources/_autosummary/navlie.filters.run_filter.rst.txt new file mode 100644 index 00000000..3f92b237 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.filters.run_filter.rst.txt @@ -0,0 +1,6 @@ +navlie.filters.run\_filter +========================== + +.. currentmodule:: navlie.filters + +.. autofunction:: run_filter \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.IMMResult.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.IMMResult.rst.txt new file mode 100644 index 00000000..c73bc08b --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.IMMResult.rst.txt @@ -0,0 +1,10 @@ +navlie.imm.IMMResult +==================== + +.. currentmodule:: navlie.imm + +.. autoclass:: IMMResult + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.IMMResultList.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.IMMResultList.rst.txt new file mode 100644 index 00000000..bfc03531 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.IMMResultList.rst.txt @@ -0,0 +1,10 @@ +navlie.imm.IMMResultList +======================== + +.. currentmodule:: navlie.imm + +.. autoclass:: IMMResultList + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.IMMState.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.IMMState.rst.txt new file mode 100644 index 00000000..31721ab9 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.IMMState.rst.txt @@ -0,0 +1,10 @@ +navlie.imm.IMMState +=================== + +.. currentmodule:: navlie.imm + +.. autoclass:: IMMState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.InteractingModelFilter.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.InteractingModelFilter.rst.txt new file mode 100644 index 00000000..d60023ce --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.InteractingModelFilter.rst.txt @@ -0,0 +1,10 @@ +navlie.imm.InteractingModelFilter +================================= + +.. currentmodule:: navlie.imm + +.. autoclass:: InteractingModelFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.gaussian_mixing.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.gaussian_mixing.rst.txt new file mode 100644 index 00000000..ceab06be --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.gaussian_mixing.rst.txt @@ -0,0 +1,6 @@ +navlie.imm.gaussian\_mixing +=========================== + +.. currentmodule:: navlie.imm + +.. autofunction:: gaussian_mixing \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.gaussian_mixing_vectorspace.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.gaussian_mixing_vectorspace.rst.txt new file mode 100644 index 00000000..ae5a3089 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.gaussian_mixing_vectorspace.rst.txt @@ -0,0 +1,6 @@ +navlie.imm.gaussian\_mixing\_vectorspace +======================================== + +.. currentmodule:: navlie.imm + +.. autofunction:: gaussian_mixing_vectorspace \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.reparametrize_gaussians_about_X_par.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.reparametrize_gaussians_about_X_par.rst.txt new file mode 100644 index 00000000..d41719d5 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.reparametrize_gaussians_about_X_par.rst.txt @@ -0,0 +1,6 @@ +navlie.imm.reparametrize\_gaussians\_about\_X\_par +================================================== + +.. currentmodule:: navlie.imm + +.. autofunction:: reparametrize_gaussians_about_X_par \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.rst.txt new file mode 100644 index 00000000..c7b7615e --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.rst.txt @@ -0,0 +1,45 @@ +navlie.imm +========== + +.. automodule:: navlie.imm + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + gaussian_mixing + gaussian_mixing_vectorspace + reparametrize_gaussians_about_X_par + run_imm_filter + update_X + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + IMMResult + IMMResultList + IMMState + InteractingModelFilter + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.imm.run_imm_filter.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.run_imm_filter.rst.txt new file mode 100644 index 00000000..664f1bb1 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.run_imm_filter.rst.txt @@ -0,0 +1,6 @@ +navlie.imm.run\_imm\_filter +=========================== + +.. currentmodule:: navlie.imm + +.. autofunction:: run_imm_filter \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.imm.update_X.rst.txt b/_build/html/_sources/_autosummary/navlie.imm.update_X.rst.txt new file mode 100644 index 00000000..a3430fed --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.imm.update_X.rst.txt @@ -0,0 +1,6 @@ +navlie.imm.update\_X +==================== + +.. currentmodule:: navlie.imm + +.. autofunction:: update_X \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.camera.PinholeCamera.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.camera.PinholeCamera.rst.txt new file mode 100644 index 00000000..f6f84b08 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.camera.PinholeCamera.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.camera.PinholeCamera +=============================== + +.. currentmodule:: navlie.lib.camera + +.. autoclass:: PinholeCamera + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.camera.PoseMatrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.camera.PoseMatrix.rst.txt new file mode 100644 index 00000000..24f8028b --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.camera.PoseMatrix.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.camera.PoseMatrix +============================ + +.. currentmodule:: navlie.lib.camera + +.. autoclass:: PoseMatrix + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.camera.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.camera.rst.txt new file mode 100644 index 00000000..1c25fb39 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.camera.rst.txt @@ -0,0 +1,32 @@ +navlie.lib.camera +================= + +.. automodule:: navlie.lib.camera + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + PinholeCamera + PoseMatrix + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedInertialGPSDataset.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedInertialGPSDataset.rst.txt new file mode 100644 index 00000000..08f43c62 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedInertialGPSDataset.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.datasets.SimulatedInertialGPSDataset +=============================================== + +.. currentmodule:: navlie.lib.datasets + +.. autoclass:: SimulatedInertialGPSDataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.rst.txt new file mode 100644 index 00000000..3b935bb7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.datasets.SimulatedInertialLandmarkDataset +==================================================== + +.. currentmodule:: navlie.lib.datasets + +.. autoclass:: SimulatedInertialLandmarkDataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedPoseRangingDataset.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedPoseRangingDataset.rst.txt new file mode 100644 index 00000000..621f9f1c --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.datasets.SimulatedPoseRangingDataset.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.datasets.SimulatedPoseRangingDataset +=============================================== + +.. currentmodule:: navlie.lib.datasets + +.. autoclass:: SimulatedPoseRangingDataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.datasets.generate_landmark_positions.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.datasets.generate_landmark_positions.rst.txt new file mode 100644 index 00000000..2538be3a --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.datasets.generate_landmark_positions.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.datasets.generate\_landmark\_positions +================================================= + +.. currentmodule:: navlie.lib.datasets + +.. autofunction:: generate_landmark_positions \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.datasets.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.datasets.rst.txt new file mode 100644 index 00000000..cbfb9b06 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.datasets.rst.txt @@ -0,0 +1,40 @@ +navlie.lib.datasets +=================== + +.. automodule:: navlie.lib.datasets + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + generate_landmark_positions + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + SimulatedInertialGPSDataset + SimulatedInertialLandmarkDataset + SimulatedPoseRangingDataset + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.G_matrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.G_matrix.rst.txt new file mode 100644 index 00000000..23ce529c --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.G_matrix.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.G\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: G_matrix \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.G_matrix_inv.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.G_matrix_inv.rst.txt new file mode 100644 index 00000000..83190a0e --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.G_matrix_inv.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.G\_matrix\_inv +============================= + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: G_matrix_inv \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.IMU.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.IMU.rst.txt new file mode 100644 index 00000000..dd7e48d0 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.IMU.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.imu.IMU +================== + +.. currentmodule:: navlie.lib.imu + +.. autoclass:: IMU + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.IMUKinematics.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.IMUKinematics.rst.txt new file mode 100644 index 00000000..aab31572 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.IMUKinematics.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.imu.IMUKinematics +============================ + +.. currentmodule:: navlie.lib.imu + +.. autoclass:: IMUKinematics + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.IMUState.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.IMUState.rst.txt new file mode 100644 index 00000000..fde4052b --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.IMUState.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.imu.IMUState +======================= + +.. currentmodule:: navlie.lib.imu + +.. autoclass:: IMUState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.L_matrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.L_matrix.rst.txt new file mode 100644 index 00000000..b1acfeb2 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.L_matrix.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.L\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: L_matrix \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.M_matrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.M_matrix.rst.txt new file mode 100644 index 00000000..e6339ca9 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.M_matrix.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.M\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: M_matrix \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.N_matrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.N_matrix.rst.txt new file mode 100644 index 00000000..ebecf6b7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.N_matrix.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.N\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: N_matrix \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.U_matrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.U_matrix.rst.txt new file mode 100644 index 00000000..6c6c3737 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.U_matrix.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.U\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: U_matrix \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.U_matrix_inv.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.U_matrix_inv.rst.txt new file mode 100644 index 00000000..28d7140c --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.U_matrix_inv.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.U\_matrix\_inv +============================= + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: U_matrix_inv \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.U_tilde_matrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.U_tilde_matrix.rst.txt new file mode 100644 index 00000000..58b61c9f --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.U_tilde_matrix.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.U\_tilde\_matrix +=============================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: U_tilde_matrix \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.adjoint_IE3.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.adjoint_IE3.rst.txt new file mode 100644 index 00000000..4b0bff12 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.adjoint_IE3.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.adjoint\_IE3 +=========================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: adjoint_IE3 \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.delta_matrix.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.delta_matrix.rst.txt new file mode 100644 index 00000000..b91120ac --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.delta_matrix.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.delta\_matrix +============================ + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: delta_matrix \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.get_unbiased_imu.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.get_unbiased_imu.rst.txt new file mode 100644 index 00000000..9b35ce2f --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.get_unbiased_imu.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.get\_unbiased\_imu +================================= + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: get_unbiased_imu \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.inverse_IE3.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.inverse_IE3.rst.txt new file mode 100644 index 00000000..e1857eca --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.inverse_IE3.rst.txt @@ -0,0 +1,6 @@ +navlie.lib.imu.inverse\_IE3 +=========================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: inverse_IE3 \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.imu.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.imu.rst.txt new file mode 100644 index 00000000..7ded5990 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.imu.rst.txt @@ -0,0 +1,51 @@ +navlie.lib.imu +============== + +.. automodule:: navlie.lib.imu + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + G_matrix + G_matrix_inv + L_matrix + M_matrix + N_matrix + U_matrix + U_matrix_inv + U_tilde_matrix + adjoint_IE3 + delta_matrix + get_unbiased_imu + inverse_IE3 + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + IMU + IMUKinematics + IMUState + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.AbsolutePosition.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.AbsolutePosition.rst.txt new file mode 100644 index 00000000..071b4177 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.AbsolutePosition.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.AbsolutePosition +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: AbsolutePosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.AbsoluteVelocity.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.AbsoluteVelocity.rst.txt new file mode 100644 index 00000000..a7dd329f --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.AbsoluteVelocity.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.AbsoluteVelocity +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: AbsoluteVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.Altitude.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.Altitude.rst.txt new file mode 100644 index 00000000..fa3777b6 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.Altitude.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.Altitude +========================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: Altitude + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.BodyFrameVelocity.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.BodyFrameVelocity.rst.txt new file mode 100644 index 00000000..2938a897 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.BodyFrameVelocity.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.BodyFrameVelocity +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: BodyFrameVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.CameraProjection.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.CameraProjection.rst.txt new file mode 100644 index 00000000..b157a313 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.CameraProjection.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.CameraProjection +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: CameraProjection + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.DoubleIntegrator.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.DoubleIntegrator.rst.txt new file mode 100644 index 00000000..04e207b3 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.DoubleIntegrator.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.DoubleIntegrator +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: DoubleIntegrator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.DoubleIntegratorWithBias.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.DoubleIntegratorWithBias.rst.txt new file mode 100644 index 00000000..613e08bc --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.DoubleIntegratorWithBias.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.DoubleIntegratorWithBias +========================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: DoubleIntegratorWithBias + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.GlobalPosition.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.GlobalPosition.rst.txt new file mode 100644 index 00000000..2a84bea5 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.GlobalPosition.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.GlobalPosition +================================ + +.. currentmodule:: navlie.lib.models + +.. autoclass:: GlobalPosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.Gravitometer.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.Gravitometer.rst.txt new file mode 100644 index 00000000..85266c50 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.Gravitometer.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.Gravitometer +============================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: Gravitometer + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.InvariantMeasurement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.InvariantMeasurement.rst.txt new file mode 100644 index 00000000..8636519d --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.InvariantMeasurement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.InvariantMeasurement +====================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: InvariantMeasurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.InvariantPointRelativePosition.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.InvariantPointRelativePosition.rst.txt new file mode 100644 index 00000000..4b018ecc --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.InvariantPointRelativePosition.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.InvariantPointRelativePosition +================================================ + +.. currentmodule:: navlie.lib.models + +.. autoclass:: InvariantPointRelativePosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.LinearMeasurement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.LinearMeasurement.rst.txt new file mode 100644 index 00000000..5ad7f33b --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.LinearMeasurement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.LinearMeasurement +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: LinearMeasurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.Magnetometer.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.Magnetometer.rst.txt new file mode 100644 index 00000000..3217a8ea --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.Magnetometer.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.Magnetometer +============================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: Magnetometer + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.OneDimensionalPositionVelocityRange.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.OneDimensionalPositionVelocityRange.rst.txt new file mode 100644 index 00000000..cb6007ef --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.OneDimensionalPositionVelocityRange.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.OneDimensionalPositionVelocityRange +===================================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: OneDimensionalPositionVelocityRange + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.PointRelativePosition.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.PointRelativePosition.rst.txt new file mode 100644 index 00000000..ae77f493 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.PointRelativePosition.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.PointRelativePosition +======================================= + +.. currentmodule:: navlie.lib.models + +.. autoclass:: PointRelativePosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.PointRelativePositionSLAM.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.PointRelativePositionSLAM.rst.txt new file mode 100644 index 00000000..35be905e --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.PointRelativePositionSLAM.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.PointRelativePositionSLAM +=========================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: PointRelativePositionSLAM + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.RangePointToAnchor.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.RangePointToAnchor.rst.txt new file mode 100644 index 00000000..f2862bcd --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.RangePointToAnchor.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.RangePointToAnchor +==================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangePointToAnchor + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.RangePoseToAnchor.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.RangePoseToAnchor.rst.txt new file mode 100644 index 00000000..96f5b7e9 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.RangePoseToAnchor.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.RangePoseToAnchor +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangePoseToAnchor + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.RangePoseToPose.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.RangePoseToPose.rst.txt new file mode 100644 index 00000000..e23e49f4 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.RangePoseToPose.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.RangePoseToPose +================================= + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangePoseToPose + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.RangeRelativePose.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.RangeRelativePose.rst.txt new file mode 100644 index 00000000..ddc3abf1 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.RangeRelativePose.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.RangeRelativePose +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangeRelativePose + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.RelativeBodyFrameVelocity.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.RelativeBodyFrameVelocity.rst.txt new file mode 100644 index 00000000..47176d46 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.RelativeBodyFrameVelocity.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.RelativeBodyFrameVelocity +=========================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RelativeBodyFrameVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.SingleIntegrator.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.SingleIntegrator.rst.txt new file mode 100644 index 00000000..2a62fd56 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.SingleIntegrator.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.models.SingleIntegrator +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: SingleIntegrator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.models.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.models.rst.txt new file mode 100644 index 00000000..a4499773 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.models.rst.txt @@ -0,0 +1,52 @@ +navlie.lib.models +================= + +.. automodule:: navlie.lib.models + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + AbsolutePosition + AbsoluteVelocity + Altitude + BodyFrameVelocity + CameraProjection + DoubleIntegrator + DoubleIntegratorWithBias + GlobalPosition + Gravitometer + InvariantMeasurement + InvariantPointRelativePosition + LinearMeasurement + Magnetometer + OneDimensionalPositionVelocityRange + PointRelativePosition + PointRelativePositionSLAM + RangePointToAnchor + RangePoseToAnchor + RangePoseToPose + RangeRelativePose + RelativeBodyFrameVelocity + SingleIntegrator + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.rst.txt new file mode 100644 index 00000000..ed38e157 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.AngularVelocityIncrement +================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: AngularVelocityIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.rst.txt new file mode 100644 index 00000000..4e80763d --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.BodyVelocityIncrement +=============================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: BodyVelocityIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.IMUIncrement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.IMUIncrement.rst.txt new file mode 100644 index 00000000..3981994d --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.IMUIncrement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.IMUIncrement +====================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: IMUIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.LinearIncrement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.LinearIncrement.rst.txt new file mode 100644 index 00000000..c5da1061 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.LinearIncrement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.LinearIncrement +========================================= + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: LinearIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedAngularVelocity.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedAngularVelocity.rst.txt new file mode 100644 index 00000000..fb60ace4 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedAngularVelocity.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedAngularVelocity +====================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedAngularVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.rst.txt new file mode 100644 index 00000000..894991a5 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedBodyVelocity +=================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedBodyVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedIMUKinematics.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedIMUKinematics.rst.txt new file mode 100644 index 00000000..1a954882 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedIMUKinematics.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedIMUKinematics +==================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedIMUKinematics + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.rst.txt new file mode 100644 index 00000000..082f830d --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedLinearModel +================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedLinearModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.rst.txt new file mode 100644 index 00000000..71d21557 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedWheelOdometry +==================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedWheelOdometry + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.RelativeMotionIncrement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.RelativeMotionIncrement.rst.txt new file mode 100644 index 00000000..f8d40c93 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.RelativeMotionIncrement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.RelativeMotionIncrement +================================================= + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: RelativeMotionIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.rst.txt new file mode 100644 index 00000000..5eaa4b5d --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.preintegration.WheelOdometryIncrement +================================================ + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: WheelOdometryIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.preintegration.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.preintegration.rst.txt new file mode 100644 index 00000000..90c46d0c --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.preintegration.rst.txt @@ -0,0 +1,41 @@ +navlie.lib.preintegration +========================= + +.. automodule:: navlie.lib.preintegration + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + AngularVelocityIncrement + BodyVelocityIncrement + IMUIncrement + LinearIncrement + PreintegratedAngularVelocity + PreintegratedBodyVelocity + PreintegratedIMUKinematics + PreintegratedLinearModel + PreintegratedWheelOdometry + RelativeMotionIncrement + WheelOdometryIncrement + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.lib.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.rst.txt new file mode 100644 index 00000000..33cf70de --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.rst.txt @@ -0,0 +1,37 @@ +navlie.lib +========== + +.. automodule:: navlie.lib + + + + + + + + + + + + + + + + + + + +.. rubric:: Modules + +.. autosummary:: + :toctree: + :template: custom-module-template.rst + :recursive: + + navlie.lib.camera + navlie.lib.datasets + navlie.lib.imu + navlie.lib.models + navlie.lib.preintegration + navlie.lib.states + diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.MatrixLieGroupState.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.MatrixLieGroupState.rst.txt new file mode 100644 index 00000000..b7bd6ed7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.MatrixLieGroupState.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.MatrixLieGroupState +===================================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: MatrixLieGroupState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.SE23State.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.SE23State.rst.txt new file mode 100644 index 00000000..3a2acab9 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.SE23State.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.SE23State +=========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SE23State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.SE2State.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.SE2State.rst.txt new file mode 100644 index 00000000..26d31deb --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.SE2State.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.SE2State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SE2State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.SE3State.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.SE3State.rst.txt new file mode 100644 index 00000000..928977a9 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.SE3State.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.SE3State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SE3State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.SL3State.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.SL3State.rst.txt new file mode 100644 index 00000000..dfe1fc10 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.SL3State.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.SL3State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SL3State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.SO2State.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.SO2State.rst.txt new file mode 100644 index 00000000..9f2678f9 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.SO2State.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.SO2State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SO2State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.SO3State.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.SO3State.rst.txt new file mode 100644 index 00000000..c5fd87ce --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.SO3State.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.SO3State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SO3State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.StampedValue.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.StampedValue.rst.txt new file mode 100644 index 00000000..83bad4eb --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.StampedValue.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.StampedValue +============================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: StampedValue + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.VectorInput.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.VectorInput.rst.txt new file mode 100644 index 00000000..0023f248 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.VectorInput.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.VectorInput +============================= + +.. currentmodule:: navlie.lib.states + +.. autoclass:: VectorInput + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.VectorState.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.VectorState.rst.txt new file mode 100644 index 00000000..e91253a0 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.VectorState.rst.txt @@ -0,0 +1,10 @@ +navlie.lib.states.VectorState +============================= + +.. currentmodule:: navlie.lib.states + +.. autoclass:: VectorState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.lib.states.rst.txt b/_build/html/_sources/_autosummary/navlie.lib.states.rst.txt new file mode 100644 index 00000000..24b7ca9b --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.lib.states.rst.txt @@ -0,0 +1,40 @@ +navlie.lib.states +================= + +.. automodule:: navlie.lib.states + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + MatrixLieGroupState + SE23State + SE2State + SE3State + SL3State + SO2State + SO3State + StampedValue + VectorInput + VectorState + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.types.Dataset.rst.txt b/_build/html/_sources/_autosummary/navlie.types.Dataset.rst.txt new file mode 100644 index 00000000..d691044d --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.Dataset.rst.txt @@ -0,0 +1,10 @@ +navlie.types.Dataset +==================== + +.. currentmodule:: navlie.types + +.. autoclass:: Dataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.types.Input.rst.txt b/_build/html/_sources/_autosummary/navlie.types.Input.rst.txt new file mode 100644 index 00000000..e1cd1004 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.Input.rst.txt @@ -0,0 +1,10 @@ +navlie.types.Input +================== + +.. currentmodule:: navlie.types + +.. autoclass:: Input + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.types.Measurement.rst.txt b/_build/html/_sources/_autosummary/navlie.types.Measurement.rst.txt new file mode 100644 index 00000000..327432f7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.Measurement.rst.txt @@ -0,0 +1,10 @@ +navlie.types.Measurement +======================== + +.. currentmodule:: navlie.types + +.. autoclass:: Measurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.types.MeasurementModel.rst.txt b/_build/html/_sources/_autosummary/navlie.types.MeasurementModel.rst.txt new file mode 100644 index 00000000..f90ca7b8 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.MeasurementModel.rst.txt @@ -0,0 +1,10 @@ +navlie.types.MeasurementModel +============================= + +.. currentmodule:: navlie.types + +.. autoclass:: MeasurementModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.types.ProcessModel.rst.txt b/_build/html/_sources/_autosummary/navlie.types.ProcessModel.rst.txt new file mode 100644 index 00000000..9619b0e5 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.ProcessModel.rst.txt @@ -0,0 +1,10 @@ +navlie.types.ProcessModel +========================= + +.. currentmodule:: navlie.types + +.. autoclass:: ProcessModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.types.State.rst.txt b/_build/html/_sources/_autosummary/navlie.types.State.rst.txt new file mode 100644 index 00000000..81afa6ff --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.State.rst.txt @@ -0,0 +1,10 @@ +navlie.types.State +================== + +.. currentmodule:: navlie.types + +.. autoclass:: State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.types.StateWithCovariance.rst.txt b/_build/html/_sources/_autosummary/navlie.types.StateWithCovariance.rst.txt new file mode 100644 index 00000000..c0f962b0 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.StateWithCovariance.rst.txt @@ -0,0 +1,10 @@ +navlie.types.StateWithCovariance +================================ + +.. currentmodule:: navlie.types + +.. autoclass:: StateWithCovariance + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.types.rst.txt b/_build/html/_sources/_autosummary/navlie.types.rst.txt new file mode 100644 index 00000000..da1b20d1 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.types.rst.txt @@ -0,0 +1,37 @@ +navlie.types +============ + +.. automodule:: navlie.types + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + Dataset + Input + Measurement + MeasurementModel + ProcessModel + State + StateWithCovariance + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.utils.GaussianResult.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.GaussianResult.rst.txt new file mode 100644 index 00000000..a920d1d2 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.GaussianResult.rst.txt @@ -0,0 +1,10 @@ +navlie.utils.GaussianResult +=========================== + +.. currentmodule:: navlie.utils + +.. autoclass:: GaussianResult + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.GaussianResultList.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.GaussianResultList.rst.txt new file mode 100644 index 00000000..2aee2fed --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.GaussianResultList.rst.txt @@ -0,0 +1,10 @@ +navlie.utils.GaussianResultList +=============================== + +.. currentmodule:: navlie.utils + +.. autoclass:: GaussianResultList + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.MonteCarloResult.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.MonteCarloResult.rst.txt new file mode 100644 index 00000000..81755eb5 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.MonteCarloResult.rst.txt @@ -0,0 +1,10 @@ +navlie.utils.MonteCarloResult +============================= + +.. currentmodule:: navlie.utils + +.. autoclass:: MonteCarloResult + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.associate_stamps.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.associate_stamps.rst.txt new file mode 100644 index 00000000..2174fc69 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.associate_stamps.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.associate\_stamps +============================== + +.. currentmodule:: navlie.utils + +.. autofunction:: associate_stamps \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.find_nearest_stamp_idx.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.find_nearest_stamp_idx.rst.txt new file mode 100644 index 00000000..1615cc7f --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.find_nearest_stamp_idx.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.find\_nearest\_stamp\_idx +====================================== + +.. currentmodule:: navlie.utils + +.. autofunction:: find_nearest_stamp_idx \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.jacobian.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.jacobian.rst.txt new file mode 100644 index 00000000..1b02c953 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.jacobian.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.jacobian +===================== + +.. currentmodule:: navlie.utils + +.. autofunction:: jacobian \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.monte_carlo.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.monte_carlo.rst.txt new file mode 100644 index 00000000..17886c27 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.monte_carlo.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.monte\_carlo +========================= + +.. currentmodule:: navlie.utils + +.. autofunction:: monte_carlo \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.plot_error.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.plot_error.rst.txt new file mode 100644 index 00000000..da67b0b7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.plot_error.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.plot\_error +======================== + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_error \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.plot_meas.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.plot_meas.rst.txt new file mode 100644 index 00000000..7a2608b1 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.plot_meas.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.plot\_meas +======================= + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_meas \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.plot_meas_by_model.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.plot_meas_by_model.rst.txt new file mode 100644 index 00000000..57a6b919 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.plot_meas_by_model.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.plot\_meas\_by\_model +================================== + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_meas_by_model \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.plot_nees.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.plot_nees.rst.txt new file mode 100644 index 00000000..5ca9c13a --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.plot_nees.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.plot\_nees +======================= + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_nees \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.plot_poses.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.plot_poses.rst.txt new file mode 100644 index 00000000..b7ae0d81 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.plot_poses.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.plot\_poses +======================== + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_poses \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.randvec.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.randvec.rst.txt new file mode 100644 index 00000000..37d661e7 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.randvec.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.randvec +==================== + +.. currentmodule:: navlie.utils + +.. autofunction:: randvec \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.rst.txt new file mode 100644 index 00000000..d1c57608 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.rst.txt @@ -0,0 +1,53 @@ +navlie.utils +============ + +.. automodule:: navlie.utils + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + associate_stamps + find_nearest_stamp_idx + jacobian + monte_carlo + plot_error + plot_meas + plot_meas_by_model + plot_nees + plot_poses + randvec + schedule_sequential_measurements + set_axes_equal + state_interp + van_loans + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + GaussianResult + GaussianResultList + MonteCarloResult + + + + + + + + + diff --git a/_build/html/_sources/_autosummary/navlie.utils.schedule_sequential_measurements.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.schedule_sequential_measurements.rst.txt new file mode 100644 index 00000000..1e2d5b81 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.schedule_sequential_measurements.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.schedule\_sequential\_measurements +=============================================== + +.. currentmodule:: navlie.utils + +.. autofunction:: schedule_sequential_measurements \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.set_axes_equal.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.set_axes_equal.rst.txt new file mode 100644 index 00000000..1c458ce9 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.set_axes_equal.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.set\_axes\_equal +============================= + +.. currentmodule:: navlie.utils + +.. autofunction:: set_axes_equal \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.state_interp.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.state_interp.rst.txt new file mode 100644 index 00000000..6cdbdbe2 --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.state_interp.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.state\_interp +========================== + +.. currentmodule:: navlie.utils + +.. autofunction:: state_interp \ No newline at end of file diff --git a/_build/html/_sources/_autosummary/navlie.utils.van_loans.rst.txt b/_build/html/_sources/_autosummary/navlie.utils.van_loans.rst.txt new file mode 100644 index 00000000..2538562c --- /dev/null +++ b/_build/html/_sources/_autosummary/navlie.utils.van_loans.rst.txt @@ -0,0 +1,6 @@ +navlie.utils.van\_loans +======================= + +.. currentmodule:: navlie.utils + +.. autofunction:: van_loans \ No newline at end of file diff --git a/_build/html/_sources/api.rst.txt b/_build/html/_sources/api.rst.txt new file mode 100644 index 00000000..4870a37d --- /dev/null +++ b/_build/html/_sources/api.rst.txt @@ -0,0 +1,17 @@ +API Documentation +------------------ +Below is a list of all the modules in the navlie package. Click on any of the links to see the documentation for that module. Alternatively, you can use the search box at the top of the page to search for a particular class/function/module. + +.. autosummary:: + :toctree: _autosummary + :recursive: + :template: custom-module-template.rst + + navlie.composite + navlie.datagen + navlie.filters + navlie.imm + navlie.types + navlie.utils + navlie.batch + navlie.lib \ No newline at end of file diff --git a/_build/html/_sources/index.rst.txt b/_build/html/_sources/index.rst.txt new file mode 100644 index 00000000..fbb725ee --- /dev/null +++ b/_build/html/_sources/index.rst.txt @@ -0,0 +1,62 @@ +.. navlie documentation master file, created by + sphinx-quickstart on Wed Aug 24 15:11:06 2022. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. toctree:: + :maxdepth: 1 + :hidden: + + Home + Tutorial + API + + +Welcome to navlie! +------------------ + +.. make a row of three figures stacked side by side +.. image:: ./fun_figs.png + :width: 100% + :align: center + +navlie is a state estimation package specifically designed for both traditional and Lie-group-based estimation problems! + +The core idea behind this project is to use abstraction in such a way that both traditional and Lie-group-based problems fall under the exact same interface. Using this, a single estimator implementation can operate on a variety of state definitions, such as the usual vector space, and any Lie group. We allow the user to define their custom state, process model, and measurement models, after which they will have a variety of algorithms available to them, including: + +- Extended Kalman Filter +- Iterated Extended Kalman Filter +- Sigmapoint Kalman Filters (Unscented, Spherical Cubature, Gauss-Hermite) +- Interacting Multiple Model Filter +- Batch MAP Estimation + +In addition, navlie contains + +- A large collection of common process and measurement models +- Out-of-the-box on-manifold numerical Jacobians using finite differencing +- Various utils for plotting, error, and consistency evaluation +- Monte Carlo experiment executor with result aggregation +- A preintegration module for linear, wheel odometry, and IMU process models + +By implementing a few classes, the user can model a large variety of problems. The following diagram summarizes the abstraction + +.. image:: ./system_diagram.png + :width: 100% + :align: center + + +Installation +^^^^^^^^^^^^ + +Clone this repo, change to its directory, and execute + +.. code-block:: bash + + git clone git@github.com:decargroup/navlie.git + cd navlie && pip install -e . + +This command should automatically install all dependencies, including our package `pymlg `_ for back-end Lie group mathematical operations. + +Examples +^^^^^^^^ +A more in-depth `tutorial `_ can be found on this website, but there are also many examples found in the `examples/` folder. Simply run these as python3 scripts. \ No newline at end of file diff --git a/_build/html/_sources/tutorial.rst.txt b/_build/html/_sources/tutorial.rst.txt new file mode 100644 index 00000000..bdcf0772 --- /dev/null +++ b/_build/html/_sources/tutorial.rst.txt @@ -0,0 +1,27 @@ + +Getting Started +--------------- + +Welcome to the navlie tutorial! The following few pages will go through a toy localization problem, where we will be running state estimation algorithms using navlie's framework. The first step is to install this package. This should be done by directly cloning the git repo and performing a local pip install: + +.. code-block:: bash + + git clone git@github.com:decargroup/navlie.git + cd navlie && pip install -e . + +All the dependencies should get installed by this command and the package should now be ready to use. Use the column on the left to go to next page of the tutorial. + + +.. note:: + + Although this package is currently registed with PyPi, installation via ``pip install navlie`` will not work. We're still figuring out how to set this up properly. Sorry! Feel free to help. + + +.. toctree:: + :hidden: + + 1. Getting Started + 2. Toy Problem - Traditional <./tutorial/traditional.ipynb> + 3. Toy Problem - Lie groups <./tutorial/lie_groups.ipynb> + 4. Specifying Jacobians <./tutorial/jacobians.ipynb> + 4. Composite States <./tutorial/composite.ipynb> \ No newline at end of file diff --git a/_build/html/_sources/tutorial/composite.ipynb.txt b/_build/html/_sources/tutorial/composite.ipynb.txt new file mode 100644 index 00000000..8a00bfdb --- /dev/null +++ b/_build/html/_sources/tutorial/composite.ipynb.txt @@ -0,0 +1,406 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Composite States\n", + "\n", + "The [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) is a class that allows you to arbitarily combine multiple states, potentially of different types, into a new state that can be used with the navlie framework.\n", + "\n", + "Let's consider the previous example where we used the following $SE(2)$ pose transformation matrix to represent the state:\n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab} & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2).\n", + "$$\n", + "\n", + "Suppose we now also want to estimate a wheel odometry bias $\\mathbf{b} \\in \\mathbb{R}^2$ in addition to the robot's pose. Our state is now \n", + "\n", + "$$\n", + "\\mathbf{x} = (\\mathbf{T}, \\mathbf{b}) \\in SE(2) \\times \\mathbb{R}^2.\n", + "$$\n", + "\n", + "This can be implemented easily using the [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) class in one of two ways: either directly or by inheritance. We'll show the former approach first." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [0.1 2. ]\n" + ] + } + ], + "source": [ + "import navlie as nav \n", + "import numpy as np\n", + "\n", + "# Define the pose and bias as their own states\n", + "T = nav.lib.SE2State(value = [0.1, 2.0, 3.0], stamp = 0.0, state_id=\"pose\")\n", + "b = nav.lib.VectorState(value = [0.1, 2.0], stamp = 0.0, state_id=\"bias\")\n", + "\n", + "# Combine into a composite state, and its ready to use!\n", + "x = nav.CompositeState([T, b], stamp=0.0)\n", + "\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``CompositeState`` class is a subclass of the ``State`` class, but who's ``value`` is a list of states, referred to as the *substates*. A convenience of this class is that the composite state's ``plus``, ``minus``, and ``copy`` methods have already been implemented for you based on the implementations in the substates. Note that the order in which the states are listed is important, and will correspond to the order of the components in the vectors involved in the ``plus`` and ``minus`` operations. This can be demonstrated with the following example." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Result after plus():\n", + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.45359612 -0.89120736 1.80531705]\n", + " [ 0.89120736 0.45359612 6.55185711]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [4.1 7. ]\n", + "\n", + "Result after minus():\n", + "[[1.]\n", + " [2.]\n", + " [3.]\n", + " [4.]\n", + " [5.]]\n" + ] + } + ], + "source": [ + "# plus() and minus() have been defined for you. Here, the first three elements\n", + "# of the vector to be added correspond to the pose (since it has 3 DOF), and the\n", + "# last two to the bias.\n", + "x_temp = x.plus(np.array([1,2,3,4,5]))\n", + "print(\"\\nResult after plus():\")\n", + "print(x_temp)\n", + "\n", + "dx = x_temp.minus(x)\n", + "print(\"\\nResult after minus():\")\n", + "print(dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we must write a process model that works with this state. We'll use the same process model as before, but now we'll also include the wheel odometry bias in the state. The bias process model will be modelled as a random walk of the form \n", + "\n", + "$$\n", + "\\mathbf{b}_{k+1} = \\mathbf{b}_k + \\Delta t \\mathbf{w}^\\mathrm{bias}_k,\n", + "$$\n", + "\n", + "where $\\mathbf{w}^{\\mathrm{bias}}_k \\sim \\mathcal{N}(0, \\mathbf{Q}^{\\mathrm{bias}})$ represents random error associated with this otherwise constant process model, which allows the bias to slowly vary. The process model for the composite state is then" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.linalg import expm\n", + "\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "class WheeledRobotWithBias(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " pose = x.value[0]\n", + " bias = x.value[1]\n", + " vel = np.array([u.value[0] - bias.value[0], u.value[1] - bias.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value[0].value = pose.value @ expm(wedge_se2(vel * dt))\n", + "\n", + " # Largely data generation and jacobian purposes, we also update the bias\n", + " # state with an input, even if the input here is always zero in the\n", + " # nominal case.\n", + " x_next.value[1].value = bias.value + u.value[2:4]*dt\n", + " return x_next\n", + " \n", + " def input_covariance(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(4) * 0.1**2\n", + "process_model = WheeledRobotWithBias(Q)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'd like to use the same measurement model as before, which was just a series of range measurements to known landmarks:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: nav.lib.SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: nav.lib.SE2State):\n", + " return self.R\n", + " \n", + "R = 0.1**2\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The problem is that this was made for an ``SE2State`` instead of our new composite state, and specifically the line `pos = x.value[0:2, 2]` is going to throw an error when we feed in a composite state. This is easy to change, but then that means we have to make a similar change for all sorts of different state definitions. An alternative is to use the [CompositeMeasurementModel](../_autosummary/navlie.composite.CompositeMeasurementModel.rst), which is just a lightweight wrapper around one measurement model that \"assigns\" the model to a specific substate, referenced to by its `state_id` field. It is used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RangeToLandmarkSE2(of substate pose)\n", + "Jacobian:\n", + "[[0. 0.46544123 0.88507893 0. 0. ]]\n" + ] + } + ], + "source": [ + "meas_models = []\n", + "for lm in landmarks:\n", + " meas_models.append(\n", + " nav.CompositeMeasurementModel(RangeToLandmarkSE2(lm, R), \"pose\")\n", + " )\n", + "\n", + "print(meas_models[0])\n", + "print(\"Jacobian:\")\n", + "print(meas_models[0].jacobian(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This does mean that the `state_id` of each substate must be unique, but this is a good practice anyway. The `CompositeMeasurementModel` will then automatically handle the extraction of the relevant substate from the composite state and pass it to the measurement model, as well as handle the corresponding Jacobian accordingly. This is a good way to avoid having to write a lot of boilerplate code for different state definitions. Notice in the above example that the Jacobian has two extra zeros at the end, which correspond to the bias state that has no effect on the measurement. This is automatically handled by the `CompositeMeasurementModel`.\n", + "\n", + "With our problem now set up, we can run a filter on it with the same snippet as usual!" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, \n", + " input_func=lambda t, x: np.array([0.5, 0.3, 0.0, 0.0]), \n", + " input_covariance= Q, \n", + " input_freq=50, \n", + " meas_model_list=meas_models, \n", + " meas_freq_list=[10, 10, 10, 10] \n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2, 0.1**2, 0.1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0,0].set_title(\"Pose Estimation Errors\")\n", + "axs[0,0].set_ylabel(\"theta (rad)\")\n", + "axs[1,0].set_ylabel(\"x (m)\")\n", + "axs[2,0].set_ylabel(\"y (m)\")\n", + "axs[2,0].set_xlabel(\"Time (s)\")\n", + "axs[0, 1].set_title(\"Bias Estimation Errors\")\n", + "axs[0, 1].set_ylabel(\"ang. vel. (rad/s)\")\n", + "axs[1, 1].set_ylabel(\"forward vel. (m/s)\")\n", + "axs[1, 1].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Inheriting from `CompositeState`\n", + "\n", + "The previous example showed how to use the `CompositeState` class directly, but it's also possible to inherit from it. This is useful if you want to add some extra methods or attributes to the composite state, or if you are going to frequently be using the same composite state. Here's an example of how you would do it:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "WheeledRobotState(stamp=0.1, state_id=None) with substates:\n", + " SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.1, dof=2, state_id=bias)\n", + " [0.1 2. ]\n", + "SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n" + ] + } + ], + "source": [ + "class WheeledRobotState(nav.CompositeState):\n", + " def __init__(self, pose_values: np.ndarray, bias_values: np.ndarray, stamp: float):\n", + " pose = nav.lib.SE2State(pose_values, stamp=stamp, state_id=\"pose\")\n", + " bias = nav.lib.VectorState(bias_values, stamp=stamp, state_id=\"bias\")\n", + " super().__init__([pose, bias], stamp=stamp)\n", + "\n", + " # Define any getter that you want for convenience! \n", + " @property\n", + " def pose(self):\n", + " return self.value[0]\n", + "\n", + " @property\n", + " def bias(self):\n", + " return self.value[1]\n", + "\n", + " def copy(self):\n", + " return WheeledRobotState(self.pose.copy(), self.bias.copy())\n", + " \n", + "x = WheeledRobotState([0.1, 2.0, 3.0], [0.1, 2.0], stamp = 0.1)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can end up looking a lot cleaner, and is potentially more flexible to work with since you can add methods and attributes to the composite state. For example, because of the getters we defined above, we can access the pose and bias more ergonomically with `x.pose` and `x.bias`." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/html/_sources/tutorial/jacobians.ipynb.txt b/_build/html/_sources/tutorial/jacobians.ipynb.txt new file mode 100644 index 00000000..ce634985 --- /dev/null +++ b/_build/html/_sources/tutorial/jacobians.ipynb.txt @@ -0,0 +1,341 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Jacobians in navlie\n", + "\n", + "As you may know, many state estimation algorithm require access to process model and measurement model Jacobians, with respect to the state and sometimes other inputs. For states belonging to Lie groups, algorithms will require _Lie Jacobians_, which differ from traditional derivatives as they conform to the constraints of the group. The abstraction provided by the $\\oplus$ and $\\ominus$ operators (implemented with `State.plus` and `State.minus` respectively) allow for a generic definition of a derivative:\n", + "\n", + "$$\n", + "\\left.\\frac{D f(\\mathcal{X})}{D \\mathcal{X}}\\right|_{\\bar{\\mathcal{X}} }\\triangleq \\left.\\frac{\\partial f(\\bar{\\mathcal{X}} \\oplus \\delta \\mathbf{x}) \\ominus f(\\bar{\\mathcal{X}})}{\\partial \\delta \\mathbf{x}}\\right|_{\\delta \\mathbf{x} = \\mathbf{0}},\n", + "$$\n", + "\n", + "which can be shown to fall back to a traditional derivatives when $\\oplus$ and $\\ominus$ are defined to be regular addition/subtraction. This derivative definition is used universally throughout navlie, and roughly follows what is done in the [Micro Lie Theory paper](https://arxiv.org/pdf/1812.01537.pdf). In that reference, seperate definitions are given for \"left\" and \"right\" derivatives, whereas we have aggregated them into a single definition, with left and right derivatives naturally arising from the choice of $\\oplus$ and $\\ominus$ operators.\n", + "\n", + "If you dont want to worry about this, the good news is that navlie computes Lie Jacobians for you by default using finite difference. However, finite difference can have some drawbacks, such as being computationally expensive and less accurate than analytic derivatives. In this notebook, we will show you how to use analytic derivatives in navlie, which offer the maximum accuracy and speed.\n", + "\n", + "## Jacobians - Traditional Approach\n", + "Recall the traditional approach to the previous example. We had defined the state to be $\\mathbf{x} = [\\theta, x, y]^T$ and the process model to be\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t \\\\\n", + "x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t \\\\\n", + "y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where $\\omega_k$ is the angular velocity and $v_k$ is the linear velocity. Since the state is just a regular vector, Lie Jacobians fall back to regular Jacobians, and standard derivative techniques lead to the following expressions for the process model Jacobian with respect to the state\n", + "\n", + "$$\n", + "\\mathbf{F} := \\frac{\\partial f(\\mathbf{x}_k, \\mathbf{u}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 1 & 0 & 0 \\\\ -v_k \\sin(\\theta_k) \\Delta t & 1 & 0 \\\\ v_k \\cos(\\theta_k) \\Delta t & 0 & 1 \\end{bmatrix}\n", + "$$\n", + "\n", + "To implement this Jacobian in navlie, all we need to do is override the `jacobian()` method in our process model, and it will get used automatically by the estimation algorithms. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import navlie as nav\n", + "import numpy as np\n", + "\n", + "from navlie.lib import VectorInput, VectorState\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + " def jacobian(self, x:VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " F = np.eye(3)\n", + " F[1, 0] = -u.value[1] * dt * np.sin(x.value[0])\n", + " F[2, 0] = u.value[1] * dt * np.cos(x.value[0])\n", + " return F\n", + "\n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, lets just double check that we did everything correctly by comparing with finite difference. All process models inherit the `jacobian_fd()` method, which computes the Jacobian using finite difference. We can use this to compare with our analytic Jacobian." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682942 1. 0. ]\n", + " [ 0.01080605 0. 1. ]]\n", + "\n", + "Finite difference:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682943 1. 0. ]\n", + " [ 0.01080604 0. 1. ]]\n" + ] + } + ], + "source": [ + "x = VectorState([1,2,3]) \n", + "u = VectorInput([0.1, 0.2]) \n", + "dt = 0.1 \n", + "\n", + "print(\"Analyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Jacobians match almost perfectly, but differ slightly due to errors in finite difference. This is expected, as finite difference is only an approximation. Nevertheless, finite difference is generally sufficiently accurate for most applications.\n", + "\n", + "
\n", + "Note: The `jacobian` methods must *always* return a 2D array.\n", + "
\n", + "\n", + "\n", + "\n", + "Moving on to the measurement model, which was previously defined to be \n", + "\n", + "$$\n", + "\\mathbf{y}_k = || \\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)} || \n", + "$$ \n", + "\n", + "where $\\mathbf{r}_k$ is the robot's position and $\\boldsymbol{\\ell}^{(i)}$ is the $i$th landmark. The measurement model Jacobian with respect to the state is\n", + "\n", + "$$ \n", + "\\mathbf{G} := \\frac{\\partial g(\\mathbf{x}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 0 & \\frac{(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})^T}{||(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})||} \\end{bmatrix},\n", + "$$\n", + "\n", + "and we can implement this in navlie by again overriding the `jacobian()` method in our measurement model. Adding this to our measurement model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[0. 0.70710678 0.70710678]]\n", + "\n", + "Finite difference:\n", + "[[0. 0.70710696 0.70710696]]\n" + ] + } + ], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + " def jacobian(self, x: VectorState) -> np.ndarray:\n", + " G = np.zeros((1, 3))\n", + " r = x.value[1:]\n", + " G[0,1:] = (r - self.landmark_position) / np.linalg.norm(r - self.landmark_position)\n", + " return G\n", + " \n", + "meas_model = RangeToLandmark(np.array([1, 2]))\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(meas_model.jacobian(x))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(meas_model.jacobian_fd(x))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can again see that the results match nicely." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jacobians - Lie Group Approach \n", + "\n", + "Now, lets see how to implement analytical Jacobians when states belong to Lie groups. In the previous example the state was $\\mathbf{T} \\in SE(2)$ and the process model was\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t).\n", + "$$\n", + "\n", + "To derive the Jacobian, we can \"perturb\" both sides of the equation and manipulate. This is a common technique for deriving Lie Jacobians, and for computing matrix-vector derivatives in general. For more details, we recommend reading [State Estimation for Robotics by Tim Barfoot](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf).\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\mathbf{T}_{k+1} &= \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + "\\bar{\\mathbf{T}}_{k+1} \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\bar{\\mathbf{T}}_{k} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\underbrace{\\bar{\\mathbf{T}}_{k+1}^{-1} \\bar{\\mathbf{T}}_{k}}_{\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\exp((\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}) \\delta \\boldsymbol{\\xi}_{k})^\\wedge) \\\\\n", + " \\delta \\boldsymbol{\\xi}_{k+1} &= \\underbrace{\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1})}_{\\mathbf{F}} \\delta \\boldsymbol{\\xi}_{k}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "There, we used the _adjoint matrix_ $\\mathbf{Ad}(\\cdot)$, to invoke the identity $\\mathbf{X}^{-1} \\exp(\\boldsymbol{\\xi}^\\wedge) \\mathbf{X} = \\exp(\\mathbf{Ad}(\\mathbf{X}) \\boldsymbol{\\xi}^\\wedge)$, which is true for any $\\mathbf{X} \\in SE(2)$. The adjoint matrix for $SE(2)$ is given by \n", + "\n", + "$$ \n", + "\\mathbf{Ad}(\\mathbf{T}) = \\begin{bmatrix} 1 & \\mathbf{0} \\\\ - \\boldsymbol{\\Omega} \\mathbf{r} & \\mathbf{C} \\end{bmatrix}\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\Omega} = \\begin{bmatrix} 0 & -1 \\\\ 1 \n", + "&0 \\end{bmatrix}$.\n", + "\n", + "
\n", + "Note: in this Jacobian derivation, we perturbed the state $\\mathbf{T} = \\bar{\\mathbf{T}} \\exp(\\delta \\boldsymbol{\\xi}^\\wedge)$ \"on the right\" because that corresponds to what was implemented in the `plus()` method of our `SE2State` class. It is important to be consistent here for everything to work.\n", + "
\n", + "\n", + "Now, we can implement this Jacobian in navlie by overriding the `jacobian()` method in our process model. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [ 0.0394695 0.92106099 0.38941834]\n", + " [ 0.19470917 -0.38941834 0.92106099]]\n", + "\n", + "Finite difference:\n", + "[[ 1.00000000e+00 -1.10747782e-11 -1.10747782e-11]\n", + " [ 3.94695038e-02 9.21060995e-01 3.89418343e-01]\n", + " [ 1.94709171e-01 -3.89418342e-01 9.21060994e-01]]\n" + ] + } + ], + "source": [ + "from navlie.lib import SE2State, VectorInput\n", + "from scipy.linalg import expm\n", + "\n", + "\n", + "def wedge_se2(x:np):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def adjoint_se2(T:np.ndarray):\n", + " C = T[:2, :2]\n", + " r = T[:2, 2]\n", + " Omega = np.array([[0, -1], [1, 0]])\n", + " Ad = np.zeros((3,3))\n", + " Ad[0,0] = 1\n", + " Ad[1:,1:] = C\n", + " Ad[1:,0] = - Omega @ r\n", + " return Ad\n", + "\n", + "\n", + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(u * dt))\n", + " return x_next\n", + " def input_covariance(self, x:SE2State, u:VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + " def jacobian(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " return adjoint_se2(expm(-wedge_se2(u * dt)))\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)\n", + "x = SE2State(expm(wedge_se2(np.array([1,2,3]))))\n", + "u = VectorInput([4, 2])\n", + "dt = 0.1\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that when using Lie groups, our Jacobian no longer has dependence on the state itself. This can be a tangible advantage when the state estimate has high uncertainty, where using a traditional approach can result in excessive linearization errors when the state estimate is far from the true value." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/html/_sources/tutorial/lie_groups.ipynb.txt b/_build/html/_sources/tutorial/lie_groups.ipynb.txt new file mode 100644 index 00000000..fd96344d --- /dev/null +++ b/_build/html/_sources/tutorial/lie_groups.ipynb.txt @@ -0,0 +1,425 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Lie group approach\n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "Another way we could approach the same state estimation task is to instead use Lie group theory, which is becoming increasingly common practice in state estimation. Lie group theory can be very abstract, and the main references that navlie refer to are the following:\n", + "\n", + "1. [A micro Lie theory for state estimation in robotics](https://arxiv.org/abs/1812.01537)\n", + "2. [T.Barfoot, State Estimation for Robotics](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf)\n", + "\n", + "\n", + "## Define the State\n", + "Instead of representing the state using a vector, we will represent the state using an element of the *special Euclidean group* $SE(2)$, sometimes called *pose transformation matrices*. Elements of this group are 3x3 matrices of the form \n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab}(\\theta) & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2)\n", + "$$\n", + "\n", + "where $\\mathbf{r}_a = [x,y]^T$ again denotes the position of the robot and $\\mathbf{C}_{ab}(\\theta) \\in SO(2)$ is a rotation matrix (sometimes called a direction cosine matrix) with the form \n", + "\n", + "$$ \n", + "\\mathbf{C}_{ab}(\\theta) = \\begin{bmatrix} \\cos \\theta & - \\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{bmatrix}.\n", + "$$\n", + "\n", + "The rotation matrix transforms vectors resolved in one frame to another frame, i.e. $\\mathbf{r}_a = \\mathbf{C}_{ab} \\mathbf{r}_b$. Unlike vectors, elements of $SO(2)$ or $SE(2)$ cannot be added together to produce another valid element of $SE(2)$, but they can be multiplied together with the result still having the same form.\n", + "\n", + "$$\n", + "\\mathbf{T}_1 \\mathbf{T}_2 \\in SE(2)\n", + "$$\n", + "\n", + " To proceed further with our mathematical setup, we need to define a few very common operators seen in Lie group theory. The first two are the \"wedge\" $(\\cdot)^\\wedge$ and \"vee\" $(\\cdot)^\\vee$ operators, which for this specific group has the form\n", + "\n", + "$$ \n", + "\\begin{bmatrix} \\theta \\\\ x \\\\ y \\end{bmatrix}^\\wedge = \\begin{bmatrix} 0 & -\\theta & x \\\\ \\theta & 0 & y \\\\ 0 & 0 & 0 \\end{bmatrix}\n", + "$$\n", + "\n", + "and the $(\\cdot)^\\vee$ operator simply does the exact inverse of $(\\cdot)^\\wedge$. We can implement them as follows.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "%reset -f\n", + "import numpy as np\n", + "\n", + "# Helper functions for SE(2)\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def vee_se2(X):\n", + " return np.array([X[1, 0], X[0, 2], X[1, 2]])\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Two other fundamental relationships appearing in Lie group theory are the exponential (denoted $\\exp$) and logarithmic (denoted $\\log$) maps. While these have a deeper definition, for our case it suffices to think of them as simply the [matrix exponential](https://en.wikipedia.org/wiki/Matrix_exponential) and [matrix logarithm](https://en.wikipedia.org/wiki/Logarithm_of_a_matrix). Using the wedge and vee operators for $SE(2)$ defined above, we can convert a 3x1 vector to an $SE(2)$ element and back as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "An element of SE2:\n", + "[[ 0.99500417 -0.09983342 0.18467933]\n", + " [ 0.09983342 0.99500417 0.30949192]\n", + " [ 0. 0. 1. ]]\n", + "\n", + "The original vector 'representing' it:\n", + "[0.1 0.2 0.3]\n" + ] + } + ], + "source": [ + "from scipy.linalg import expm, logm\n", + "\n", + "T = expm(wedge_se2(np.array([0.1, 0.2, 0.3])))\n", + "print(\"An element of SE2:\")\n", + "print(T)\n", + "\n", + "x = vee_se2(logm(T))\n", + "print(\"\\nThe original vector 'representing' it:\")\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have the tools we need to abstract-ify our problem a little bit. As commonly seen in the literature, we can define the so-called \"oplus\" and \"ominus\" operators as follows (sometimes called \"boxplus\" $\\boxplus$ and \"boxminus\" $\\boxminus$):\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbf{T}_2 &= \\mathbf{T}_1 \\oplus \\boldsymbol{\\xi} := \\mathbf{T}_1 \\exp(\\boldsymbol{\\xi}^\\wedge) \\\\\n", + "\\boldsymbol{\\varepsilon} &= \\mathbf{T}_2 \\ominus \\mathbf{T}_1 := \\log(\\mathbf{T}_2^{-1} \\mathbf{T}_1)^\\vee\n", + "\\end{aligned}\n", + "$$ \n", + "\n", + "Here, both $\\boldsymbol{\\varepsilon}, \\boldsymbol{\\xi} \\in \\mathbb{R}^3$ are 3x1 vectors. The $\\oplus: SE(2) \\times \\mathbb{R}^3 \\to SE(2)$ operator \"adds\" a vector to an $SE(2)$ element to produce another $SE(2)$ element, and the $\\ominus:SE(2) \\times SE(2) \\to \\mathbb{R}^3$ operator \"subtracts\" two $SE(2)$ elements to produce a vector that represents the \"difference\" between them. \n", + "\n", + "\n", + "With this context, lets implement an $SE(2)$ state inside navlie's framework. To define a custom state, you must subclass the `nav.State` abstract class and you *must* implement the `plus`, `minus`, and `copy` methods. These methods play exactly the role of $\\oplus$ and $\\ominus$ described above, while the `copy` method is used to create a deep copy of that state object. In addition, state objects must hold an integer property named `dof` that specifies the *degrees of freedom* associated with that state. For $SE(2)$, this is 3." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.0, dof=3, state_id=None)\n", + " [[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n" + ] + } + ], + "source": [ + "import navlie as nav\n", + "\n", + "class SE2State(nav.State):\n", + " def __init__(self, value :np.ndarray, stamp: float):\n", + " super().__init__(value=value, dof=3, stamp=stamp)\n", + "\n", + " def plus(self, dx: np.ndarray):\n", + " new_value = self.value @ expm(wedge_se2(dx))\n", + " return SE2State(new_value, self.stamp)\n", + "\n", + " def minus(self, other: \"SE2State\"):\n", + " other_inv = np.linalg.inv(other.value)\n", + " return vee_se2(logm(other_inv @ self.value))\n", + " \n", + " def copy(self):\n", + " return SE2State(self.value.copy(), self.stamp)\n", + "\n", + "x = SE2State(np.eye(3), 0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Process Model\n", + "\n", + "Now, we must adapt the process model to work with our new `SE2State`. It is well known that the rotational kinematics can be written directly in terms of rotation matrices using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{C}}_{ab} = \\mathbf{C}_{ab}\\begin{bmatrix}0 & -\\omega \\\\ \\omega & 0 \\end{bmatrix} \n", + "$$\n", + "\n", + "and that the translational kinematics can be written in vector form using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{r}}_a = \\mathbf{C}_{ab} \\begin{bmatrix} v \\\\ 0 \\end{bmatrix} .\n", + "$$\n", + "\n", + "By stacking these into matrices it follows that \n", + "$$ \n", + "\\dot{\\mathbf{T}} = \\mathbf{T} \\boldsymbol{\\varpi}^\\wedge\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\varpi} = [\\omega, v, 0]^T$. This equation is now a linear, matrix-valued ODE, and can be integrated exactly over a short duration $\\Delta t = t_{k+1} - t_k$ using the matrix exponential. This gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}_k^\\wedge \\Delta t)\n", + "$$\n", + "\n", + "which we can implement as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " vel = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(vel * dt))\n", + " return x_next\n", + " \n", + " def input_covariance(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Measurement Model\n", + "\n", + "Finally, our measurement model remains largely unchanged. We just need to extract the position from an `SE2State` object now, as done below." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: SE2State):\n", + " return self.R\n", + " \n", + "\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmarkSE2(landmark, 0.1**2) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run the Filter!\n", + "\n", + "And that's it! All remaining snippets are now _literally_ copy-pasted from our previous approach with zero modifications. Using the abstraction framework in navlie, we can easily switch between different state representations and process/measurement models without having to change any of data generation or filtering code. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.02, dof=3, state_id=None)\n", + " [[ 9.99950000e-01 -9.99983333e-03 5.99990000e-03]\n", + " [ 9.99983333e-03 9.99950000e-01 2.99997500e-05]\n", + " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00]]\n", + "VectorInput(stamp=0.04, state_id=None)\n", + " [0.52438924 0.40056502]\n", + "Measurement(stamp=0.0, state_id=None) of PoseRangeToLandMark\n", + " 2.299276237837416\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.5, 0.3]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[1])\n", + "print(input_data[2])\n", + "print(meas_data[3])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Built-in Lie group states \n", + "While we implemented our own `SE2State` from scratch here for pedagogical purposes, navlie comes with many built-in Lie group states that you can use out of the box. Some of the built-in Lie group states include:\n", + "\n", + "- `nav.lib.SO2State`: representing 2D rotations using, beloning to the group $SO(2)$\n", + "- `nav.lib.SO3State`: representing 3D rotations using, beloning to the group $SO(3)$\n", + "- `nav.lib.SE2State`: representing 2D poses using, beloning to the group $SE(2)$\n", + "- `nav.lib.SE3State`: representing 3D poses using, beloning to the group $SE(3)$\n", + "- `nav.lib.SE23State`: representing \"extended\" poses that also contain velocity information, belonging to the group $SE_2(3)$\n", + "- `nav.lib.SL3State`: representing 3D homographies, belonging to the group $SL(3)$\n", + "\n", + "Each of these classes stores the value as a square numpy array in the `x.value` property. Moreover, closed-form formulas for the exponential and logarithmic maps have been implemented for each of these states, which is faster than using `scipy.linalg.expm` and `scipy.linalg.logm`. These underlying operations have even been implemented in C++ for maximum speed. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/html/_sources/tutorial/traditional.ipynb.txt b/_build/html/_sources/tutorial/traditional.ipynb.txt new file mode 100644 index 00000000..f18bd608 --- /dev/null +++ b/_build/html/_sources/tutorial/traditional.ipynb.txt @@ -0,0 +1,393 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Traditional Approach\n", + "\n", + "In this tutorial, we'll simulate a simple 2D localization problem as per the figure below. We'll assume that we have a robot following a simple body-frame-velocity model, which has access to noisy measurements of its forward velocity $v$ and angular velocity $\\omega$. In addition, this robot will have a time-of-flight sensor that gives it range measurements to a few known landmarks in the environment. \n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "\n", + "## Define the State\n", + "The first step is to define the state of the robot. We'll start with a more traditional approach and define the state of the robot to be a vector of the form $\\mathbf{x} = [\\theta, x, y ]^T$, where $x$ and $y$ are the robot's position in the world and $\\theta$ is its orientation. We'll also define the control inputs to be $\\mathbf{u} = [\\omega, v]^T$, the robot's forward and angular velocity. The process (motion) model of the robot is then given by:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\dot{\\theta} &= \\omega,\\\\\n", + " \\dot{x} &= v \\cos(\\theta), \\\\\n", + " \\dot{y} &= v \\sin(\\theta). \n", + "\\end{aligned}\n", + "$$\n", + "\n", + "However, this is in continuous time, and we need to discretize it to use it in a filter. For now, we'll use the simple Euler discretization method, which gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t, \\\\\n", + " x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t, \\\\\n", + " y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t.\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Lets now code up our state and process model using navlie's framework. Since our state is just a regular 3x1 vector, we can use a standard type from the built-in library: [navlie.lib.VectorState](../_autosummary/navlie.lib.states.VectorState.rst)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "np.random.seed(0)\n", + "import navlie as nav\n", + "from navlie.lib import VectorState\n", + "\n", + "x = VectorState([0, 0, 0], stamp=0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `VectorState` is a subclass of the abstract [State](../_autosummary/navlie.types.State.rst) class in navlie, which is one of the core primitive types. The value of the state is stored as a numpy array, and can be accessed directly through `x.value`. \n", + "\n", + "\n", + "## Define the Process Model\n", + "For the process model, we'll choose to define our own from scratch here. Process models in navlie *must* inherit from the abstract [navlie.ProcessModel](../_autosummary/navlie.types.ProcessModel.rst) class and implement the `evaluate` and either the `input_covariance` or `covariance` methods." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "from navlie.lib import VectorInput\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The methods in navlie process models must always accept the arguments shown above: a `State` object, an `Input` object, and a float `dt`. The `evaluate` method must always return a valid (i.e. subclass of a) `State` object, and the `input_covariance` method must always return a square numpy array. There are more optional methods that can be implemented for performance reasons, but we will cover those later.\n", + "\n", + "## Define the Measurement Model(s)\n", + "Moving on to the measurement model, if $\\mathbf{r}_a = [x,y]^T$ denotes the position vector of the robot resolved in the world frame, and $\\mathbf{\\ell}^{(i)}_{a} \\in \\mathbb{R}^2$ is the 2 x 1 position vector of landmark $i$, then the measurement model for each landmark is simply \n", + "\n", + "$$ \n", + "y_i = ||\\mathbf{r}_a - \\mathbf{\\ell}^{(i)}_{a}||\n", + "$$\n", + "\n", + "In navlie, measurement models must be implemented in a similar way to process models: inherit from the [navlie.MeasurementModel](../_autosummary/navlie.types.MeasurementModel.rst) abstract class, and then implement the `evaluate` and `covariance` methods. Here's an example for this problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmark(landmark) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## (Simulation only) Generate fake data\n", + "\n", + "The next step is to generate some fake data for our simulation (although navlie is also compatible with real data). To do this, we will use the [DataGenerator](../_autosummary/navlie.datagen.DataGenerator.rst) class which is used as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n", + "VectorInput(stamp=0.0, state_id=None)\n", + " [0.4867558 0.40227221]\n", + "Measurement(stamp=0.0, state_id=None) of RangeToLandmark\n", + " 1.5906187969698615\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.3, 0.5]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[0])\n", + "print(input_data[0])\n", + "print(meas_data[0])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output of the `DataGenerator.generate` method is three lists: a list of ground-truth `State` objects, a list of `Input` objects, and a list of [Measurement](../_autosummary/navlie.types.Measurement.rst) objects, with the input/measurement lists possibly being corrupted by random noise if the `noise=True` flag is set. Each item in these lists correspond to different points in time. We can plot the trajectory as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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DRJof/PLldD7b5LrP4K1fDWFghziHE5nT5cgNZcZ3zV+fzc2vpJPSognv3T7UioDh+RvSuNfdifyzZ5fy3y376/mE8SVWCMwxPlidxR1vrOLstrH851fWKWx+cOeoLjx2xdkA3Pjv5Xy8zi4v9RdWCEy1t5Zn8JtZqxmQ0pxXbhpo4wabE1yZlswz1/YD4LbXV/LOikyHE5mGYIXAAPB2egZT3l3LOV0SeOnGgfbUUHNSP+nVmn/fOACA3769hjlr9jicyJwpKwSGeeuyuf/dtZzTJZ6Z1/cnItQuDzV1O++sRF77xSAA7nxzFV98Z3f8+zIrBAFu0Zb9/Po/q+jXrjnPXtff7hEwp2x4l/jq00Q3vPgtK3cfdDiR+bGsEASwFbsOcOtrK+iS2JQXJg2w59Gb0/aTXq3506W9ALjsmSXsyLX7DHyRFYIAtSuviJtfWUHrZpG88ouB1TcNGXO6rhnUrvrS0vMeX8ThIxUOJzKnywpBAMovLufGl5ZTpcqLkwYQHx3udCTj4+4c1YULuicC0PPhBVTZs4l8ihWCAFNWUcWvXksn80AJz12XRof4Jk5HMn7i+RsGEOYemKjzA/McTmNOhxWCADNtzgaWbT/AX67oZY8JMA1uyx9dDxiuUvj1f1Y5nMacKisEAeSdFZm88c1ubh3RiUv7tnU6jvFDIlL91NIPVu/h0402DrIvsEIQIDbuKeCB99cxpGMLfntRV6fjGD/WNCKUd28bAsDNr6STU3jE4USmPlYIAkB+STm3vb6C2KhQZlzd1waYNx7Xv30ct43sBMCA6Z/ha085DjT2i+DnVJUH3l9H1sESnrm2HwlN7Qoh0zjuH92NSPdd6j97dqnDaUxdrBD4uQ9W7+GjtdncfWFX+re3zmHTuI72FyzfeZCvttpjKLyVFQI/lnmwmP+ZvZ609s25dUQnp+OYABQSHMQ7t7r6C6574VuOVFQ6nMjUxgqBn6qsUu55aw0K/G1iH4KDxOlIJkClpcRxQfeWAPR6+BOH05jaWCHwU69/s4tvdxzgoUt6kBwX5XQcE+Cev8E1QmJZZRVz19qANt7GCoEfys4v4a/zt3BOl3iu7G/3Cxjv8Nk95wJwxxsrqaiscjiNqckKgR96+IMNVFRVMX1CL0TslJDxDp0TmzK0UwsALnn6a4fTmJo8VghEJFlE/isiG0Vkg4j8upZ1RopIvoisdr8e8lSeQLFgw14+2biP31zQlXYt7JSQ8S5HB7PZlF3Ausx8h9OYozx5RFAB3KuqPYDBwB0i0qOW9b5S1T7u1yMezOP3SssreWTORrq1asovhndwOo4xJwgKEl6+aSAAlzy92OE05iiPFQJVzVbVle73hcAmIMlT32fghcU7yDpUwsOXpBJqdw8bLzWia0L1+1eX7XIwiTmqUX4tRCQF6At8U8viISKyRkQ+FpHUk3z+FhFJF5H0nBy7KaU2+wtLeea/27ioR0uGuM/DGuOtlv1uFAD/M3u9jV3gBTxeCEQkGngX+I2qFhy3eCXQXlV7A38HZte2DVV9TlXTVDUtISGhtlUC3hOffEdZZRW//0l3p6MYU69WzSLonRwLwOQ3Vzobxni2EIhIKK4i8Lqqvnf8clUtUNXD7vfzgFARifdkJn+0bX8hs9IzuH5ICik20IzxEW//ynXH8bx1eykttzuOneTJq4YEeAHYpKpPnGSdVu71EJGB7jx5nsrkr576fBtRocHccV5np6MYc8rCQoL4WZrrPpcbXvzW4TSBzZNHBMOA64Dza1we+hMRuVVEbnWvcwWwXkTWADOAq9SeV3tavttXyEdr93DD0BTimoQ5HceY0/LoZWcD8M2OA5SU2VGBU0I8tWFVXQzUeTeTqj4NPO2pDIHgqc+20iQshJvP6eh0FGNOW1CQ8PPB7Xht2W6ueX4Z798+zOlIAcmuMfRhW/cVMnddNpOGptDcjgaMj/rf8T0BWLX7kD2d1CFWCHzYC4t3EB4SxE1285jxYSLCZX1dtxj99u21DqcJTFYIfFTu4SO8tyqLy/u3tb4B4/P+coWrr2DOmj0OJwlMVgh81GvLdlFWUcVNw+xowPi+0OAgOia4Ln1+/qvtDqcJPFYIfFBpeSWvLt3F+d0S6ZwY7XQcYxrErFtc9xX8ce4mh5MEHisEPuiTjfvIKypj0tAUp6MY02ASmoZXv9+UffxDCIwnWSHwQbOW7yYpNpLhne0mbONfnruuPwDXPl/bY8mMp1gh8DG784r5elseEwckE2TjEBs/c1FqKwAOFJXZw+gakRUCH/P2igyCBK6wISiNnxrS0fX03GcWbXM4SeCwQuBDVJX3VmZxTpcE2sRGOh3HGI94+pq+ADz+yXcOJwkcVgh8yKqMQ2QdKmF8nzZORzHGY1pE/9BpbM8fahxWCHzI3LXZhAUHcUGPlk5HMcajrhqQDMBjC7Y4nCQwWCHwEVVVyrx12ZzbNYGYiFCn4xjjUQ+MdQ2w9OLXOxxOEhisEPiIVRkHyc4vZezZrZyOYozHNa2xs2OD1nieFQIfsXDzfoKDhPO72WkhExgmuPvCZn5pj5zwNCsEPuKL73Lo3645zSLttJAJDPeP6QbA/31qVw95mhUCH5BTeIT1WQWMOCvB6SgmQERHN/wzrKZNm8bjjz9+yuu3bnbql0inpKSQm5tb5zoPPPAAycnJJ7TNG9p6Oupra3FxMWPHjqVbt26kpqYyderUerdphcAHfLU1B4ARXa0QmMASE+EaRHFdZv5J16msPLU+hEsuuYRvv/XtsZFPta2//e1v2bx5M6tWreLrr7/m448/rnN9KwQ+YPHWXFo0CaNH6xino5gANmfOHAYNGkTfvn254IIL2LdvH+Da+73pppsYOXIkHTt2ZMaMGdWfmT59Ol27dmX48OFs2fLDpaAjR47k7rvvJi0tje7du7N8+XIuu+wyunTpwoMPPli9XviiJ8h+6decM6gvzz33XPX86Oho7r33Xnr37s3SpUur55eUlDBmzBhmzpx5Qv7BgwfTunVrr23rhAkT6N+/P6mpqWfU1qioKM477zwAwsLC6NevH5mZmXU3WFV96tW/f38NNMP/8rne+mq60zFMAGnSpMkJ8w4cOKBVVVWqqjpz5ky95557VFX14Ycf1iFDhmhpaanm5ORoXFyclpWVaXp6uvbs2VOLioo0Pz9fO3XqpI899piqqo4YMUKnTJmiqqpPPvmktm7dWvfs2aOlpaWalJSkubm5qqq6d3+Otr//I02+511NTU2tng/orFmzqrO1b99ed+zYoaNGjdKXX375tNrmLW3Ny8tTVdXi4uIGa+vBgwe1Q4cO+v333yuQrif5XfXY4PUikgy8ArQEFHhOVZ86bh0BngJ+AhQDk1R1pacy+aJ9BaVkHCjhhiEpTkcxfm72qiweW7CFPYdKKCmvZPaqLCa4h5AEyMzMZOLEiWRnZ1NWVkaHDj8MijR27FjCw8MJDw8nMTGRffv28dVXX3HppZcSFRUFwLhx4475vqPTvXr1IjU1tXpvvWPHjmRkZNCiRQv++Y+n2fPiywDkHznA1q1badGiBcHBwVx++eXHbG/8+PFMmTKFa6+91ifbOmPGDN5//30AMjIyzritFRUVXH311dx111107Nixzj8PT54aqgDuVdUewGDgDhHpcdw6Y4Au7tctwD89mMcnpe88CEBaSpzDSYw/m70qi9+9t46sQyUooAq/e28ds1dlVa9z5513MnnyZNatW8ezzz5LaWlp9bLw8B8eCxEcHExFRUW933n0M0FBQcd8PigoiIqKChYtWsRnn31G+xufoM1NT9O959nV3xkREUFwcPAx2xs2bBjz58/HtRN9cpVV6rVtXbp0KWvWrKFv375n3NZbbrmFLl268Jvf/KbefB4rBKqafXTvXlULgU1A0nGrjQdecR/FLANiReTUTuIFiPRdB4gIDSK1jfUPGM95bMEWSo67caukvPKYRzzk5+eTlOT6L/zyyy/Xu81zzz2X2bNnU1JSQmFhIXPmzDmtTPn5+TRv3pzbL0ilPC+D9OV1d/Q+8sgjNG/enDvuuKPO9coqq7y2rVFRUWzevJlly5bVuX59bX3wwQfJz8/nySefPKXvb5TOYhFJAfoCx482kQRk1JjO5MRigYjcIiLpIpKek5PjsZzeaG1mPr2SmhEabP36xnP2HCo5ZlrLj5D5jxv4ZvrPaNu2LU888QTTpk3jyiuvpH///sTH1z8oUr9+/Zg4cSK9e/dmzJgxDBgw4LQyjR49moqKCv45eRwHv3iZ0NZn1fuZp556ipKSEqZMmXLCsilTptC2bVuqylxtO7T4da9ra/fu3Zk6dSqDBw/+0W3NzMxk+vTpbNy4kX79+tGnTx+ef/75Orcl9R1GnSkRiQa+AKar6nvHLfsIeFRVF7unPwfuV9X0k20vLS1N09NPutivVFUpZ//hEy7rl8Qj43s6Hcf4sWGPLiTruGIAkBQbyddTz3cg0bFSps4FYOejY894W97eVk8RkRWqmlbbMo/uZopIKPAu8PrxRcAtC0iuMd3WPc8AmQdLOHykgu522ajxsPsuPovI0GPPQ0eGBnPfxfXvhfuaQGrrqfJYIXBfEfQCsElVnzjJah8C14vLYCBfVbM9lcnXbNrrGsC7W6umDicx/m5C3yT+fFkvkmIjEVx7x3++rNcxV9I4KSzE9VO1v7C0njXr5+1tdYLHLh8FhgHXAetEZLV73u+BdgCq+i9gHq5LR7fhunz0Rg/m8TmbswsRgbOsEJhGMKFvktf+GF7aJ4lZ6Rl8tCabm4Z3qP8D9fDmtjrBY4XAfd6/ztHV3TdL1N3FH8B25hXRplkkUWGerNfGeL/zuycyKz2DL77LaZBCYI5ll6J4sYwDxSTH2djExgzp5BrQfvG2uh8sZ34cKwRebPeBYpKbRzkdwxjHHR2Vr7LKs1c5BiorBF6qpKyS/YVHaBdnhcAY41lWCLzU0euc29qpIWOMh1kh8FJ5h48AkBAd4XASY7yLp2+CDURWCLxUXlEZAHFNwhxOYox3iI92/V/YV3DE4ST+xwqBlzpaCI7+4zcm0HVJdN1P892+QoeT+B8rBF7qwGFXIWhuRwTGAD/cWGmFoOFZIfBSh0rKaBIWbE8dNcYt2X0FXebBEx8YZ86M/cp4qdLyKiLDgutf0ZgA0TzKdS/BoeIyh5P4HysEXupIeSURoVYIjDmqeZTrNOnB4nKHk/gfKwReqrTCCoExNTWzIwKPsULgpUrLq4gItb8eY446ekRwqMSOCBpavb80InKniDRvjDDmB1WqBEmdD281JqAEu/8/2POGGt6p7HK2BJaLyFsiMto94IzxsGAR+wdvTA1llVUAhNmVdA2u3j9RVX0Q6IJrtLFJwFYR+ZOIdPJwtoAWFGSFwJiaKqpchcAuqW54p/Qn6h5AZq/7VQE0B94Rkb96MFtACxahyp6pYky18grX/4fQEDsp0dDqHfpKRH4NXA/kAs8D96lquYgEAVuBKZ6NGJiCg4UKOyIwplppRSUA4SF2NV1DO5UxEOOAy1R1V82ZqlolIj/1TCzTJCyYoiMVTscwxmvsK3ANXN8yJtzhJP6n3kKgqg/XsWxTw8YxR8VEhFJYaoXAmKOy3I+WaNPMxuhoaNbr4qWaRoRSXFZJuftKCWMC3dHBmtrEWiFoaB4rBCLyoojsF5H1J1k+UkTyRWS1+/WQp7L4ophI18HaYTsqMAaAPe5CkNTcCkFD8+QRwUvA6HrW+UpV+7hfj3gwi89pFum6nf6g3U5vDADbc4sAaN/CxvFuaB4rBKr6JXDAU9v3d61iXENU2mhMxrhsz3EVgs4J0Q4n8T9O9xEMEZE1IvKxiKSebCURuUVE0kUkPScnpzHzOaZVM1ch2Ftgz143pqYQu6GswTn5J7oSaK+qvYG/A7NPtqKqPqeqaaqalpCQ0Fj5HHW0EGTnlzqcxBjj7xwrBKpaoKqH3e/nAaEiEu9UHm8TFRZCs8hQ9lohMMZ4mGOFQERaHX2AnYgMdGfJcyqPN0qKjWT3gWKnYxjjuCPuu4qNZ5zKncU/ioi8CYwE4kUkE3gYCAVQ1X8BVwC3iUgFUAJc5X6mkXHrlBjN6oyDTscwxnFLvnftIw7sEOdwEv/ksUKgqlfXs/xp4GlPfb8/6JTQhI/W7qHUhq00Ae6TDfsAuKhHS4eT+CfrfvdinROjUf3hsjljAtWnG/cCcHFqK4eT+CcrBF6sk/t66a37Cx1OYoyzcg+7bqxMjrObyTzBCoEX65QQTVhwEBv3FDgdxRjjx6wQeLGwkCC6t27K6oxDTkcxxjEHi+wxK55mhcDLnd02lvVZ+TZspQlYb6/IAGBiWrLDSfyXFQIvd3bbZhSVVbI957DTUYxxxKvLXGNi/Xxwe4eT+C8rBF6uT3IsAKt2H3I0hzFOyTjget5Wr7bNHE7iv6wQeLnOidG0aBLG0u1207UJPFV2SrRRWCHwciLCkE4tWPJ9LnbjtQk089ZnAzAgpbnDSfybFQIfMLRTPPsKjlQPzGFMoHjik+8AuOfCsxxO4t+sEPiAoZ1aALBkW67DSYxpXEd3foa4/w8Yz7BC4APat4giOS6S/24JjEF5jAEoKC13OkLAsELgA0SEC7q3ZPG2XIqO2GD2JjAcPS00aWiKs0ECgBUCH3FRj1aUVVTx5Xd2VGACw0tLdgJw70VdnQ0SAKwQ+IgBKc2JjQrl0437nI5ijMfVvJO+aUSog0kCgxUCHxESHMT53RL5bNM+G63J+L3nv9oOwMizAmOMcqdZIfAhl/RuQ0FpBYus09h4WHR0dINvc9q0aTz++OOntO6fP94MwF8vP/uU1k9JSSE3t+6r6lasWEGvXr3o3Lkzd911V/V9OU639XSdSltHjx5N7969SU1N5dZbb6Wysu6dRysEPuSczvHER4fz/sosp6MY4zGHa1wQkRgTUe/69f3IHXXbbbcxc+ZMtm7dytatW5k/f/6PzuiUU23rW2+9xZo1a1i/fj05OTm8/fbbda5vhcCHhAQHMa53GxZu3k9+sV1aZxrXnDlzGDRoEH379uWCCy5g3z5Xf9W0adO46aabGDlyJB07dmTGjBnVn5k+fTpdu3Zl+PDhbNmypXr+yJEjufvuu0lLS6N79+4sX76cyy67jC5dunDB1bcBrquFJkyYQP/+/UlNTeW5556r/nx0dDT33nsvvXv3ZunSpdXzS0pKGDNmDDNnzjwme3Z2NgUFBQwePBgR4frrr2f27NmOt/XBBx+sXq+h2goQExMDQEVFBWVlZYjISdsKgKr61Kt///4ayNZlHtL293+kry7d6XQU48eaNGlywrwDBw5oVVWVqqrOnDlT77nnHlVVffjhh3XIkCFaWlqqOTk5GhcXp2VlZZqenq49e/bUoqIizc/P106dOuljjz2mqqojRozQKVOmqKrqk08+qa1bt9Y9e/ZoaWmpBke30LZ3vaElZRWal5enqqrFxcWampqqubm5qqoK6KxZs6qztW/fXnfs2KGjRo3Sl19++YTsy5cv11GjRlVPf/nllzp27FjH25qUlFTdpoZq61EXXXSRxsbG6tVXX60VFRUKpOtJflc9Nni9iLwI/BTYr6o9a1kuwFPAT4BiYJKqrvRUHn+R2iaGbq2a8sY3u7l2ULv6K70xDSQzM5OJEyeSnZ1NWVkZHTp0qF42duxYwsPDCQ8PJzExkX379vHVV19x6aWXEhXlGl5y3Lhxx2zv6HSvXr1ITU2ldevWrM08REhsKyoLcokIDebRGTN4//33AcjIyGDr1q20aNGC4OBgLr/88mO2N378eKZMmcK1117rE20F6NixIxkZGbRo0YIZDdzWBQsWUFpayrXXXsvChQvrbK8nTw29BIyuY/kYoIv7dQvwTw9m8RsiwnVD2rMxu4CVuw86Hcf4kdmrshj26EI6TJ1LSXkls1cd2xd15513MnnyZNatW8ezzz5LaWlp9bLw8PDq98HBwVRU1H/j49HPBAUFVb8f9/TXIMK0n3Zj0aJFfPbZZyxdupQ1a9bQt2/f6u+MiIggODj4mO0NGzaM+fPn1/pwxqSkJDIzM39o6+K1pOfgaFuPTldUVDRoW2uKiIhg/PjxfPDBB3Wu57FCoKpfAgfqWGU88Ir7KGYZECsirT2Vx59M6JNE0/AQXlm6y+koxk/MXpXF795bR9ahEhRQhd+9t+6YH8j8/HySkpIAePnll+vd5rnnnsvs2bMpKSmhsLCQOXPm1Ll+SdkPHaH92jcnPz+f5s2bExUVxebNm1m2bFmdn3/kkUdo3rw5d9xxxwnLWrduTUxMDMuWLeP9lZk8+8JLaLs0x9p6vIZs6+HDh8nOdj21taKigrlz59KtW7c6t+dkZ3ESkFFjOtM9z9SjSXgIl/dvy7x12eQUHnE6jvEDjy3YQkn5Dz/EWn6ErU/+nIkj+9C2bVueeOIJpk2bxpVXXkn//v2Jj4+vd5v9+vVj4sSJ9O7dmzFjxjBgwIA617/37dUAtHRfKTR69GgqKiro3r07U6dOZfDgwfV+51NPPUVJSQlTpkw5YdkzzzzDL3/5S66+cCBBzVoS0THNsbYeryHbWlRUxLhx4zj77LPp06cPiYmJ3HrrrXVuS+o7tDgTIpICfHSSPoKPgEdVdbF7+nPgflVNr2XdW3CdPqJdu3b9d+2yPeHvcw4z6v++4K7zO3PPRfaIXnNmOkydS22/BALseHSsx79fVenwu3kAbJ0+htBgz+2jOt1Wp4jIClVNq22Zk0cEWUDN0ajbuuedQFWfU9U0VU1LSLA7DQE6JURzUY+WvLRk5zHXXRvzY7SJjTyt+Q3tb5+6HjDXrVVTjxYBcL6t3sjJQvAhcL24DAbyVTXbwTw+5/bzOlNQWsHry+wIyZyZ+y4+i8jQYzskI0ODue/ixjnanLFwGwCzfjXE49/ldFu9kScvH30TGAnEi0gm8DAQCqCq/wLm4bp0dBuuy0dv9FQWf9UnOZbhneN5fvEObhiaQsRx/7iNOVUT+rq65x5bsIU9h0poExvJfRefVT3fk15duhOAuCZhNIv0/APmnGyrt/JoH4EnpKWlaXr6Cd0IAWvJ97lcM/Mb/jAulRvsue3GB6VMnQvAst+NolWz+h8pYX4cb+0jMA1gSMcWDOoQx98XbrVBa4zP+dcX3wMQFRZsRcBBVgh8nIhw/5hu5B4u44XFO5yOY8wpU1UedT9l9Ksp5zmcJrBZIfAD/do15+LUljz7xffkHbb7Coxv+P376wHo0TqGFtHh9axtPMkKgZ+47+JulJRX8nf31RfGeLPS8kre/HY3AO/dPtThNMYKgZ/onBjN1QPb8eqyXWzKLnA6jjF1GvV/XwBwRf+2drWbF7BC4Efuu/gsYiJCeOiD9fU+jMoYp2zYk0/WoRIAHrvi1EYgM55lhcCPxEaFcf/obizfeZDZq20UM+Odxs5YDMC/Jw2wx6h7CSsEfuZnacn0To5l+tzNNoqZ8TpPfba1+v153RIdTGJqskLgZ4KChOkTenKwuIxHPtrodBxjquUdPsLfPnM9U2jl/1zocBpTkxUCP9QzqRm3j+zEuyszWbh5n9NxjAGg/x8/A+CeC7sS1yTM4TSmJisEfmry+Z05q2VTpr67zk4RGcf9/fMfTgndNaqLg0lMbawQ+KnwkGAev7I3eUVlPPzheqfjmAC2N7+U/3M/Zjr9wQscTmNqY4XAj/Vq24w7z+/M7NV7eGdFZv0fMKaBqSqD//w5APeP7ka83UHslawQ+Lk7z+/CoA5x/M/s9Wzbf9jpOCbA/OzZpQCEhQRx28hODqcxJ2OFwM8FBwlPXdWXyLBgJr+xktIa49Ia40nz12ezfOdBADb84WKH05i6WCEIAK2aRfB/P+vN5r2FPPzBBrvr2HjcvoJSbn1tJQAf3Tnc48NPmjNjfzsB4ryzEpl8XmdmpWfwylIb2tJ4TkVlFYP+5OoXuPP8zvRMauZwIlMfKwQB5J4Lu3JB90Qe+WgjS7blOh3H+KnOD3wMQIf4Jtx7UeCOA+xLrBAEkKAg4W8T+9Axvgm3v7GS3XnFTkcyfuaO11dWv1947wgHk5jTYYUgwDSNCGXm9WmowqSXvuVAUZnTkYyf+Oei75m7LhuAddMusgfK+RArBAEoJb4JM69PI/NgCTe9tJziMhvr2JyZeeuy+ct817CTn90zgqYRoQ4nMqfDo4VAREaLyBYR2SYiU2tZPklEckRktfv1S0/mMT8Y2CGOGVf1ZW3mISa/sYqKyiqnIxkftXL3QW53nxJ64+ZBdE6MdjiROV0eKwQiEgz8AxgD9ACuFpEetaw6S1X7uF/PeyqPOdHonq343wk9Wbh5P/e/u46qKrus1JyerfsKueyZJYBrkJmhneIdTmR+jBAPbnsgsE1VtwOIyH+A8YA9G9mLXDuoPXmHy3ji0+8ICRL+fFkvgoLs3K6p3/c5h7nwb18C8OtRXbgyLdnhRObH8mQhSAIyakxnAoNqWe9yETkX+A64W1Uzjl9BRG4BbgFo166dB6IGtrtGdaGisooZC7cRFATTJ1gxMHXbkVtUPe7wrSM6cfeFXR1OZM6E053Fc4AUVT0b+BR4ubaVVPU5VU1T1bSEhIRGDRgo7r6wK5PP68yb32bw4Afr7TSROakduUWc9/giAG4+pwNTx3RzNpA5Y548IsgCah4rtnXPq6aqeTUmnwf+6sE8pg4iwr0XdaVKlWcWfU/xkQoeu7K3PRrAHGPV7oNc6u4TmDQ0hQfG1tbtZ3yNJwvBcqCLiHTAVQCuAq6puYKItFbVbPfkOGCTB/OYeogI9118Fk3CQ3hswRYOlZTzzLX9iArz5D8T4ys+27iPX76SDrj6BOx0kP/w2O6eqlYAk4EFuH7g31LVDSLyiIiMc692l4hsEJE1wF3AJE/lMadGRLjjvM48elkvvvwuh2uf/4ZDxXbTWaB7/Ztd1UXgL5f3siLgZ8TXnkSZlpam6enpTscICPPXZ3PXm6tJah7J8zek0SnBrg8PRHfPWs37q1xndV+clMb53Vo6nMj8GCKyQlXTaltmJ4DNSY3u2ZrXbx5Efkk5l/7ja77amuN0JNOIqqqUHg/Nry4Cc+8abkXAT1khMHUakBLHB3cMo3WzSCb9ezmvLN1p4xkEgPzicjr+fh7FZa6BjNY8fBGpbexx0v7KCoGpV3JcFO/ePpTzzkrgoQ82cO9ba+z5RH7si+9y6P3IJwBEhgaz/U8/oVmkPTvIn1khMKckOjyEZ69L49ejuvD+6izGP/01W/cVOh3LNLA731zFDS9+C8C1g9qx6X9H282FAcAKgTllwUHC3Rd25dWbBnGwuIxxT3/NOysy7VSRHygoLSdl6lzmrNkDwFu/GsL0S3s5nMo0FisE5rQN7xLPvLvO4ey2zfjt22u4/fWV5B0+4nQs8yP959vdnD3tk+rpjY9czMAOcQ4mMo3N7hQyP0piTARv3DyY577czt8+/Y7lO7/kT5f24qLUVk5HM6eotLyS1IcXUOl+nMiNw1J4+JJUh1MZJ9gRgfnRgoOE20Z24sM7h5HYNIJbXl3BPbNW29GBD3grPYNu/zO/ugh8cd9IKwIBzI4IzBnr1iqG2XcM4+mFW3lm0fcs3LKf+0d3Y2JasnU0epm9+aUM/vPn1dOX9G7D36/u62Ai4w3szmLToLbuK+SB2ev5dscB+rWL5Y8TetGjTYzTsQKeqjL5jVXVYwoDfDXlPJLjohxMZRpTXXcWWyEwDU5VeW9lFtPnbeJQcRlX9k/m7gu70qpZhNPRAtK/v97BH+b8MB7UH8alcsPQFOcCGUfUVQjs1JBpcCLC5f3bMqp7In9fuI1Xlu7kgzVZ3HxOR341ohPR4fbPrjEs3prLz1/4pnq6V1Iz3rltCOEhwQ6mMt7IjgiMx2UcKOavC7YwZ80eWjQJ4+ZzO/Lzwe2tIHjIku9zuWbmN8fM+/aBUSQ2tSOyQGanhoxXWJNxiMc/2cJXW3OJjQrlF8M6cMOwFGIi7PEFDWHRlv1M+vfyY+Z9dOdweibZM4KMFQLjZVZnHOLvn2/l8837aRoRwjUD23HdkPa0bW4dl6dLVXnuy+38+ePNx8yffccw+iTHOhPKeCUrBMYrrc/K55+Lvmf+hr2oKhf2aMmkoR0Y3DEOEbvstC6Hj1Rw22sr+Gpr7jHz5911jl2lZWplhcB4tT2HSnht2S7e/HY3B4vL6ZIYzRX923Jp3yQSY+y8dk3vrMjkt2+vOWZe99YxvPqLgcRHhzuUyvgCKwTGJ5SWV/Lh6j3MSs9gxa6DBAmc2zWBy/u5rkAK1LGT12Ye4rbXVpJ1qOSY+bec25Gpo7vZTXvmlFghMD5ne85h3l2ZyXsrs8jOLyU8JIgRXRMY3bMVo7q1pFmUf3cwL9mWy69nrSan8NjHdXRKaMLzNwygQ3wTh5IZX2WFwPisyirlmx15LFi/lwUb9rG3oJSQIGFAShzDu8RzTpd4Uts0I9jH94oPFpXxj/9u4/nFO05YFhYSxIyr+jC6Z2sHkhl/YYXA+IWqKmVN5iHmb9jLF1ty2LzXNTBObFQowzrF0799c/q0iyW1TYzX3zS1O6+Yl5bs5MWvT/zhB2gZE84TP+vDsM7xjZzM+CvHCoGIjAaeAoKB51X10eOWhwOvAP2BPGCiqu6sa5tWCMxR+wtLWbItj8XbclmyLZc9+aUAhAUH0b1NDL3bNqNLy6Z0TYyma8umNG8S1ugZq6qUFbsPMndtNh+t3UPu4bKTrnvTsA5MPr8zcQ7kNP7PkUdMiEgw8A/gQiATWC4iH6rqxhqr/QI4qKqdReQq4C/ARE9lMv4lsWkEE/omMaFvEgD7CkpZtfsQqzIOsmr3Id5bmcXhIz+MrRwfHU6H+CjaxEbSJjaSpNhI2sRGENcknNjIUGKjQmkaEXrKp5lKyirZmVfErrwiduYVs2VvIct3HiDzYEm9n40KC+amYR24bkh7WtqVUcZhnrwMYyCwTVW3A4jIf4DxQM1CMB6Y5n7/DvC0iIj62vkq4xVaxkQwumcrRvd0DY6jquzJL2XrvkK27jvMd/sK2X2gmJXuPfSKqhP/mYlAdFgIYSFBhAYHsbeg9IxzdW8dw0/Pbs3YXq1JsU5e44U8WQiSgIwa05nAoJOto6oVIpIPtACOuUtGRG4BbgFo166dp/IaPyMiJLn3/EeelXjMssoqJafwCFmHSjhUXMah4nIOlZSTX1xGQWkF5ZVVVFQqO/KK+HbHgVq3HxospLRoQvsWTUhpEUWXltGkpcTRMb6J3RBnfIpPXJitqs8Bz4Grj8DhOMYPBAcJrZpF2KOxjcGzQ1VmAck1ptu659W6joiEAM1wdRobY4xpJJ4sBMuBLiLSQUTCgKuAD49b50PgBvf7K4CF1j9gjDGNy2Onhtzn/CcDC3BdPvqiqm4QkUeAdFX9EHgBeFVEtgEHcBULY4wxjcijfQSqOg+Yd9y8h2q8LwWu9GQGY4wxdfPkqSFjjDE+wAqBMcYEOCsExhgT4KwQGGNMgPO5p4+KSA6wy+kcJxHPcXdF+7FAaisEVnutrf6pvaom1LbA5wqBNxOR9JM93c/fBFJbIbDaa20NPHZqyBhjApwVAmOMCXBWCBrWc04HaESB1FYIrPZaWwOM9REYY0yAsyMCY4wJcFYIjDEmwFkhaGAi8piIbBaRtSLyvojEOp3JU0TkShHZICJVIuKXl+CJyGgR2SIi20RkqtN5PElEXhSR/SKy3uksniYiySLyXxHZ6P43/GunMznJCkHD+xToqapnA98Bv3M4jyetBy4DvnQ6iCeISDDwD2AM0AO4WkR6OJvKo14CRjsdopFUAPeqag9gMHCHn//d1skKQQNT1U9UtcI9uQzXyGx+SVU3qeoWp3N40EBgm6puV9Uy4D/AeIczeYyqfolrXBC/p6rZqrrS/b4Q2IRrDPWAZIXAs24CPnY6hPnRkoCMGtOZBPCPhb8SkRSgL/CNw1Ec4xOD13sbEfkMaFXLogdU9QP3Og/gOvx8vTGzNbRTaasxvkpEooF3gd+oaoHTeZxiheBHUNUL6louIpOAnwKjfH0M5vra6ueygOQa023d84wfEJFQXEXgdVV9z+k8TrJTQw1MREYDU4BxqlrsdB5zRpYDXUSkg4iE4RpT+0OHM5kGICKCa8z0Tar6hNN5nGaFoOE9DTQFPhWR1SLyL6cDeYqIXCoimcAQYK6ILHA6U0Nyd/pPBhbg6kx8S1U3OJvKc0TkTWApcJaIZIrIL5zO5EHDgOuA893/T1eLyE+cDuUUe8SEMcYEODsiMMaYAGeFwBhjApwVAmOMCXBWCIwxJsBZITDGmABnhcAYYwKcFQJjjAlwVgiMOUMiMsA9/kSEiDRxP9++p9O5jDlVdkOZMQ1ARP4IRACRQKaq/tnhSMacMisExjQA97OIlgOlwFBVrXQ4kjGnzE4NGdMwWgDRuJ4zFeFwFmNOix0RGNMARORDXCOYdQBaq+pkhyMZc8psPAJjzpCIXA+Uq+ob7nGOl4jI+aq60OlsxpwKOyIwxpgAZ30ExhgT4KwQGGNMgLNCYIwxAc4KgTHGBDgrBMYYE+CsEBhjTICzQmCMMQHu/wGAM5bvW0+i9wAAAABJRU5ErkJggg==", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Plot the state trajectory\n", + "pos = np.array([state.value[1:] for state in state_data])\n", + "plt.plot(pos[:, 0], pos[:, 1])\n", + "plt.scatter(landmarks[:, 0], landmarks[:, 1])\n", + "# add labels\n", + "for i, landmark in enumerate(landmarks):\n", + " plt.annotate(f\"Landmark {i}\", landmark)\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "plt.title(\"Simulated Trajectory\")\n", + "plt.axis(\"equal\")\n", + "\n", + "\n", + "# Plot the input data\n", + "plt.figure()\n", + "u_array = np.array([u.value for u in input_data])\n", + "u_stamps = np.array([u.stamp for u in input_data])\n", + "plt.plot(u_stamps, u_array[:, 0], label=\"omega\")\n", + "plt.plot(u_stamps, u_array[:, 1], label=\"v\")\n", + "plt.xlabel(\"Time (s)\")\n", + "plt.ylabel(\"Input\")\n", + "plt.title(\"Input Data\")\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run a filter!\n", + "\n", + "Finally, lets run an extended Kalman filter on this data to get a state estimate that uses only the noisy measurements. In the below filter, we instantiate the [ExtendedKalmanFilter](../_autosummary/navlie.filters.ExtendedKalmanFilter.rst) to use on our data, and looping over the input measurements while also calling the correction step whenever a measurement occurs." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "\n", + "# You can try other filters too!\n", + "# kalman_filter = nav.UnscentedKalmanFilter(process_model)\n", + "# kalman_filter = nav.IteratedKalmanFIlter(process_model)\n", + "\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filters in navlie are all designed to be *stateless*: this means that the actual state estimate is stored externally to the filter objects, in this case in a container called [StateWithCovariance](../_autosummary/navlie.types.StateWithCovariance.rst). Although this adds a slight burden on the user, it has the advantage of being more transparent, and also providing the ability to combine different filters in the same loop! For example, you could use an EKF for the prediction, but a UKF for the correction, or even to use different filters for different measurement models!\n", + "\n", + "\n", + "Once estimates have been obtained, we will often be interested in evaluating the performance. The [GaussianResultList](../_autosummary/navlie.utils.GaussianResultList.rst) object is a useful container for evaluating the quality of the state estimates when ground truth data is available. It calculates useful metrics such as raw error, Mahalanobis distance, and normalized estimation error squared (NEES). " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "# results.nees \n", + "# results.three_sigma\n", + "# results.error\n", + "# results.md # mahalanobis distance\n", + "# # and more...\n", + "\n", + "# Some plotting functions that work directly with GaussianResultList\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a final note, `GaussianResultList` will invoke the `State.minus` method of the state objects to calculate the error. As we will see next, this allows us to implement a custom measure of error, when it might not make sense to directly subtract two of our state objects." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/html/_static/basic.css b/_build/html/_static/basic.css new file mode 100644 index 00000000..b97662dd --- /dev/null +++ b/_build/html/_static/basic.css @@ -0,0 +1,921 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; 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i.fas{vertical-align:middle;font-style:normal;font-size:1.5rem;line-height:1.25}#navbar-icon-links i.fa-github-square:before{color:#333}#navbar-icon-links i.fa-twitter-square:before{color:#55acee}#navbar-icon-links i.fa-gitlab:before{color:#548}#navbar-icon-links i.fa-bitbucket:before{color:#0052cc}.tocsection{border-left:1px solid #eee;padding:.3rem 1.5rem}.tocsection i{padding-right:.5rem}.editthispage{padding-top:2rem}.editthispage a{color:var(--pst-color-sidebar-link-active)}.xr-wrap[hidden]{display:block!important}.toctree-checkbox{position:absolute;display:none}.toctree-checkbox~ul{display:none}.toctree-checkbox~label i{transform:rotate(0deg)}.toctree-checkbox:checked~ul{display:block}.toctree-checkbox:checked~label i{transform:rotate(180deg)}.bd-sidebar li{position:relative}.bd-sidebar label{position:absolute;top:0;right:0;height:30px;width:30px;cursor:pointer;display:flex;justify-content:center;align-items:center}.bd-sidebar label:hover{background:rgba(var(--pst-color-sidebar-expander-background-hover),1)}.bd-sidebar label i{display:inline-block;font-size:.75rem;text-align:center}.bd-sidebar label i:hover{color:rgba(var(--pst-color-sidebar-link-hover),1)}.bd-sidebar li.has-children>.reference{padding-right:30px}div.doctest>div.highlight span.gp,span.linenos,table.highlighttable td.linenos{user-select:none;-webkit-user-select:text;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none}.docutils.container{padding-left:unset;padding-right:unset} \ No newline at end of file diff --git a/_build/html/_static/css/theme.css b/_build/html/_static/css/theme.css new file mode 100644 index 00000000..2e03fe37 --- /dev/null +++ b/_build/html/_static/css/theme.css @@ -0,0 +1,120 @@ +/* Provided by the Sphinx base theme template at build time */ +@import "../basic.css"; + +:root { + /***************************************************************************** + * Theme config + **/ + --pst-header-height: 60px; + + /***************************************************************************** + * Font size + **/ + --pst-font-size-base: 15px; /* base font size - applied at body / html level */ + + /* heading font sizes */ + --pst-font-size-h1: 36px; + --pst-font-size-h2: 32px; + --pst-font-size-h3: 26px; + --pst-font-size-h4: 21px; + --pst-font-size-h5: 18px; + --pst-font-size-h6: 16px; + + /* smaller then heading font sizes*/ + --pst-font-size-milli: 12px; + + --pst-sidebar-font-size: .9em; + --pst-sidebar-caption-font-size: .9em; + + /***************************************************************************** + * Font family + **/ + /* These are adapted from https://systemfontstack.com/ */ + --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue", + Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol; + --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco, + Liberation Mono, Lucida Console, monospace; + + --pst-font-family-base: var(--pst-font-family-base-system); + --pst-font-family-heading: var(--pst-font-family-base); + --pst-font-family-monospace: var(--pst-font-family-monospace-system); + + /***************************************************************************** + * Color + * + * Colors are defined in rgb string way, "red, green, blue" + **/ + --pst-color-primary: 19, 6, 84; + --pst-color-success: 40, 167, 69; + --pst-color-info: 0, 123, 255; /*23, 162, 184;*/ + --pst-color-warning: 255, 193, 7; + --pst-color-danger: 220, 53, 69; + --pst-color-text-base: 51, 51, 51; + + --pst-color-h1: var(--pst-color-primary); + --pst-color-h2: var(--pst-color-primary); + --pst-color-h3: var(--pst-color-text-base); + --pst-color-h4: var(--pst-color-text-base); + --pst-color-h5: var(--pst-color-text-base); + --pst-color-h6: var(--pst-color-text-base); + --pst-color-paragraph: var(--pst-color-text-base); + --pst-color-link: 0, 91, 129; + --pst-color-link-hover: 227, 46, 0; + --pst-color-headerlink: 198, 15, 15; + --pst-color-headerlink-hover: 255, 255, 255; + --pst-color-preformatted-text: 34, 34, 34; + --pst-color-preformatted-background: 250, 250, 250; + --pst-color-inline-code: 232, 62, 140; + + --pst-color-active-navigation: 19, 6, 84; + --pst-color-navbar-link: 77, 77, 77; + --pst-color-navbar-link-hover: var(--pst-color-active-navigation); + --pst-color-navbar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-link: 77, 77, 77; + --pst-color-sidebar-link-hover: var(--pst-color-active-navigation); + --pst-color-sidebar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-expander-background-hover: 244, 244, 244; + --pst-color-sidebar-caption: 77, 77, 77; + --pst-color-toc-link: 119, 117, 122; + --pst-color-toc-link-hover: var(--pst-color-active-navigation); + --pst-color-toc-link-active: var(--pst-color-active-navigation); + + /***************************************************************************** + * Icon + **/ + + /* font awesome icons*/ + --pst-icon-check-circle: '\f058'; + --pst-icon-info-circle: '\f05a'; + --pst-icon-exclamation-triangle: '\f071'; + --pst-icon-exclamation-circle: '\f06a'; + --pst-icon-times-circle: '\f057'; + --pst-icon-lightbulb: '\f0eb'; + + /***************************************************************************** + * Admonitions + **/ + + --pst-color-admonition-default: var(--pst-color-info); + --pst-color-admonition-note: var(--pst-color-info); + --pst-color-admonition-attention: var(--pst-color-warning); + --pst-color-admonition-caution: var(--pst-color-warning); + --pst-color-admonition-warning: var(--pst-color-warning); + --pst-color-admonition-danger: var(--pst-color-danger); + --pst-color-admonition-error: var(--pst-color-danger); + --pst-color-admonition-hint: var(--pst-color-success); + --pst-color-admonition-tip: var(--pst-color-success); + --pst-color-admonition-important: var(--pst-color-success); + + --pst-icon-admonition-default: var(--pst-icon-info-circle); + --pst-icon-admonition-note: var(--pst-icon-info-circle); + --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle); + --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-error: var(--pst-icon-times-circle); + --pst-icon-admonition-hint: var(--pst-icon-lightbulb); + --pst-icon-admonition-tip: var(--pst-icon-lightbulb); + --pst-icon-admonition-important: var(--pst-icon-exclamation-circle); + +} diff --git a/_build/html/_static/doctools.js b/_build/html/_static/doctools.js new file mode 100644 index 00000000..d06a71d7 --- /dev/null +++ b/_build/html/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); + }, + + /** + * Initialise the domain index toggle buttons + */ + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); + } + }; + + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); + }, + + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); + } + break; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); + } + break; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } + }); + }, +}; + +// quick alias for translations +const _ = Documentation.gettext; + +_ready(Documentation.init); diff --git a/_build/html/_static/documentation_options.js b/_build/html/_static/documentation_options.js new file mode 100644 index 00000000..ba054525 --- /dev/null +++ b/_build/html/_static/documentation_options.js @@ -0,0 +1,14 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '0.1.0', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: true, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, +}; \ No newline at end of file diff --git a/_build/html/_static/file.png b/_build/html/_static/file.png new file mode 100644 index 00000000..a858a410 Binary files /dev/null and b/_build/html/_static/file.png differ diff --git a/_build/html/_static/js/index.be7d3bbb2ef33a8344ce.js b/_build/html/_static/js/index.be7d3bbb2ef33a8344ce.js new file mode 100644 index 00000000..b71f7fcc --- /dev/null +++ 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m=c.getTransitionDurationFromElement(a);e(a).one(c.TRANSITION_END,(function(){e(u).removeClass(i+" "+o).addClass("active"),e(a).removeClass("active "+o+" "+i),s._isSliding=!1,setTimeout((function(){return e(s._element).trigger(d)}),0)})).emulateTransitionEnd(m)}else e(a).removeClass("active"),e(u).addClass("active"),this._isSliding=!1,e(this._element).trigger(d);f&&this.cycle()}},t._jQueryInterface=function(n){return this.each((function(){var i=e(this).data("bs.carousel"),o=a(a({},_),e(this).data());"object"==typeof n&&(o=a(a({},o),n));var r="string"==typeof n?n:o.slide;if(i||(i=new t(this,o),e(this).data("bs.carousel",i)),"number"==typeof n)i.to(n);else if("string"==typeof r){if(void 0===i[r])throw new TypeError('No method named "'+r+'"');i[r]()}else o.interval&&o.ride&&(i.pause(),i.cycle())}))},t._dataApiClickHandler=function(n){var i=c.getSelectorFromElement(this);if(i){var o=e(i)[0];if(o&&e(o).hasClass("carousel")){var 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n,i,o=this;if(!(this._isTransitioning||e(this._element).hasClass("show")||(this._parent&&0===(n=[].slice.call(this._parent.querySelectorAll(".show, .collapsing")).filter((function(t){return"string"==typeof o._config.parent?t.getAttribute("data-parent")===o._config.parent:t.classList.contains("collapse")}))).length&&(n=null),n&&(i=e(n).not(this._selector).data("bs.collapse"))&&i._isTransitioning))){var r=e.Event("show.bs.collapse");if(e(this._element).trigger(r),!r.isDefaultPrevented()){n&&(t._jQueryInterface.call(e(n).not(this._selector),"hide"),i||e(n).data("bs.collapse",null));var s=this._getDimension();e(this._element).removeClass("collapse").addClass("collapsing"),this._element.style[s]=0,this._triggerArray.length&&e(this._triggerArray).removeClass("collapsed").attr("aria-expanded",!0),this.setTransitioning(!0);var a="scroll"+(s[0].toUpperCase()+s.slice(1)),l=c.getTransitionDurationFromElement(this._element);e(this._element).one(c.TRANSITION_END,(function(){e(o._element).removeClass("collapsing").addClass("collapse show"),o._element.style[s]="",o.setTransitioning(!1),e(o._element).trigger("shown.bs.collapse")})).emulateTransitionEnd(l),this._element.style[s]=this._element[a]+"px"}}},n.hide=function(){var t=this;if(!this._isTransitioning&&e(this._element).hasClass("show")){var n=e.Event("hide.bs.collapse");if(e(this._element).trigger(n),!n.isDefaultPrevented()){var i=this._getDimension();this._element.style[i]=this._element.getBoundingClientRect()[i]+"px",c.reflow(this._element),e(this._element).addClass("collapsing").removeClass("collapse show");var o=this._triggerArray.length;if(o>0)for(var r=0;r0},i._getOffset=function(){var t=this,e={};return"function"==typeof this._config.offset?e.fn=function(e){return e.offsets=a(a({},e.offsets),t._config.offset(e.offsets,t._element)||{}),e}:e.offset=this._config.offset,e},i._getPopperConfig=function(){var t={placement:this._getPlacement(),modifiers:{offset:this._getOffset(),flip:{enabled:this._config.flip},preventOverflow:{boundariesElement:this._config.boundary}}};return"static"===this._config.display&&(t.modifiers.applyStyle={enabled:!1}),a(a({},t),this._config.popperConfig)},t._jQueryInterface=function(n){return this.each((function(){var i=e(this).data("bs.dropdown");if(i||(i=new t(this,"object"==typeof n?n:null),e(this).data("bs.dropdown",i)),"string"==typeof n){if(void 0===i[n])throw new TypeError('No method named "'+n+'"');i[n]()}}))},t._clearMenus=function(n){if(!n||3!==n.which&&("keyup"!==n.type||9===n.which))for(var 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version is copied as a separate JS file, is available */ + +/** + * Porter Stemmer + */ +var Stemmer = function() { + + var step2list = { + ational: 'ate', + tional: 'tion', + enci: 'ence', + anci: 'ance', + izer: 'ize', + bli: 'ble', + alli: 'al', + entli: 'ent', + eli: 'e', + ousli: 'ous', + ization: 'ize', + ation: 'ate', + ator: 'ate', + alism: 'al', + iveness: 'ive', + fulness: 'ful', + ousness: 'ous', + aliti: 'al', + iviti: 'ive', + biliti: 'ble', + logi: 'log' + }; + + var step3list = { + icate: 'ic', + ative: '', + alize: 'al', + iciti: 'ic', + ical: 'ic', + ful: '', + ness: '' + }; + + var c = "[^aeiou]"; // consonant + var v = "[aeiouy]"; // vowel + var C = c + "[^aeiouy]*"; // consonant sequence + var V = v + "[aeiou]*"; // vowel sequence + + var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0 + var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1 + var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1 + var s_v = "^(" + C + ")?" + v; // vowel in stem + + this.stemWord = function (w) { + var stem; + var suffix; + var firstch; + var origword = w; + + if (w.length < 3) + return w; + + var re; + var re2; + var re3; + var re4; + + firstch = w.substr(0,1); + if (firstch == "y") + w = firstch.toUpperCase() + w.substr(1); + + // Step 1a + re = /^(.+?)(ss|i)es$/; + re2 = /^(.+?)([^s])s$/; + + if (re.test(w)) + w = w.replace(re,"$1$2"); + else if (re2.test(w)) + w = w.replace(re2,"$1$2"); + + // Step 1b + re = /^(.+?)eed$/; + re2 = /^(.+?)(ed|ing)$/; + if (re.test(w)) { + var fp = re.exec(w); + re = new RegExp(mgr0); + if (re.test(fp[1])) { + re = /.$/; + w = w.replace(re,""); + } + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1]; + re2 = new RegExp(s_v); + if (re2.test(stem)) { + w = stem; + re2 = /(at|bl|iz)$/; + re3 = new RegExp("([^aeiouylsz])\\1$"); + re4 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + if (re.test(stem)) + w = stem; + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1] + fp[2]; + re2 = new RegExp(mgr1); + if (re2.test(stem)) + w = stem; + } + + // Step 5 + re = /^(.+?)e$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + re2 = new RegExp(meq1); + re3 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) + w = stem; + } + re = /ll$/; + re2 = new RegExp(mgr1); + if (re.test(w) && re2.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + + // and turn initial Y back to y + if (firstch == "y") + w = firstch.toLowerCase() + w.substr(1); + return w; + } +} + diff --git a/_build/html/_static/minus.png b/_build/html/_static/minus.png new file mode 100644 index 00000000..d96755fd Binary files /dev/null and b/_build/html/_static/minus.png differ diff --git a/_build/html/_static/nbsphinx-broken-thumbnail.svg b/_build/html/_static/nbsphinx-broken-thumbnail.svg new file mode 100644 index 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"undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = docUrlRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = docUrlRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms) + ); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + `Search finished, found ${resultCount} page(s) matching the search query.` + ); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() }); + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent !== undefined) return docContent.textContent; + console.warn( + "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + /** + * execute search (requires search index to be loaded) + */ + query: (query) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + // array of [docname, title, anchor, descr, score, filename] + let results = []; + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + results.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id] of foundEntries) { + let score = Math.round(100 * queryLower.length / entry.length) + results.push([ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // lookup as object + objectTerms.forEach((term) => + results.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + results.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item))); + + // now sort the results by score (in opposite order of appearance, since the + // display function below uses pop() to retrieve items) and then + // alphabetically + results.sort((a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; + }); + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + results = results.reverse(); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord) && !terms[word]) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord) && !titleTerms[word]) + arr.push({ files: titleTerms[word], score: Scorer.partialTitle }); + }); + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1) + fileMap.get(file).push(word); + else fileMap.set(file, [word]); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords) => { + const text = Search.htmlToText(htmlText); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/_build/html/_static/sphinx_highlight.js b/_build/html/_static/sphinx_highlight.js new file mode 100644 index 00000000..aae669d7 --- /dev/null +++ b/_build/html/_static/sphinx_highlight.js @@ -0,0 +1,144 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + parent.insertBefore( + span, + parent.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(SphinxHighlight.highlightSearchWords); +_ready(SphinxHighlight.initEscapeListener); diff --git a/_build/html/_static/vendor/fontawesome/5.13.0/LICENSE.txt b/_build/html/_static/vendor/fontawesome/5.13.0/LICENSE.txt new file mode 100644 index 00000000..f31bef92 --- /dev/null +++ b/_build/html/_static/vendor/fontawesome/5.13.0/LICENSE.txt @@ -0,0 +1,34 @@ +Font Awesome Free License +------------------------- + +Font Awesome Free is free, open source, and GPL friendly. You can use it for +commercial projects, open source projects, or really almost whatever you want. +Full Font Awesome Free license: https://fontawesome.com/license/free. + +# Icons: CC BY 4.0 License (https://creativecommons.org/licenses/by/4.0/) +In the Font Awesome Free download, the CC BY 4.0 license applies to all icons +packaged as SVG and JS file types. + +# Fonts: SIL OFL 1.1 License (https://scripts.sil.org/OFL) +In the Font Awesome Free download, the SIL OFL license applies to all icons +packaged as web and desktop font files. + +# Code: MIT License (https://opensource.org/licenses/MIT) +In the Font Awesome Free download, the MIT license applies to all non-font and +non-icon files. + +# Attribution +Attribution is required by MIT, SIL OFL, and CC BY licenses. Downloaded Font +Awesome Free files already contain embedded comments with sufficient +attribution, so you shouldn't need to do anything additional when using these +files normally. + +We've kept attribution comments terse, so we ask that you do not actively work +to remove them from files, especially code. They're a great way for folks to +learn about Font Awesome. + +# Brand Icons +All brand icons are trademarks of their respective owners. The use of these +trademarks does not indicate endorsement of the trademark holder by Font +Awesome, nor vice versa. **Please do not use brand logos for any purpose except +to represent the company, product, or service to which they refer.** diff --git a/_build/html/_static/vendor/fontawesome/5.13.0/css/all.min.css b/_build/html/_static/vendor/fontawesome/5.13.0/css/all.min.css new file mode 100644 index 00000000..3d28ab20 --- /dev/null +++ b/_build/html/_static/vendor/fontawesome/5.13.0/css/all.min.css @@ -0,0 +1,5 @@ +/*! + * Font Awesome Free 5.13.0 by @fontawesome - https://fontawesome.com + * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) + */ 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00000000..748f33e6 --- /dev/null +++ b/_build/html/_static/webpack-macros.html @@ -0,0 +1,25 @@ + +{% macro head_pre_icons() %} + + + +{% endmacro %} + +{% macro head_pre_fonts() %} +{% endmacro %} + +{% macro head_pre_bootstrap() %} + + +{% endmacro %} + +{% macro head_js_preload() %} + +{% endmacro %} + +{% macro body_post() %} + +{% endmacro %} \ No newline at end of file diff --git a/_build/html/api.html b/_build/html/api.html new file mode 100644 index 00000000..163e11ac --- /dev/null +++ b/_build/html/api.html @@ -0,0 +1,1109 @@ + + + + + + + + API Documentation — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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API Documentation

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Below is a list of all the modules in the navlie package. Click on any of the links to see the documentation for that module. Alternatively, you can use the search box at the top of the page to search for a particular class/function/module.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +

navlie.composite

navlie.datagen

Tools for data generation.

navlie.filters

Module containing many predict-correct style filters.

navlie.imm

Module for the Interacting Multiple Model (IMM) filter.

navlie.types

This module contains the core primitive types used throughout navlie.

navlie.utils

Collection of miscellaneous utility functions and classes.

navlie.batch

A subpackage for batch least-squares estimation.

navlie.lib

The built-in library of common state, process model, and measurement model implementations.

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previous

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Composite States

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next

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navlie.composite

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+ © Copyright 2022.
+

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+Created using Sphinx 7.1.2.
+

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+ + \ No newline at end of file diff --git a/_build/html/genindex.html b/_build/html/genindex.html new file mode 100644 index 00000000..374dec61 --- /dev/null +++ b/_build/html/genindex.html @@ -0,0 +1,2554 @@ + + + + + + + Index — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Index

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+ A + | B + | C + | D + | E + | F + | G + | H + | I + | J + | L + | M + | N + | O + | P + | R + | S + | T + | U + | V + | W + +
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+ © Copyright 2022.
+

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+ +
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+Created using Sphinx 7.1.2.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/_build/html/index.html b/_build/html/index.html new file mode 100644 index 00000000..8998f847 --- /dev/null +++ b/_build/html/index.html @@ -0,0 +1,247 @@ + + + + + + + + Welcome to navlie! — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ On this page +
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+

Welcome to navlie!

+_images/fun_figs.png +

navlie is a state estimation package specifically designed for both traditional and Lie-group-based estimation problems!

+

The core idea behind this project is to use abstraction in such a way that both traditional and Lie-group-based problems fall under the exact same interface. Using this, a single estimator implementation can operate on a variety of state definitions, such as the usual vector space, and any Lie group. We allow the user to define their custom state, process model, and measurement models, after which they will have a variety of algorithms available to them, including:

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  • Extended Kalman Filter

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  • Iterated Extended Kalman Filter

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  • Sigmapoint Kalman Filters (Unscented, Spherical Cubature, Gauss-Hermite)

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  • Interacting Multiple Model Filter

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  • Batch MAP Estimation

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In addition, navlie contains

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  • A large collection of common process and measurement models

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  • Out-of-the-box on-manifold numerical Jacobians using finite differencing

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  • Various utils for plotting, error, and consistency evaluation

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  • Monte Carlo experiment executor with result aggregation

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  • A preintegration module for linear, wheel odometry, and IMU process models

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By implementing a few classes, the user can model a large variety of problems. The following diagram summarizes the abstraction

+_images/system_diagram.png +
+

Installation

+

Clone this repo, change to its directory, and execute

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git clone git@github.com:decargroup/navlie.git
+cd navlie && pip install -e .
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+
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This command should automatically install all dependencies, including our package pymlg for back-end Lie group mathematical operations.

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Examples

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A more in-depth tutorial can be found on this website, but there are also many examples found in the examples/ folder. Simply run these as python3 scripts.

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next

+

Getting Started

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+ © Copyright 2022.
+

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+ + \ No newline at end of file diff --git a/_build/html/searchindex.js b/_build/html/searchindex.js new file mode 100644 index 00000000..8224f2d8 --- /dev/null +++ b/_build/html/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"docnames": ["_autosummary/navlie.batch", "_autosummary/navlie.batch.estimator", "_autosummary/navlie.batch.estimator.BatchEstimator", "_autosummary/navlie.batch.gaussian_mixtures", "_autosummary/navlie.batch.gaussian_mixtures.GaussianMixtureResidual", "_autosummary/navlie.batch.gaussian_mixtures.HessianSumMixtureResidual", "_autosummary/navlie.batch.gaussian_mixtures.MaxMixtureResidual", "_autosummary/navlie.batch.gaussian_mixtures.MaxSumMixtureResidual", "_autosummary/navlie.batch.gaussian_mixtures.SumMixtureResidual", "_autosummary/navlie.batch.losses", "_autosummary/navlie.batch.losses.CauchyLoss", "_autosummary/navlie.batch.losses.L2Loss", "_autosummary/navlie.batch.losses.LossFunction", "_autosummary/navlie.batch.problem", 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"_autosummary/navlie.lib.imu.G_matrix.rst", "_autosummary/navlie.lib.imu.G_matrix_inv.rst", "_autosummary/navlie.lib.imu.IMU.rst", "_autosummary/navlie.lib.imu.IMUKinematics.rst", "_autosummary/navlie.lib.imu.IMUState.rst", "_autosummary/navlie.lib.imu.L_matrix.rst", "_autosummary/navlie.lib.imu.M_matrix.rst", "_autosummary/navlie.lib.imu.N_matrix.rst", "_autosummary/navlie.lib.imu.U_matrix.rst", "_autosummary/navlie.lib.imu.U_matrix_inv.rst", "_autosummary/navlie.lib.imu.U_tilde_matrix.rst", "_autosummary/navlie.lib.imu.adjoint_IE3.rst", "_autosummary/navlie.lib.imu.delta_matrix.rst", "_autosummary/navlie.lib.imu.get_unbiased_imu.rst", "_autosummary/navlie.lib.imu.inverse_IE3.rst", "_autosummary/navlie.lib.models.rst", "_autosummary/navlie.lib.models.AbsolutePosition.rst", "_autosummary/navlie.lib.models.AbsoluteVelocity.rst", "_autosummary/navlie.lib.models.Altitude.rst", "_autosummary/navlie.lib.models.BodyFrameVelocity.rst", "_autosummary/navlie.lib.models.CameraProjection.rst", 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"navlie.lib.models.PointRelativePosition", "navlie.lib.models.PointRelativePositionSLAM", "navlie.lib.models.RangePointToAnchor", "navlie.lib.models.RangePoseToAnchor", "navlie.lib.models.RangePoseToPose", "navlie.lib.models.RangeRelativePose", "navlie.lib.models.RelativeBodyFrameVelocity", "navlie.lib.models.SingleIntegrator", "navlie.lib.preintegration", "navlie.lib.preintegration.AngularVelocityIncrement", "navlie.lib.preintegration.BodyVelocityIncrement", "navlie.lib.preintegration.IMUIncrement", "navlie.lib.preintegration.LinearIncrement", "navlie.lib.preintegration.PreintegratedAngularVelocity", "navlie.lib.preintegration.PreintegratedBodyVelocity", "navlie.lib.preintegration.PreintegratedIMUKinematics", "navlie.lib.preintegration.PreintegratedLinearModel", "navlie.lib.preintegration.PreintegratedWheelOdometry", "navlie.lib.preintegration.RelativeMotionIncrement", "navlie.lib.preintegration.WheelOdometryIncrement", "navlie.lib.states", "navlie.lib.states.MatrixLieGroupState", 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153, 154], "dictionari": [2, 26], "from": [2, 4, 5, 6, 7, 8, 9, 10, 24, 25, 26, 28, 31, 32, 33, 35, 36, 38, 43, 45, 53, 60, 64, 67, 68, 74, 80, 81, 82, 83, 93, 94, 97, 98, 103, 104, 105, 106, 107, 108, 118, 126, 127, 128, 132, 134, 137, 144, 152, 153, 154], "error": [4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 17, 18, 19, 20, 25, 37, 42, 43, 64, 80, 82, 83, 95, 97, 98, 104, 105, 106, 107, 108, 127, 131, 132, 133, 138, 149, 151, 152, 153, 154], "weight": [4, 5, 6, 7, 8, 9, 10, 11, 12, 38, 39, 46, 47], "abc": [4, 12, 20, 123, 124, 126, 127, 128], "gaussian": [4, 5, 6, 7, 8, 24, 25, 45, 46, 47, 48, 50, 64, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 126, 127, 131], "mixtur": [4, 5, 6, 7, 8, 45, 47], "can": [4, 17, 19, 26, 28, 52, 60, 64, 103, 112, 119, 120, 125, 127, 128, 129, 132, 133, 136, 142, 143, 146, 147, 148, 149, 151, 152, 153, 154], "instanc": [4, 39, 45, 49, 109, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 128], 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88, 94, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 124, 126, 127, 129, 142, 147, 151, 152, 153], "differ": [4, 5, 6, 7, 8, 17, 18, 19, 20, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 43, 60, 64, 65, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 121, 125, 126, 127, 128, 132, 133, 134, 136, 151, 152, 153, 154], "how": [4, 43, 52, 132, 150, 151, 152], "overal": [4, 144], "jacobian": [4, 5, 6, 7, 8, 15, 17, 18, 19, 20, 24, 25, 26, 32, 34, 64, 65, 66, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 103, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 121, 126, 127, 128, 149, 151], "therefor": 4, "subclass": [4, 112, 151, 153, 154], "overwrit": [4, 102], "mix_error": [4, 5, 6, 7, 8], "mix_jacobian": [4, 5, 6, 7, 8], "which": [4, 5, 6, 7, 8, 9, 16, 20, 23, 24, 26, 29, 31, 32, 33, 34, 35, 36, 42, 45, 86, 93, 100, 101, 102, 103, 109, 110, 126, 127, 131, 132, 133, 137, 141, 144, 149, 151, 152, 153, 154], "abstract": [4, 12, 20, 109, 123, 124, 126, 127, 128, 149, 152, 153, 154], "error_value_list": [4, 5, 6, 7, 8], "sqrt_info_matrix_list": [4, 5, 6, 7, 8], "tupl": [4, 5, 6, 7, 8, 15, 17, 18, 19, 20, 24, 38, 74, 77, 78, 79, 81, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 103, 126, 134, 138, 139, 140, 141, 147], "thi": [4, 5, 6, 7, 8, 11, 12, 13, 15, 19, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 48, 52, 53, 60, 63, 64, 65, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 132, 133, 136, 137, 143, 144, 149, 150, 151, 152, 153, 154], "comput": [4, 5, 6, 7, 8, 15, 16, 17, 20, 28, 31, 32, 33, 35, 36, 39, 42, 50, 53, 66, 86, 87, 103, 131, 133, 136, 137, 147, 152], "factor": [4, 5, 6, 7, 8], "all": 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120, 122, 123, 125, 128, 129, 131, 132, 133, 137, 138, 142, 146, 149, 151, 153, 154], "evaluate_component_residu": [4, 5, 6, 7, 8], "compute_jacobian": [4, 5, 6, 7, 8, 17, 18, 19, 20], "evalu": [4, 5, 6, 7, 8, 10, 17, 18, 19, 20, 23, 24, 25, 26, 29, 32, 34, 53, 64, 65, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 121, 125, 126, 127, 128, 149, 151, 152, 153, 154], "jacobian_fd": [4, 5, 6, 7, 8, 17, 18, 19, 20, 24, 25, 64, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 126, 127, 152], "step_siz": [4, 5, 6, 7, 8, 17, 18, 19, 20, 24, 25, 26, 64, 65, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 121, 126, 127, 128, 136], "06": [4, 5, 6, 7, 8, 17, 18, 19, 20, 24, 25, 64, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 126, 127], "calcul": [4, 5, 6, 7, 8, 17, 18, 19, 20, 24, 25, 26, 31, 32, 33, 34, 35, 36, 43, 47, 64, 65, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 121, 126, 127, 128, 132, 133, 136, 154], "finit": [4, 5, 6, 7, 8, 17, 18, 19, 20, 24, 25, 26, 64, 65, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 121, 126, 127, 128, 136, 149, 152], "point": [4, 5, 6, 7, 8, 17, 18, 19, 20, 31, 32, 33, 34, 35, 36, 38, 43, 53, 82, 87, 93, 127, 132, 146, 154], "respect": [4, 5, 6, 7, 8, 17, 18, 19, 20, 24, 25, 26, 38, 64, 65, 66, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 121, 126, 127, 128, 152], "exampl": [4, 5, 6, 7, 8, 17, 18, 19, 20, 26, 43, 52, 55, 65, 132, 136, 151, 152, 154], "first": [4, 5, 6, 7, 8, 15, 17, 18, 19, 20, 93, 97, 127, 132, 134, 150, 151, 153, 154], "element": [4, 5, 6, 7, 8, 17, 18, 19, 20, 43, 48, 50, 64, 65, 93, 112, 113, 114, 115, 116, 117, 118, 121, 128, 132, 142, 151, 153], "0": [4, 5, 6, 7, 8, 10, 11, 17, 18, 19, 20, 25, 28, 34, 43, 56, 57, 58, 63, 64, 79, 80, 82, 83, 85, 89, 97, 98, 103, 104, 105, 106, 107, 108, 113, 114, 115, 126, 127, 132, 133, 134, 136, 141, 146, 147, 151, 152, 153, 154], "second": [4, 5, 6, 7, 8, 15, 17, 18, 19, 20, 24, 25, 64, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 104, 105, 106, 107, 108, 126, 127, 134], "etc": [4, 5, 6, 7, 8, 17, 18, 19, 20], "no_use_complex_numb": 5, "normalization_const": 5, "gaussianmixtureresidu": [5, 6, 7, 8], "hessian": 5, "sum": [5, 42, 131], "patch": 5, "compat": [5, 49, 77, 78, 79, 85, 89, 95, 136, 154], "nonlinear": [5, 9, 11, 12, 13, 15, 32, 35], "follow": [5, 6, 7, 60, 64, 86, 128, 149, 150, 151, 152, 153, 154], "refer": [5, 6, 7, 8, 45, 64, 80, 151, 152, 153], "misc": 5, "korotkine2024hessian": 5, "titl": [5, 6, 7, 8, 154], "likelihood": 5, "author": [5, 6, 7, 8], "vassili": 5, "korotkin": 5, "mitchel": 5, "cohen": 5, "jame": 5, "richard": 5, "forb": 5, "year": [5, 6, 7, 8], "2024": 5, "eprint": 5, "2404": 5, "05452": 5, "archiveprefix": 5, "arxiv": 5, "primaryclass": 5, "ro": [5, 115, 118], "sum_mixture_residu": 5, "summixtureresidu": 5, "articl": [6, 7, 8], "olson2013infer": 6, "infer": 6, "network": 6, "robust": [6, 9, 10, 11, 15], "robot": [6, 7, 8, 58, 77, 78, 79, 80, 81, 91, 92, 94, 95, 96, 97, 110, 151, 152, 153, 154], "map": [6, 149, 153], "olson": 6, "edwin": 6, "agarw": 6, "pratik": 6, "journal": [6, 7, 8], "intern": [6, 22, 100, 101, 109, 110, 119, 120, 124], "research": 6, "volum": [6, 7, 8], "32": [6, 153], "page": [6, 7, 8, 148, 150], "826": 6, "840": 6, "2013": 6, "publish": 6, "sage": 6, "public": 6, "uk": 6, "london": 6, "england": 6, "damping_const": 7, "10": [7, 8, 45, 57, 58, 132, 137, 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"navlie.composite.CompositeInput.set_stamp_for_all"]], "stamp (navlie.composite.compositeinput attribute)": [[22, "navlie.composite.CompositeInput.stamp"]], "state_id (navlie.composite.compositeinput attribute)": [[22, "navlie.composite.CompositeInput.state_id"]], "to_list() (navlie.composite.compositeinput method)": [[22, "navlie.composite.CompositeInput.to_list"]], "compositemeasurement (class in navlie.composite)": [[23, "navlie.composite.CompositeMeasurement"]], "minus() (navlie.composite.compositemeasurement method)": [[23, "navlie.composite.CompositeMeasurement.minus"]], "model (navlie.composite.compositemeasurement attribute)": [[23, "navlie.composite.CompositeMeasurement.model"]], "stamp (navlie.composite.compositemeasurement attribute)": [[23, "navlie.composite.CompositeMeasurement.stamp"]], "state_id (navlie.composite.compositemeasurement attribute)": [[23, "navlie.composite.CompositeMeasurement.state_id"]], "value (navlie.composite.compositemeasurement attribute)": [[23, "navlie.composite.CompositeMeasurement.value"]], "compositemeasurementmodel (class in navlie.composite)": [[24, "navlie.composite.CompositeMeasurementModel"]], "covariance() (navlie.composite.compositemeasurementmodel method)": [[24, "navlie.composite.CompositeMeasurementModel.covariance"]], "evaluate() (navlie.composite.compositemeasurementmodel method)": [[24, "navlie.composite.CompositeMeasurementModel.evaluate"]], "evaluate_with_jacobian() (navlie.composite.compositemeasurementmodel method)": [[24, "navlie.composite.CompositeMeasurementModel.evaluate_with_jacobian"]], "jacobian() (navlie.composite.compositemeasurementmodel method)": [[24, "navlie.composite.CompositeMeasurementModel.jacobian"]], "jacobian_fd() (navlie.composite.compositemeasurementmodel method)": [[24, "navlie.composite.CompositeMeasurementModel.jacobian_fd"]], "sqrt_information() (navlie.composite.compositemeasurementmodel method)": [[24, "navlie.composite.CompositeMeasurementModel.sqrt_information"]], 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"navlie.composite.CompositeProcessModel.jacobian_fd"]], "sqrt_information() (navlie.composite.compositeprocessmodel method)": [[25, "navlie.composite.CompositeProcessModel.sqrt_information"]], "compositestate (class in navlie.composite)": [[26, "navlie.composite.CompositeState"]], "add_state() (navlie.composite.compositestate method)": [[26, "navlie.composite.CompositeState.add_state"]], "copy() (navlie.composite.compositestate method)": [[26, "navlie.composite.CompositeState.copy"]], "dof (navlie.composite.compositestate attribute)": [[26, "navlie.composite.CompositeState.dof"]], "get_dof_by_id() (navlie.composite.compositestate method)": [[26, "navlie.composite.CompositeState.get_dof_by_id"]], "get_index_by_id() (navlie.composite.compositestate method)": [[26, "navlie.composite.CompositeState.get_index_by_id"]], "get_matrix_block_by_ids() (navlie.composite.compositestate method)": [[26, "navlie.composite.CompositeState.get_matrix_block_by_ids"]], "get_slice_by_id() 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(navlie.lib.camera.pinholecamera property)": [[53, "navlie.lib.camera.PinholeCamera.sigma_normalized_image_coords"]], "to_normalized_coords() (navlie.lib.camera.pinholecamera method)": [[53, "navlie.lib.camera.PinholeCamera.to_normalized_coords"]], "to_pixel_coors() (navlie.lib.camera.pinholecamera method)": [[53, "navlie.lib.camera.PinholeCamera.to_pixel_coors"]], "posematrix (class in navlie.lib.camera)": [[54, "navlie.lib.camera.PoseMatrix"]], "attitude (navlie.lib.camera.posematrix property)": [[54, "navlie.lib.camera.PoseMatrix.attitude"]], "copy() (navlie.lib.camera.posematrix method)": [[54, "navlie.lib.camera.PoseMatrix.copy"]], "position (navlie.lib.camera.posematrix property)": [[54, "navlie.lib.camera.PoseMatrix.position"]], "navlie.lib.datasets": [[55, "module-navlie.lib.datasets"]], "simulatedinertialgpsdataset (class in navlie.lib.datasets)": [[56, "navlie.lib.datasets.SimulatedInertialGPSDataset"]], "get_ground_truth() (navlie.lib.datasets.simulatedinertialgpsdataset 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"navlie.lib.states.VectorState.value"]], "navlie.types": [[122, "module-navlie.types"]], "dataset (class in navlie.types)": [[123, "navlie.types.Dataset"]], "get_ground_truth() (navlie.types.dataset method)": [[123, "navlie.types.Dataset.get_ground_truth"]], "get_input_data() (navlie.types.dataset method)": [[123, "navlie.types.Dataset.get_input_data"]], "get_measurement_data() (navlie.types.dataset method)": [[123, "navlie.types.Dataset.get_measurement_data"]], "input (class in navlie.types)": [[124, "navlie.types.Input"]], "copy() (navlie.types.input method)": [[124, "navlie.types.Input.copy"]], "covariance (navlie.types.input attribute)": [[124, "navlie.types.Input.covariance"]], "dof (navlie.types.input attribute)": [[124, "navlie.types.Input.dof"]], "plus() (navlie.types.input method)": [[124, "navlie.types.Input.plus"]], "stamp (navlie.types.input attribute)": [[124, "navlie.types.Input.stamp"]], "state_id (navlie.types.input attribute)": [[124, "navlie.types.Input.state_id"]], "measurement (class in navlie.types)": [[125, "navlie.types.Measurement"]], "minus() (navlie.types.measurement method)": [[125, "navlie.types.Measurement.minus"]], "model (navlie.types.measurement attribute)": [[125, "navlie.types.Measurement.model"]], "stamp (navlie.types.measurement attribute)": [[125, "navlie.types.Measurement.stamp"]], "state_id (navlie.types.measurement attribute)": [[125, "navlie.types.Measurement.state_id"]], "value (navlie.types.measurement attribute)": [[125, "navlie.types.Measurement.value"]], "measurementmodel (class in navlie.types)": [[126, "navlie.types.MeasurementModel"]], "covariance() (navlie.types.measurementmodel method)": [[126, "navlie.types.MeasurementModel.covariance"]], "evaluate() (navlie.types.measurementmodel method)": [[126, "navlie.types.MeasurementModel.evaluate"]], "evaluate_with_jacobian() (navlie.types.measurementmodel method)": [[126, "navlie.types.MeasurementModel.evaluate_with_jacobian"]], "jacobian() (navlie.types.measurementmodel method)": [[126, "navlie.types.MeasurementModel.jacobian"]], "jacobian_fd() (navlie.types.measurementmodel method)": [[126, "navlie.types.MeasurementModel.jacobian_fd"]], "sqrt_information() (navlie.types.measurementmodel method)": [[126, "navlie.types.MeasurementModel.sqrt_information"]], "processmodel (class in navlie.types)": [[127, "navlie.types.ProcessModel"]], "covariance() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.covariance"]], "evaluate() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.evaluate"]], "evaluate_with_jacobian() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.evaluate_with_jacobian"]], "input_covariance() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.input_covariance"]], "input_jacobian_fd() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.input_jacobian_fd"]], "jacobian() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.jacobian"]], "jacobian_fd() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.jacobian_fd"]], "sqrt_information() (navlie.types.processmodel method)": [[127, "navlie.types.ProcessModel.sqrt_information"]], "state (class in navlie.types)": [[128, "navlie.types.State"]], "copy() (navlie.types.state method)": [[128, "navlie.types.State.copy"]], "dof (navlie.types.state attribute)": [[128, "navlie.types.State.dof"]], "minus() (navlie.types.state method)": [[128, "navlie.types.State.minus"]], "minus_jacobian() (navlie.types.state method)": [[128, "navlie.types.State.minus_jacobian"]], "minus_jacobian_fd() (navlie.types.state method)": [[128, "navlie.types.State.minus_jacobian_fd"]], "plus() (navlie.types.state method)": [[128, "navlie.types.State.plus"]], "plus_jacobian() (navlie.types.state method)": [[128, "navlie.types.State.plus_jacobian"]], "plus_jacobian_fd() (navlie.types.state method)": [[128, "navlie.types.State.plus_jacobian_fd"]], "stamp (navlie.types.state attribute)": [[128, "navlie.types.State.stamp"]], "state_id (navlie.types.state attribute)": [[128, "navlie.types.State.state_id"]], "value (navlie.types.state attribute)": [[128, "navlie.types.State.value"]], "statewithcovariance (class in navlie.types)": [[129, "navlie.types.StateWithCovariance"]], "copy() (navlie.types.statewithcovariance method)": [[129, "navlie.types.StateWithCovariance.copy"]], "covariance (navlie.types.statewithcovariance attribute)": [[129, "navlie.types.StateWithCovariance.covariance"]], "stamp (navlie.types.statewithcovariance property)": [[129, "navlie.types.StateWithCovariance.stamp"]], "state (navlie.types.statewithcovariance attribute)": [[129, "navlie.types.StateWithCovariance.state"]], "symmetrize() (navlie.types.statewithcovariance method)": [[129, "navlie.types.StateWithCovariance.symmetrize"]], "navlie.utils": [[130, "module-navlie.utils"]], "gaussianresult (class in navlie.utils)": [[131, "navlie.utils.GaussianResult"]], "covariance (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.covariance"]], "ees (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.ees"]], "error (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.error"]], "md (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.md"]], "nees (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.nees"]], "rmse (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.rmse"]], "stamp (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.stamp"]], "state (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.state"]], "state_true (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.state_true"]], "three_sigma (navlie.utils.gaussianresult attribute)": [[131, "navlie.utils.GaussianResult.three_sigma"]], "gaussianresultlist (class in navlie.utils)": [[132, "navlie.utils.GaussianResultList"]], "covariance (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.covariance"]], "dof (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.dof"]], "ees (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.ees"]], "error (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.error"]], "from_estimates() (navlie.utils.gaussianresultlist static method)": [[132, "navlie.utils.GaussianResultList.from_estimates"]], "md (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.md"]], "nees (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.nees"]], "nees_lower_bound() (navlie.utils.gaussianresultlist method)": [[132, "navlie.utils.GaussianResultList.nees_lower_bound"]], "nees_upper_bound() (navlie.utils.gaussianresultlist method)": [[132, "navlie.utils.GaussianResultList.nees_upper_bound"]], "rmse (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.rmse"]], "stamp (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.stamp"]], "state (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.state"]], "state_true (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.state_true"]], "three_sigma (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.three_sigma"]], "value (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.value"]], "value_true (navlie.utils.gaussianresultlist attribute)": [[132, "navlie.utils.GaussianResultList.value_true"]], "montecarloresult (class in navlie.utils)": [[133, "navlie.utils.MonteCarloResult"]], "average_ees (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.average_ees"]], "average_nees (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.average_nees"]], "dof (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.dof"]], "expected_nees (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.expected_nees"]], "nees_lower_bound() (navlie.utils.montecarloresult method)": [[133, "navlie.utils.MonteCarloResult.nees_lower_bound"]], "nees_upper_bound() (navlie.utils.montecarloresult method)": [[133, "navlie.utils.MonteCarloResult.nees_upper_bound"]], "num_trials (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.num_trials"]], "rmse (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.rmse"]], "stamp (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.stamp"]], "total_rmse (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.total_rmse"]], "trial_results (navlie.utils.montecarloresult attribute)": [[133, "navlie.utils.MonteCarloResult.trial_results"]], "associate_stamps() (in module navlie.utils)": [[134, "navlie.utils.associate_stamps"]], "find_nearest_stamp_idx() (in module navlie.utils)": [[135, "navlie.utils.find_nearest_stamp_idx"]], "jacobian() (in module navlie.utils)": [[136, "navlie.utils.jacobian"]], "monte_carlo() (in module navlie.utils)": [[137, "navlie.utils.monte_carlo"]], "plot_error() (in module navlie.utils)": [[138, "navlie.utils.plot_error"]], "plot_meas() (in module navlie.utils)": [[139, "navlie.utils.plot_meas"]], "plot_meas_by_model() (in module navlie.utils)": [[140, "navlie.utils.plot_meas_by_model"]], "plot_nees() (in module navlie.utils)": [[141, "navlie.utils.plot_nees"]], "plot_poses() (in module navlie.utils)": [[142, "navlie.utils.plot_poses"]], "randvec() (in module navlie.utils)": [[143, "navlie.utils.randvec"]], "schedule_sequential_measurements() (in module navlie.utils)": [[144, "navlie.utils.schedule_sequential_measurements"]], "set_axes_equal() (in module navlie.utils)": [[145, "navlie.utils.set_axes_equal"]], "state_interp() (in module navlie.utils)": [[146, "navlie.utils.state_interp"]], "van_loans() (in module navlie.utils)": [[147, "navlie.utils.van_loans"]]}}) \ No newline at end of file diff --git a/_build/html/tutorial.html b/_build/html/tutorial.html new file mode 100644 index 00000000..1bd776a7 --- /dev/null +++ b/_build/html/tutorial.html @@ -0,0 +1,244 @@ + + + + + + + + Getting Started — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ +
+ +
+

Getting Started

+

Welcome to the navlie tutorial! The following few pages will go through a toy localization problem, where we will be running state estimation algorithms using navlie’s framework. The first step is to install this package. This should be done by directly cloning the git repo and performing a local pip install:

+
git clone git@github.com:decargroup/navlie.git
+cd navlie && pip install -e .
+
+
+

All the dependencies should get installed by this command and the package should now be ready to use. Use the column on the left to go to next page of the tutorial.

+
+

Note

+

Although this package is currently registed with PyPi, installation via pip install navlie will not work. We’re still figuring out how to set this up properly. Sorry! Feel free to help.

+
+
+
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+ + +
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+ + +
+

previous

+

Welcome to navlie!

+
+ + +
+

next

+

Toy Problem - Traditional Approach

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+ + +
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+ +
+

+ © Copyright 2022.
+

+
+ +
+

+Created using Sphinx 7.1.2.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/_build/html/tutorial/composite.html b/_build/html/tutorial/composite.html new file mode 100644 index 00000000..c0e74500 --- /dev/null +++ b/_build/html/tutorial/composite.html @@ -0,0 +1,556 @@ + + + + + + + + Composite States — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + + +
+ + +
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+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

Composite States

+

The CompositeState is a class that allows you to arbitarily combine multiple states, potentially of different types, into a new state that can be used with the navlie framework.

+

Let’s consider the previous example where we used the following \(SE(2)\) pose transformation matrix to represent the state:

+
+\[\begin{split}\mathbf{T} = \begin{bmatrix} \mathbf{C}_{ab} & \mathbf{r}_a \\ \mathbf{0} & 1 \end{bmatrix} \in SE(2).\end{split}\]
+

Suppose we now also want to estimate a wheel odometry bias \(\mathbf{b} \in \mathbb{R}^2\) in addition to the robot’s pose. Our state is now

+
+\[\mathbf{x} = (\mathbf{T}, \mathbf{b}) \in SE(2) \times \mathbb{R}^2.\]
+

This can be implemented easily using the CompositeState class in one of two ways: either directly or by inheritance. We’ll show the former approach first.

+
+
[48]:
+
+
+
import navlie as nav
+import numpy as np
+
+# Define the pose and bias as their own states
+T = nav.lib.SE2State(value = [0.1, 2.0, 3.0], stamp = 0.0, state_id="pose")
+b = nav.lib.VectorState(value = [0.1, 2.0], stamp = 0.0, state_id="bias")
+
+# Combine into a composite state, and its ready to use!
+x = nav.CompositeState([T, b], stamp=0.0)
+
+print(x)
+
+
+
+
+
+
+
+
+CompositeState(stamp=0.0, state_id=None) with substates:
+    SE2State(stamp=0.0, state_id=pose, direction=right)
+        [[ 0.99500417 -0.09983342  1.84679329]
+         [ 0.09983342  0.99500417  3.09491919]
+         [ 0.          0.          1.        ]]
+    VectorState(stamp=0.0, dof=2, state_id=bias)
+        [0.1 2. ]
+
+
+

The CompositeState class is a subclass of the State class, but who’s value is a list of states, referred to as the substates. A convenience of this class is that the composite state’s plus, minus, and copy methods have already been implemented for you based on the implementations in the substates. Note that the order in which the states are listed is important, and will correspond to the order of the components in the vectors involved in the plus and minus +operations. This can be demonstrated with the following example.

+
+
[49]:
+
+
+
# plus() and minus() have been defined for you. Here, the first three elements
+# of the vector to be added correspond to the pose (since it has 3 DOF), and the
+# last two to the bias.
+x_temp = x.plus(np.array([1,2,3,4,5]))
+print("\nResult after plus():")
+print(x_temp)
+
+dx = x_temp.minus(x)
+print("\nResult after minus():")
+print(dx)
+
+
+
+
+
+
+
+
+
+Result after plus():
+CompositeState(stamp=0.0, state_id=None) with substates:
+    SE2State(stamp=0.0, state_id=pose, direction=right)
+        [[ 0.45359612 -0.89120736  1.80531705]
+         [ 0.89120736  0.45359612  6.55185711]
+         [ 0.          0.          1.        ]]
+    VectorState(stamp=0.0, dof=2, state_id=bias)
+        [4.1 7. ]
+
+Result after minus():
+[[1.]
+ [2.]
+ [3.]
+ [4.]
+ [5.]]
+
+
+

Next, we must write a process model that works with this state. We’ll use the same process model as before, but now we’ll also include the wheel odometry bias in the state. The bias process model will be modelled as a random walk of the form

+
+\[\mathbf{b}_{k+1} = \mathbf{b}_k + \Delta t \mathbf{w}^\mathrm{bias}_k,\]
+

where \(\mathbf{w}^{\mathrm{bias}}_k \sim \mathcal{N}(0, \mathbf{Q}^{\mathrm{bias}})\) represents random error associated with this otherwise constant process model, which allows the bias to slowly vary. The process model for the composite state is then

+
+
[50]:
+
+
+
from scipy.linalg import expm
+
+def wedge_se2(x):
+    return np.array([[   0, -x[0], x[1]],
+                     [x[0],     0, x[2]],
+                     [   0,     0,    0]])
+
+class WheeledRobotWithBias(nav.ProcessModel):
+    def __init__(self, input_covariance_matrix):
+        self.Q = input_covariance_matrix
+
+    def evaluate(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):
+        pose = x.value[0]
+        bias = x.value[1]
+        vel = np.array([u.value[0] - bias.value[0], u.value[1] - bias.value[1], 0])
+        x_next = x.copy()
+        x_next.value[0].value = pose.value @ expm(wedge_se2(vel * dt))
+
+        # Largely data generation and jacobian purposes, we also update the bias
+        # state with an input, even if the input here is always zero in the
+        # nominal case.
+        x_next.value[1].value = bias.value + u.value[2:4]*dt
+        return x_next
+
+    def input_covariance(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):
+        return self.Q
+
+Q = np.eye(4) * 0.1**2
+process_model = WheeledRobotWithBias(Q)
+
+
+
+

We’d like to use the same measurement model as before, which was just a series of range measurements to known landmarks:

+
+
[51]:
+
+
+
class RangeToLandmarkSE2(nav.MeasurementModel):
+    def __init__(
+        self,
+        landmark_position: np.ndarray,
+        measurement_covariance: float,
+    ):
+        self.landmark_position = landmark_position
+        self.R = measurement_covariance
+
+    def evaluate(self, x: nav.lib.SE2State):
+        pos = x.value[0:2, 2]
+        return np.linalg.norm(pos - self.landmark_position)
+
+    def covariance(self, x: nav.lib.SE2State):
+        return self.R
+
+R = 0.1**2
+landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])
+
+
+
+

The problem is that this was made for an SE2State instead of our new composite state, and specifically the line pos = x.value[0:2, 2] is going to throw an error when we feed in a composite state. This is easy to change, but then that means we have to make a similar change for all sorts of different state definitions. An alternative is to use the CompositeMeasurementModel, which is just a lightweight wrapper around one +measurement model that “assigns” the model to a specific substate, referenced to by its state_id field. It is used as follows:

+
+
[52]:
+
+
+
meas_models = []
+for lm in landmarks:
+    meas_models.append(
+        nav.CompositeMeasurementModel(RangeToLandmarkSE2(lm, R), "pose")
+    )
+
+print(meas_models[0])
+print("Jacobian:")
+print(meas_models[0].jacobian(x))
+
+
+
+
+
+
+
+
+RangeToLandmarkSE2(of substate pose)
+Jacobian:
+[[0.         0.46544123 0.88507893 0.         0.        ]]
+
+
+

This does mean that the state_id of each substate must be unique, but this is a good practice anyway. The CompositeMeasurementModel will then automatically handle the extraction of the relevant substate from the composite state and pass it to the measurement model, as well as handle the corresponding Jacobian accordingly. This is a good way to avoid having to write a lot of boilerplate code for different state definitions. Notice in the above example that the Jacobian has two extra zeros +at the end, which correspond to the bias state that has no effect on the measurement. This is automatically handled by the CompositeMeasurementModel.

+

With our problem now set up, we can run a filter on it with the same snippet as usual!

+
+
[53]:
+
+
+
dg = nav.DataGenerator(
+    process_model=process_model,
+    input_func=lambda t, x: np.array([0.5, 0.3, 0.0, 0.0]),
+    input_covariance= Q,
+    input_freq=50,
+    meas_model_list=meas_models,
+    meas_freq_list=[10, 10, 10, 10]
+)
+
+state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)
+
+# First, define the filter
+kalman_filter = nav.ExtendedKalmanFilter(process_model)
+P0 = np.diag([0.1**2, 1**2, 1**2, 0.1**2, 0.1**2])  # Initial covariance
+x = nav.StateWithCovariance(x, P0)  # Estimate and covariance in one container
+
+meas_idx = 0
+y = meas_data[meas_idx]
+estimates = []
+for k in range(len(input_data) - 1):
+    u = input_data[k]
+
+    # Fuse any measurements that have occurred.
+    while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):
+        x = kalman_filter.correct(x, y, u)
+
+        # Load the next measurement
+        meas_idx += 1
+        if meas_idx < len(meas_data):
+            y = meas_data[meas_idx]
+
+    # Predict until the next input is available
+    dt = input_data[k + 1].stamp - x.state.stamp
+    x = kalman_filter.predict(x, u, dt)
+
+    estimates.append(x.copy())
+
+
+results = nav.GaussianResultList.from_estimates(estimates, state_data)
+
+import matplotlib.pyplot as plt
+fig, axs = nav.plot_error(results)
+axs[0,0].set_title("Pose Estimation Errors")
+axs[0,0].set_ylabel("theta (rad)")
+axs[1,0].set_ylabel("x (m)")
+axs[2,0].set_ylabel("y (m)")
+axs[2,0].set_xlabel("Time (s)")
+axs[0, 1].set_title("Bias Estimation Errors")
+axs[0, 1].set_ylabel("ang. vel. (rad/s)")
+axs[1, 1].set_ylabel("forward vel. (m/s)")
+axs[1, 1].set_xlabel("Time (s)")
+
+fig, ax = nav.plot_nees(results)
+ax.set_title("NEES")
+ax.set_xlabel("Time (s)")
+plt.show()
+
+
+
+
+
+
+
+../_images/tutorial_composite_11_0.png +
+
+
+
+
+
+../_images/tutorial_composite_11_1.png +
+
+
+

Inheriting from CompositeState

+

The previous example showed how to use the CompositeState class directly, but it’s also possible to inherit from it. This is useful if you want to add some extra methods or attributes to the composite state, or if you are going to frequently be using the same composite state. Here’s an example of how you would do it:

+
+
[55]:
+
+
+
class WheeledRobotState(nav.CompositeState):
+    def __init__(self, pose_values: np.ndarray, bias_values: np.ndarray, stamp: float):
+        pose = nav.lib.SE2State(pose_values, stamp=stamp, state_id="pose")
+        bias = nav.lib.VectorState(bias_values, stamp=stamp, state_id="bias")
+        super().__init__([pose, bias], stamp=stamp)
+
+    # Define any getter that you want for convenience!
+    @property
+    def pose(self):
+        return self.value[0]
+
+    @property
+    def bias(self):
+        return self.value[1]
+
+    def copy(self):
+        return WheeledRobotState(self.pose.copy(), self.bias.copy())
+
+x = WheeledRobotState([0.1, 2.0, 3.0], [0.1, 2.0], stamp = 0.1)
+print(x)
+
+
+
+
+
+
+
+
+WheeledRobotState(stamp=0.1, state_id=None) with substates:
+    SE2State(stamp=0.1, state_id=pose, direction=right)
+        [[ 0.99500417 -0.09983342  1.84679329]
+         [ 0.09983342  0.99500417  3.09491919]
+         [ 0.          0.          1.        ]]
+    VectorState(stamp=0.1, dof=2, state_id=bias)
+        [0.1 2. ]
+SE2State(stamp=0.1, state_id=pose, direction=right)
+    [[ 0.99500417 -0.09983342  1.84679329]
+     [ 0.09983342  0.99500417  3.09491919]
+     [ 0.          0.          1.        ]]
+
+
+

This can end up looking a lot cleaner, and is potentially more flexible to work with since you can add methods and attributes to the composite state. For example, because of the getters we defined above, we can access the pose and bias more ergonomically with x.pose and x.bias.

+
+
+ + +
+ + + +
+ + +
+

previous

+

Jacobians in navlie

+
+ + +
+

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+

API Documentation

+
+ + +
+ +
+ + +
+
+ + +
+
+ +
+

+ © Copyright 2022.
+

+
+ +
+

+Created using Sphinx 7.1.2.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/_build/html/tutorial/composite.ipynb b/_build/html/tutorial/composite.ipynb new file mode 100644 index 00000000..8a00bfdb --- /dev/null +++ b/_build/html/tutorial/composite.ipynb @@ -0,0 +1,406 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Composite States\n", + "\n", + "The [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) is a class that allows you to arbitarily combine multiple states, potentially of different types, into a new state that can be used with the navlie framework.\n", + "\n", + "Let's consider the previous example where we used the following $SE(2)$ pose transformation matrix to represent the state:\n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab} & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2).\n", + "$$\n", + "\n", + "Suppose we now also want to estimate a wheel odometry bias $\\mathbf{b} \\in \\mathbb{R}^2$ in addition to the robot's pose. Our state is now \n", + "\n", + "$$\n", + "\\mathbf{x} = (\\mathbf{T}, \\mathbf{b}) \\in SE(2) \\times \\mathbb{R}^2.\n", + "$$\n", + "\n", + "This can be implemented easily using the [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) class in one of two ways: either directly or by inheritance. We'll show the former approach first." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [0.1 2. ]\n" + ] + } + ], + "source": [ + "import navlie as nav \n", + "import numpy as np\n", + "\n", + "# Define the pose and bias as their own states\n", + "T = nav.lib.SE2State(value = [0.1, 2.0, 3.0], stamp = 0.0, state_id=\"pose\")\n", + "b = nav.lib.VectorState(value = [0.1, 2.0], stamp = 0.0, state_id=\"bias\")\n", + "\n", + "# Combine into a composite state, and its ready to use!\n", + "x = nav.CompositeState([T, b], stamp=0.0)\n", + "\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``CompositeState`` class is a subclass of the ``State`` class, but who's ``value`` is a list of states, referred to as the *substates*. A convenience of this class is that the composite state's ``plus``, ``minus``, and ``copy`` methods have already been implemented for you based on the implementations in the substates. Note that the order in which the states are listed is important, and will correspond to the order of the components in the vectors involved in the ``plus`` and ``minus`` operations. This can be demonstrated with the following example." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Result after plus():\n", + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.45359612 -0.89120736 1.80531705]\n", + " [ 0.89120736 0.45359612 6.55185711]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [4.1 7. ]\n", + "\n", + "Result after minus():\n", + "[[1.]\n", + " [2.]\n", + " [3.]\n", + " [4.]\n", + " [5.]]\n" + ] + } + ], + "source": [ + "# plus() and minus() have been defined for you. Here, the first three elements\n", + "# of the vector to be added correspond to the pose (since it has 3 DOF), and the\n", + "# last two to the bias.\n", + "x_temp = x.plus(np.array([1,2,3,4,5]))\n", + "print(\"\\nResult after plus():\")\n", + "print(x_temp)\n", + "\n", + "dx = x_temp.minus(x)\n", + "print(\"\\nResult after minus():\")\n", + "print(dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we must write a process model that works with this state. We'll use the same process model as before, but now we'll also include the wheel odometry bias in the state. The bias process model will be modelled as a random walk of the form \n", + "\n", + "$$\n", + "\\mathbf{b}_{k+1} = \\mathbf{b}_k + \\Delta t \\mathbf{w}^\\mathrm{bias}_k,\n", + "$$\n", + "\n", + "where $\\mathbf{w}^{\\mathrm{bias}}_k \\sim \\mathcal{N}(0, \\mathbf{Q}^{\\mathrm{bias}})$ represents random error associated with this otherwise constant process model, which allows the bias to slowly vary. The process model for the composite state is then" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.linalg import expm\n", + "\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "class WheeledRobotWithBias(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " pose = x.value[0]\n", + " bias = x.value[1]\n", + " vel = np.array([u.value[0] - bias.value[0], u.value[1] - bias.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value[0].value = pose.value @ expm(wedge_se2(vel * dt))\n", + "\n", + " # Largely data generation and jacobian purposes, we also update the bias\n", + " # state with an input, even if the input here is always zero in the\n", + " # nominal case.\n", + " x_next.value[1].value = bias.value + u.value[2:4]*dt\n", + " return x_next\n", + " \n", + " def input_covariance(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(4) * 0.1**2\n", + "process_model = WheeledRobotWithBias(Q)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'd like to use the same measurement model as before, which was just a series of range measurements to known landmarks:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: nav.lib.SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: nav.lib.SE2State):\n", + " return self.R\n", + " \n", + "R = 0.1**2\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The problem is that this was made for an ``SE2State`` instead of our new composite state, and specifically the line `pos = x.value[0:2, 2]` is going to throw an error when we feed in a composite state. This is easy to change, but then that means we have to make a similar change for all sorts of different state definitions. An alternative is to use the [CompositeMeasurementModel](../_autosummary/navlie.composite.CompositeMeasurementModel.rst), which is just a lightweight wrapper around one measurement model that \"assigns\" the model to a specific substate, referenced to by its `state_id` field. It is used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RangeToLandmarkSE2(of substate pose)\n", + "Jacobian:\n", + "[[0. 0.46544123 0.88507893 0. 0. ]]\n" + ] + } + ], + "source": [ + "meas_models = []\n", + "for lm in landmarks:\n", + " meas_models.append(\n", + " nav.CompositeMeasurementModel(RangeToLandmarkSE2(lm, R), \"pose\")\n", + " )\n", + "\n", + "print(meas_models[0])\n", + "print(\"Jacobian:\")\n", + "print(meas_models[0].jacobian(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This does mean that the `state_id` of each substate must be unique, but this is a good practice anyway. The `CompositeMeasurementModel` will then automatically handle the extraction of the relevant substate from the composite state and pass it to the measurement model, as well as handle the corresponding Jacobian accordingly. This is a good way to avoid having to write a lot of boilerplate code for different state definitions. Notice in the above example that the Jacobian has two extra zeros at the end, which correspond to the bias state that has no effect on the measurement. This is automatically handled by the `CompositeMeasurementModel`.\n", + "\n", + "With our problem now set up, we can run a filter on it with the same snippet as usual!" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, \n", + " input_func=lambda t, x: np.array([0.5, 0.3, 0.0, 0.0]), \n", + " input_covariance= Q, \n", + " input_freq=50, \n", + " meas_model_list=meas_models, \n", + " meas_freq_list=[10, 10, 10, 10] \n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2, 0.1**2, 0.1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0,0].set_title(\"Pose Estimation Errors\")\n", + "axs[0,0].set_ylabel(\"theta (rad)\")\n", + "axs[1,0].set_ylabel(\"x (m)\")\n", + "axs[2,0].set_ylabel(\"y (m)\")\n", + "axs[2,0].set_xlabel(\"Time (s)\")\n", + "axs[0, 1].set_title(\"Bias Estimation Errors\")\n", + "axs[0, 1].set_ylabel(\"ang. vel. (rad/s)\")\n", + "axs[1, 1].set_ylabel(\"forward vel. (m/s)\")\n", + "axs[1, 1].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Inheriting from `CompositeState`\n", + "\n", + "The previous example showed how to use the `CompositeState` class directly, but it's also possible to inherit from it. This is useful if you want to add some extra methods or attributes to the composite state, or if you are going to frequently be using the same composite state. Here's an example of how you would do it:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "WheeledRobotState(stamp=0.1, state_id=None) with substates:\n", + " SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.1, dof=2, state_id=bias)\n", + " [0.1 2. ]\n", + "SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n" + ] + } + ], + "source": [ + "class WheeledRobotState(nav.CompositeState):\n", + " def __init__(self, pose_values: np.ndarray, bias_values: np.ndarray, stamp: float):\n", + " pose = nav.lib.SE2State(pose_values, stamp=stamp, state_id=\"pose\")\n", + " bias = nav.lib.VectorState(bias_values, stamp=stamp, state_id=\"bias\")\n", + " super().__init__([pose, bias], stamp=stamp)\n", + "\n", + " # Define any getter that you want for convenience! \n", + " @property\n", + " def pose(self):\n", + " return self.value[0]\n", + "\n", + " @property\n", + " def bias(self):\n", + " return self.value[1]\n", + "\n", + " def copy(self):\n", + " return WheeledRobotState(self.pose.copy(), self.bias.copy())\n", + " \n", + "x = WheeledRobotState([0.1, 2.0, 3.0], [0.1, 2.0], stamp = 0.1)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can end up looking a lot cleaner, and is potentially more flexible to work with since you can add methods and attributes to the composite state. For example, because of the getters we defined above, we can access the pose and bias more ergonomically with `x.pose` and `x.bias`." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/html/tutorial/jacobians.html b/_build/html/tutorial/jacobians.html new file mode 100644 index 00000000..85718358 --- /dev/null +++ b/_build/html/tutorial/jacobians.html @@ -0,0 +1,485 @@ + + + + + + + + Jacobians in navlie — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ On this page +
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+

Jacobians in navlie

+

As you may know, many state estimation algorithm require access to process model and measurement model Jacobians, with respect to the state and sometimes other inputs. For states belonging to Lie groups, algorithms will require Lie Jacobians, which differ from traditional derivatives as they conform to the constraints of the group. The abstraction provided by the \(\oplus\) and \(\ominus\) operators (implemented with State.plus and State.minus respectively) allow for a generic +definition of a derivative:

+
+\[\left.\frac{D f(\mathcal{X})}{D \mathcal{X}}\right|_{\bar{\mathcal{X}} }\triangleq \left.\frac{\partial f(\bar{\mathcal{X}} \oplus \delta \mathbf{x}) \ominus f(\bar{\mathcal{X}})}{\partial \delta \mathbf{x}}\right|_{\delta \mathbf{x} = \mathbf{0}},\]
+

which can be shown to fall back to a traditional derivatives when \(\oplus\) and \(\ominus\) are defined to be regular addition/subtraction. This derivative definition is used universally throughout navlie, and roughly follows what is done in the Micro Lie Theory paper. In that reference, seperate definitions are given for “left” and “right” derivatives, whereas we have aggregated them into a single definition, with left and right derivatives +naturally arising from the choice of \(\oplus\) and \(\ominus\) operators.

+

If you dont want to worry about this, the good news is that navlie computes Lie Jacobians for you by default using finite difference. However, finite difference can have some drawbacks, such as being computationally expensive and less accurate than analytic derivatives. In this notebook, we will show you how to use analytic derivatives in navlie, which offer the maximum accuracy and speed.

+
+

Jacobians - Traditional Approach

+

Recall the traditional approach to the previous example. We had defined the state to be \(\mathbf{x} = [\theta, x, y]^T\) and the process model to be

+
+\[\begin{split}\begin{aligned} +\theta_{k+1} &= \theta_k + \omega_k \Delta t \\ +x_{k+1} &= x_k + v_k \cos(\theta_k) \Delta t \\ +y_{k+1} &= y_k + v_k \sin(\theta_k) \Delta t +\end{aligned}\end{split}\]
+

where \(\omega_k\) is the angular velocity and \(v_k\) is the linear velocity. Since the state is just a regular vector, Lie Jacobians fall back to regular Jacobians, and standard derivative techniques lead to the following expressions for the process model Jacobian with respect to the state

+
+\[\begin{split}\mathbf{F} := \frac{\partial f(\mathbf{x}_k, \mathbf{u}_k)}{\partial \mathbf{x}_k} = \begin{bmatrix} 1 & 0 & 0 \\ -v_k \sin(\theta_k) \Delta t & 1 & 0 \\ v_k \cos(\theta_k) \Delta t & 0 & 1 \end{bmatrix}\end{split}\]
+

To implement this Jacobian in navlie, all we need to do is override the jacobian() method in our process model, and it will get used automatically by the estimation algorithms. Adding this to our process model from before:

+
+
[2]:
+
+
+
import navlie as nav
+import numpy as np
+
+from navlie.lib import VectorInput, VectorState
+
+Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation
+
+class WheeledRobot(nav.ProcessModel):
+    def __init__(self, input_covariance):
+        self.Q = input_covariance
+
+    def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:
+        x_next = x.copy()
+        x_next.value[0] += u.value[0] * dt
+        x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])
+        x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])
+        return x_next
+
+    def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:
+        return self.Q
+
+    def jacobian(self, x:VectorState, u: VectorInput, dt: float) -> np.ndarray:
+        F = np.eye(3)
+        F[1, 0] = -u.value[1] * dt * np.sin(x.value[0])
+        F[2, 0] = u.value[1] * dt * np.cos(x.value[0])
+        return F
+
+process_model = WheeledRobot(Q) # instantiate it
+
+
+
+

Now, lets just double check that we did everything correctly by comparing with finite difference. All process models inherit the jacobian_fd() method, which computes the Jacobian using finite difference. We can use this to compare with our analytic Jacobian.

+
+
[3]:
+
+
+
x = VectorState([1,2,3])
+u = VectorInput([0.1, 0.2])
+dt = 0.1
+
+print("Analyical:")
+print(process_model.jacobian(x, u, dt))
+
+print("\nFinite difference:")
+print(process_model.jacobian_fd(x, u, dt))
+
+
+
+
+
+
+
+
+Analyical:
+[[ 1.          0.          0.        ]
+ [-0.01682942  1.          0.        ]
+ [ 0.01080605  0.          1.        ]]
+
+Finite difference:
+[[ 1.          0.          0.        ]
+ [-0.01682943  1.          0.        ]
+ [ 0.01080604  0.          1.        ]]
+
+
+

The Jacobians match almost perfectly, but differ slightly due to errors in finite difference. This is expected, as finite difference is only an approximation. Nevertheless, finite difference is generally sufficiently accurate for most applications.

+

Note: The jacobian methods must always return a 2D array.

+

Moving on to the measurement model, which was previously defined to be

+
+\[\mathbf{y}_k = || \mathbf{r}_k - \boldsymbol{\ell}^{(i)} ||\]
+

where \(\mathbf{r}_k\) is the robot’s position and \(\boldsymbol{\ell}^{(i)}\) is the \(i\)th landmark. The measurement model Jacobian with respect to the state is

+
+\[\mathbf{G} := \frac{\partial g(\mathbf{x}_k)}{\partial \mathbf{x}_k} = \begin{bmatrix} 0 & \frac{(\mathbf{r}_k - \boldsymbol{\ell}^{(i)})^T}{||(\mathbf{r}_k - \boldsymbol{\ell}^{(i)})||} \end{bmatrix},\]
+

and we can implement this in navlie by again overriding the jacobian() method in our measurement model. Adding this to our measurement model from before:

+
+
[4]:
+
+
+
class RangeToLandmark(nav.MeasurementModel):
+    def __init__(self, landmark_position: np.ndarray):
+        self.landmark_position = landmark_position
+
+    def evaluate(self, x: VectorState) -> np.ndarray:
+        return np.linalg.norm(x.value[1:] - self.landmark_position)
+
+    def covariance(self, x: VectorState) -> np.ndarray:
+        return 0.1**2
+
+    def jacobian(self, x: VectorState) -> np.ndarray:
+        G = np.zeros((1, 3))
+        r = x.value[1:]
+        G[0,1:] = (r - self.landmark_position) / np.linalg.norm(r - self.landmark_position)
+        return G
+
+meas_model = RangeToLandmark(np.array([1, 2]))
+
+print("\nAnalyical:")
+print(meas_model.jacobian(x))
+
+print("\nFinite difference:")
+print(meas_model.jacobian_fd(x))
+
+
+
+
+
+
+
+
+
+Analyical:
+[[0.         0.70710678 0.70710678]]
+
+Finite difference:
+[[0.         0.70710696 0.70710696]]
+
+
+

We can again see that the results match nicely.

+
+
+

Jacobians - Lie Group Approach

+

Now, lets see how to implement analytical Jacobians when states belong to Lie groups. In the previous example the state was \(\mathbf{T} \in SE(2)\) and the process model was

+
+\[\mathbf{T}_{k+1} = \mathbf{T}_k \exp(\boldsymbol{\varpi}^\wedge_k \Delta t).\]
+

To derive the Jacobian, we can “perturb” both sides of the equation and manipulate. This is a common technique for deriving Lie Jacobians, and for computing matrix-vector derivatives in general. For more details, we recommend reading State Estimation for Robotics by Tim Barfoot.

+
+\[\begin{split}\begin{aligned} +\mathbf{T}_{k+1} &= \mathbf{T}_k \exp(\boldsymbol{\varpi}^\wedge_k \Delta t) \\ +\bar{\mathbf{T}}_{k+1} \exp(\delta \boldsymbol{\xi}_{k+1}^\wedge) &= \bar{\mathbf{T}}_{k} \exp(\delta \boldsymbol{\xi}_{k}^\wedge) \exp(\boldsymbol{\varpi}^\wedge_k \Delta t) \\ + \exp(\delta \boldsymbol{\xi}_{k+1}^\wedge) &= \underbrace{\bar{\mathbf{T}}_{k+1}^{-1} \bar{\mathbf{T}}_{k}}_{\exp(\boldsymbol{\varpi}^\wedge \Delta t)^{-1}} \exp(\delta \boldsymbol{\xi}_{k}^\wedge) \exp(\boldsymbol{\varpi}^\wedge_k \Delta t) \\ + \exp(\delta \boldsymbol{\xi}_{k+1}^\wedge) &= \exp((\mathbf{Ad}(\exp(\boldsymbol{\varpi}^\wedge \Delta t)^{-1}) \delta \boldsymbol{\xi}_{k})^\wedge) \\ + \delta \boldsymbol{\xi}_{k+1} &= \underbrace{\mathbf{Ad}(\exp(\boldsymbol{\varpi}^\wedge \Delta t)^{-1})}_{\mathbf{F}} \delta \boldsymbol{\xi}_{k} +\end{aligned}\end{split}\]
+

There, we used the adjoint matrix \(\mathbf{Ad}(\cdot)\), to invoke the identity \(\mathbf{X}^{-1} \exp(\boldsymbol{\xi}^\wedge) \mathbf{X} = \exp(\mathbf{Ad}(\mathbf{X}) \boldsymbol{\xi}^\wedge)\), which is true for any \(\mathbf{X} \in SE(2)\). The adjoint matrix for \(SE(2)\) is given by

+
+\[\begin{split}\mathbf{Ad}(\mathbf{T}) = \begin{bmatrix} 1 & \mathbf{0} \\ - \boldsymbol{\Omega} \mathbf{r} & \mathbf{C} \end{bmatrix}\end{split}\]
+

where \(\boldsymbol{\Omega} = \begin{bmatrix} 0 & -1 \\ 1 &0 \end{bmatrix}\).

+

Note: in this Jacobian derivation, we perturbed the state \(\mathbf{T} = \bar{\mathbf{T}} \exp(\delta \boldsymbol{\xi}^\wedge)\) “on the right” because that corresponds to what was implemented in the plus() method of our SE2State class. It is important to be consistent here for everything to work.

+

Now, we can implement this Jacobian in navlie by overriding the jacobian() method in our process model. Adding this to our process model from before:

+
+
[6]:
+
+
+
from navlie.lib import SE2State, VectorInput
+from scipy.linalg import expm
+
+
+def wedge_se2(x:np):
+    return np.array([[   0, -x[0], x[1]],
+                     [x[0],     0, x[2]],
+                     [   0,     0,    0]])
+
+def adjoint_se2(T:np.ndarray):
+    C = T[:2, :2]
+    r = T[:2, 2]
+    Omega = np.array([[0, -1], [1, 0]])
+    Ad = np.zeros((3,3))
+    Ad[0,0] = 1
+    Ad[1:,1:] = C
+    Ad[1:,0] = - Omega @ r
+    return Ad
+
+
+class WheeledRobotSE2(nav.ProcessModel):
+    def __init__(self, input_covariance_matrix):
+        self.Q = input_covariance_matrix
+
+    def evaluate(self, x:SE2State, u:VectorInput, dt:float):
+        u = np.array([u.value[0], u.value[1], 0])
+        x_next = x.copy()
+        x_next.value = x.value @ expm(wedge_se2(u * dt))
+        return x_next
+    def input_covariance(self, x:SE2State, u:VectorInput, dt:float):
+        return self.Q
+
+    def jacobian(self, x:SE2State, u:VectorInput, dt:float):
+        u = np.array([u.value[0], u.value[1], 0])
+        return adjoint_se2(expm(-wedge_se2(u * dt)))
+
+Q = np.eye(2) * 0.1**2
+process_model = WheeledRobotSE2(Q)
+x = SE2State(expm(wedge_se2(np.array([1,2,3]))))
+u = VectorInput([4, 2])
+dt = 0.1
+
+print("\nAnalyical:")
+print(process_model.jacobian(x, u, dt))
+
+print("\nFinite difference:")
+print(process_model.jacobian_fd(x, u, dt))
+
+
+
+
+
+
+
+
+
+Analyical:
+[[ 1.          0.          0.        ]
+ [ 0.0394695   0.92106099  0.38941834]
+ [ 0.19470917 -0.38941834  0.92106099]]
+
+Finite difference:
+[[ 1.00000000e+00 -1.10747782e-11 -1.10747782e-11]
+ [ 3.94695038e-02  9.21060995e-01  3.89418343e-01]
+ [ 1.94709171e-01 -3.89418342e-01  9.21060994e-01]]
+
+
+

Note that when using Lie groups, our Jacobian no longer has dependence on the state itself. This can be a tangible advantage when the state estimate has high uncertainty, where using a traditional approach can result in excessive linearization errors when the state estimate is far from the true value.

+
+
+ + +
+ + + +
+ + +
+

previous

+

Toy Problem - Lie group approach

+
+ + +
+

next

+

Composite States

+
+ + +
+ +
+ + +
+
+ + +
+
+ +
+

+ © Copyright 2022.
+

+
+ +
+

+Created using Sphinx 7.1.2.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/_build/html/tutorial/jacobians.ipynb b/_build/html/tutorial/jacobians.ipynb new file mode 100644 index 00000000..49b93bd8 --- /dev/null +++ b/_build/html/tutorial/jacobians.ipynb @@ -0,0 +1,340 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Jacobians in navlie\n", + "\n", + "As you may know, many state estimation algorithm require access to process model and measurement model Jacobians, with respect to the state and sometimes other inputs. For states belonging to Lie groups, algorithms will require _Lie Jacobians_, which differ from traditional derivatives as they conform to the constraints of the group. The abstraction provided by the $\\oplus$ and $\\ominus$ operators (implemented with `State.plus` and `State.minus` respectively) allow for a generic definition of a derivative:\n", + "\n", + "$$\n", + "\\left.\\frac{D f(\\mathcal{X})}{D \\mathcal{X}}\\right|_{\\bar{\\mathcal{X}} }\\triangleq \\left.\\frac{\\partial f(\\bar{\\mathcal{X}} \\oplus \\delta \\mathbf{x}) \\ominus f(\\bar{\\mathcal{X}})}{\\partial \\delta \\mathbf{x}}\\right|_{\\delta \\mathbf{x} = \\mathbf{0}},\n", + "$$\n", + "\n", + "which can be shown to fall back to a traditional derivatives when $\\oplus$ and $\\ominus$ are defined to be regular addition/subtraction. This derivative definition is used universally throughout navlie, and roughly follows what is done in the [Micro Lie Theory paper](https://arxiv.org/pdf/1812.01537.pdf). In that reference, seperate definitions are given for \"left\" and \"right\" derivatives, whereas we have aggregated them into a single definition, with left and right derivatives naturally arising from the choice of $\\oplus$ and $\\ominus$ operators.\n", + "\n", + "If you dont want to worry about this, the good news is that navlie computes Lie Jacobians for you by default using finite difference. However, finite difference can have some drawbacks, such as being computationally expensive and less accurate than analytic derivatives. In this notebook, we will show you how to use analytic derivatives in navlie, which offer the maximum accuracy and speed.\n", + "\n", + "## Jacobians - Traditional Approach\n", + "Recall the traditional approach to the previous example. We had defined the state to be $\\mathbf{x} = [\\theta, x, y]^T$ and the process model to be\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t \\\\\n", + "x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t \\\\\n", + "y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where $\\omega_k$ is the angular velocity and $v_k$ is the linear velocity. Since the state is just a regular vector, Lie Jacobians fall back to regular Jacobians, and standard derivative techniques lead to the following expressions for the process model Jacobian with respect to the state\n", + "\n", + "$$\n", + "\\mathbf{F} := \\frac{\\partial f(\\mathbf{x}_k, \\mathbf{u}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 1 & 0 & 0 \\\\ -v_k \\sin(\\theta_k) \\Delta t & 1 & 0 \\\\ v_k \\cos(\\theta_k) \\Delta t & 0 & 1 \\end{bmatrix}\n", + "$$\n", + "\n", + "To implement this Jacobian in navlie, all we need to do is override the `jacobian()` method in our process model, and it will get used automatically by the estimation algorithms. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import navlie as nav\n", + "import numpy as np\n", + "\n", + "from navlie.lib import VectorInput, VectorState\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + " def jacobian(self, x:VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " F = np.eye(3)\n", + " F[1, 0] = -u.value[1] * dt * np.sin(x.value[0])\n", + " F[2, 0] = u.value[1] * dt * np.cos(x.value[0])\n", + " return F\n", + "\n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, lets just double check that we did everything correctly by comparing with finite difference. All process models inherit the `jacobian_fd()` method, which computes the Jacobian using finite difference. We can use this to compare with our analytic Jacobian." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682942 1. 0. ]\n", + " [ 0.01080605 0. 1. ]]\n", + "\n", + "Finite difference:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682943 1. 0. ]\n", + " [ 0.01080604 0. 1. ]]\n" + ] + } + ], + "source": [ + "x = VectorState([1,2,3]) \n", + "u = VectorInput([0.1, 0.2]) \n", + "dt = 0.1 \n", + "\n", + "print(\"Analyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Jacobians match almost perfectly, but differ slightly due to errors in finite difference. This is expected, as finite difference is only an approximation. Nevertheless, finite difference is generally sufficiently accurate for most applications.\n", + "\n", + "
\n", + "Note: The `jacobian` methods must *always* return a 2D array.\n", + "
\n", + "\n", + "\n", + "\n", + "Moving on to the measurement model, which was previously defined to be \n", + "\n", + "$$\n", + "\\mathbf{y}_k = || \\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)} || \n", + "$$ \n", + "\n", + "where $\\mathbf{r}_k$ is the robot's position and $\\boldsymbol{\\ell}^{(i)}$ is the $i$th landmark. The measurement model Jacobian with respect to the state is\n", + "\n", + "$$ \n", + "\\mathbf{G} := \\frac{\\partial g(\\mathbf{x}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 0 & \\frac{(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})^T}{||(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})||} \\end{bmatrix},\n", + "$$\n", + "\n", + "and we can implement this in navlie by again overriding the `jacobian()` method in our measurement model. Adding this to our measurement model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[0. 0.70710678 0.70710678]]\n", + "\n", + "Finite difference:\n", + "[[0. 0.70710696 0.70710696]]\n" + ] + } + ], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + " def jacobian(self, x: VectorState) -> np.ndarray:\n", + " G = np.zeros((1, 3))\n", + " r = x.value[1:]\n", + " G[0,1:] = (r - self.landmark_position) / np.linalg.norm(r - self.landmark_position)\n", + " return G\n", + " \n", + "meas_model = RangeToLandmark(np.array([1, 2]))\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(meas_model.jacobian(x))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(meas_model.jacobian_fd(x))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can again see that the results match nicely." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jacobians - Lie Group Approach \n", + "\n", + "Now, lets see how to implement analytical Jacobians when states belong to Lie groups. In the previous example the state was $\\mathbf{T} \\in SE(2)$ and the process model was\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t).\n", + "$$\n", + "\n", + "To derive the Jacobian, we can \"perturb\" both sides of the equation and manipulate. This is a common technique for deriving Lie Jacobians, and for computing matrix-vector derivatives in general. For more details, we recommend reading [State Estimation for Robotics by Tim Barfoot](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf).\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\mathbf{T}_{k+1} &= \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + "\\bar{\\mathbf{T}}_{k+1} \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\bar{\\mathbf{T}}_{k} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\underbrace{\\bar{\\mathbf{T}}_{k+1}^{-1} \\bar{\\mathbf{T}}_{k}}_{\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\exp((\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}) \\delta \\boldsymbol{\\xi}_{k})^\\wedge) \\\\\n", + " \\delta \\boldsymbol{\\xi}_{k+1} &= \\underbrace{\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1})}_{\\mathbf{F}} \\delta \\boldsymbol{\\xi}_{k}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "There, we used the _adjoint matrix_ $\\mathbf{Ad}(\\cdot)$, to invoke the identity $\\mathbf{X}^{-1} \\exp(\\boldsymbol{\\xi}^\\wedge) \\mathbf{X} = \\exp(\\mathbf{Ad}(\\mathbf{X}) \\boldsymbol{\\xi}^\\wedge)$, which is true for any $\\mathbf{X} \\in SE(2)$. The adjoint matrix for $SE(2)$ is given by \n", + "\n", + "$$ \n", + "\\mathbf{Ad}(\\mathbf{T}) = \\begin{bmatrix} 1 & \\mathbf{0} \\\\ - \\boldsymbol{\\Omega} \\mathbf{r} & \\mathbf{C} \\end{bmatrix}\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\Omega} = \\begin{bmatrix} 0 & -1 \\\\ 1 \n", + "&0 \\end{bmatrix}$.\n", + "\n", + "
\n", + "Note: in this Jacobian derivation, we perturbed the state $\\mathbf{T} = \\bar{\\mathbf{T}} \\exp(\\delta \\boldsymbol{\\xi}^\\wedge)$ \"on the right\" because that corresponds to what was implemented in the `plus()` method of our `SE2State` class. It is important to be consistent here for everything to work.\n", + "
\n", + "\n", + "Now, we can implement this Jacobian in navlie by overriding the `jacobian()` method in our process model. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [ 0.0394695 0.92106099 0.38941834]\n", + " [ 0.19470917 -0.38941834 0.92106099]]\n", + "\n", + "Finite difference:\n", + "[[ 1.00000000e+00 -1.10747782e-11 -1.10747782e-11]\n", + " [ 3.94695038e-02 9.21060995e-01 3.89418343e-01]\n", + " [ 1.94709171e-01 -3.89418342e-01 9.21060994e-01]]\n" + ] + } + ], + "source": [ + "from navlie.lib import SE2State, VectorInput\n", + "from scipy.linalg import expm\n", + "\n", + "\n", + "def wedge_se2(x:np):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def adjoint_se2(T:np.ndarray):\n", + " C = T[:2, :2]\n", + " r = T[:2, 2]\n", + " Omega = np.array([[0, -1], [1, 0]])\n", + " Ad = np.zeros((3,3))\n", + " Ad[0,0] = 1\n", + " Ad[1:,1:] = C\n", + " Ad[1:,0] = - Omega @ r\n", + " return Ad\n", + "\n", + "\n", + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(u * dt))\n", + " return x_next\n", + " def input_covariance(self, x:SE2State, u:VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + " def jacobian(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " return adjoint_se2(expm(-wedge_se2(u * dt)))\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)\n", + "x = SE2State(expm(wedge_se2(np.array([1,2,3]))))\n", + "u = VectorInput([4, 2])\n", + "dt = 0.1\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that when using Lie groups, our Jacobian no longer has dependence on the state itself. This can be a tangible advantage when the state estimate has high uncertainty, where using a traditional approach can result in excessive linearization errors when the state estimate is far from the true value." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/html/tutorial/lie_groups.html b/_build/html/tutorial/lie_groups.html new file mode 100644 index 00000000..69255e94 --- /dev/null +++ b/_build/html/tutorial/lie_groups.html @@ -0,0 +1,566 @@ + + + + + + + + Toy Problem - Lie group approach — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

Toy Problem - Lie group approach

+

Toy Problem

+

Another way we could approach the same state estimation task is to instead use Lie group theory, which is becoming increasingly common practice in state estimation. Lie group theory can be very abstract, and the main references that navlie refer to are the following:

+
    +

  1. A micro Lie theory for state estimation in robotics

    2. +

  2. T.Barfoot, State Estimation for Robotics

    3. +
+
+

Define the State

+

Instead of representing the state using a vector, we will represent the state using an element of the special Euclidean group \(SE(2)\), sometimes called pose transformation matrices. Elements of this group are 3x3 matrices of the form

+
+\[\begin{split}\mathbf{T} = \begin{bmatrix} \mathbf{C}_{ab}(\theta) & \mathbf{r}_a \\ \mathbf{0} & 1 \end{bmatrix} \in SE(2)\end{split}\]
+

where \(\mathbf{r}_a = [x,y]^T\) again denotes the position of the robot and \(\mathbf{C}_{ab}(\theta) \in SO(2)\) is a rotation matrix (sometimes called a direction cosine matrix) with the form

+
+\[\begin{split}\mathbf{C}_{ab}(\theta) = \begin{bmatrix} \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}.\end{split}\]
+

The rotation matrix transforms vectors resolved in one frame to another frame, i.e. \(\mathbf{r}_a = \mathbf{C}_{ab} \mathbf{r}_b\). Unlike vectors, elements of \(SO(2)\) or \(SE(2)\) cannot be added together to produce another valid element of \(SE(2)\), but they can be multiplied together with the result still having the same form.

+
+\[\mathbf{T}_1 \mathbf{T}_2 \in SE(2)\]
+

To proceed further with our mathematical setup, we need to define a few very common operators seen in Lie group theory. The first two are the “wedge” \((\cdot)^\wedge\) and “vee” \((\cdot)^\vee\) operators, which for this specific group has the form

+
+\[\begin{split}\begin{bmatrix} \theta \\ x \\ y \end{bmatrix}^\wedge = \begin{bmatrix} 0 & -\theta & x \\ \theta & 0 & y \\ 0 & 0 & 0 \end{bmatrix}\end{split}\]
+

and the \((\cdot)^\vee\) operator simply does the exact inverse of \((\cdot)^\wedge\). We can implement them as follows.

+
+
[28]:
+
+
+
%reset -f
+import numpy as np
+
+# Helper functions for SE(2)
+def wedge_se2(x):
+    return np.array([[   0, -x[0], x[1]],
+                     [x[0],     0, x[2]],
+                     [   0,     0,    0]])
+
+def vee_se2(X):
+    return np.array([X[1, 0], X[0, 2], X[1, 2]])
+
+
+
+

Two other fundamental relationships appearing in Lie group theory are the exponential (denoted \(\exp\)) and logarithmic (denoted \(\log\)) maps. While these have a deeper definition, for our case it suffices to think of them as simply the matrix exponential and matrix logarithm. Using the wedge and vee operators for \(SE(2)\) defined above, we can convert a 3x1 vector to +an \(SE(2)\) element and back as follows

+
+
[32]:
+
+
+
from scipy.linalg import expm, logm
+
+T = expm(wedge_se2(np.array([0.1, 0.2, 0.3])))
+print("An element of SE2:")
+print(T)
+
+x = vee_se2(logm(T))
+print("\nThe original vector 'representing' it:")
+print(x)
+
+
+
+
+
+
+
+
+An element of SE2:
+[[ 0.99500417 -0.09983342  0.18467933]
+ [ 0.09983342  0.99500417  0.30949192]
+ [ 0.          0.          1.        ]]
+
+The original vector 'representing' it:
+[0.1 0.2 0.3]
+
+
+

We now have the tools we need to abstract-ify our problem a little bit. As commonly seen in the literature, we can define the so-called “oplus” and “ominus” operators as follows (sometimes called “boxplus” \(\boxplus\) and “boxminus” \(\boxminus\)):

+
+\[\begin{split}\begin{aligned} +\mathbf{T}_2 &= \mathbf{T}_1 \oplus \boldsymbol{\xi} := \mathbf{T}_1 \exp(\boldsymbol{\xi}^\wedge) \\ +\boldsymbol{\varepsilon} &= \mathbf{T}_2 \ominus \mathbf{T}_1 := \log(\mathbf{T}_2^{-1} \mathbf{T}_1)^\vee +\end{aligned}\end{split}\]
+

Here, both \(\boldsymbol{\varepsilon}, \boldsymbol{\xi} \in \mathbb{R}^3\) are 3x1 vectors. The \(\oplus: SE(2) \times \mathbb{R}^3 \to SE(2)\) operator “adds” a vector to an \(SE(2)\) element to produce another \(SE(2)\) element, and the \(\ominus:SE(2) \times SE(2) \to \mathbb{R}^3\) operator “subtracts” two \(SE(2)\) elements to produce a vector that represents the “difference” between them.

+

With this context, lets implement an \(SE(2)\) state inside navlie’s framework. To define a custom state, you must subclass the nav.State abstract class and you must implement the plus, minus, and copy methods. These methods play exactly the role of \(\oplus\) and \(\ominus\) described above, while the copy method is used to create a deep copy of that state object. In addition, state objects must hold an integer property named dof that specifies the degrees +of freedom associated with that state. For \(SE(2)\), this is 3.

+
+
[8]:
+
+
+
import navlie as nav
+
+class SE2State(nav.State):
+    def __init__(self, value :np.ndarray, stamp: float):
+        super().__init__(value=value, dof=3, stamp=stamp)
+
+    def plus(self, dx: np.ndarray):
+        new_value = self.value @ expm(wedge_se2(dx))
+        return SE2State(new_value, self.stamp)
+
+    def minus(self, other: "SE2State"):
+        other_inv = np.linalg.inv(other.value)
+        return vee_se2(logm(other_inv @ self.value))
+
+    def copy(self):
+        return SE2State(self.value.copy(), self.stamp)
+
+x = SE2State(np.eye(3), 0.0)
+print(x)
+
+
+
+
+
+
+
+
+SE2State(stamp=0.0, dof=3, state_id=None)
+    [[1. 0. 0.]
+     [0. 1. 0.]
+     [0. 0. 1.]]
+
+
+
+
+

Define the Process Model

+

Now, we must adapt the process model to work with our new SE2State. It is well known that the rotational kinematics can be written directly in terms of rotation matrices using

+
+\[\begin{split}\dot{\mathbf{C}}_{ab} = \mathbf{C}_{ab}\begin{bmatrix}0 & -\omega \\ \omega & 0 \end{bmatrix}\end{split}\]
+

and that the translational kinematics can be written in vector form using

+
+\[\begin{split}\dot{\mathbf{r}}_a = \mathbf{C}_{ab} \begin{bmatrix} v \\ 0 \end{bmatrix} .\end{split}\]
+

By stacking these into matrices it follows that

+
+\[\dot{\mathbf{T}} = \mathbf{T} \boldsymbol{\varpi}^\wedge\]
+

where \(\boldsymbol{\varpi} = [\omega, v, 0]^T\). This equation is now a linear, matrix-valued ODE, and can be integrated exactly over a short duration \(\Delta t = t_{k+1} - t_k\) using the matrix exponential. This gives us the following discrete-time process model:

+
+\[\mathbf{T}_{k+1} = \mathbf{T}_k \exp(\boldsymbol{\varpi}_k^\wedge \Delta t)\]
+

which we can implement as follows

+
+
[9]:
+
+
+
class WheeledRobotSE2(nav.ProcessModel):
+    def __init__(self, input_covariance_matrix):
+        self.Q = input_covariance_matrix
+
+    def evaluate(self, x:SE2State, u:nav.lib.VectorInput, dt:float):
+        vel = np.array([u.value[0], u.value[1], 0])
+        x_next = x.copy()
+        x_next.value = x.value @ expm(wedge_se2(vel * dt))
+        return x_next
+
+    def input_covariance(self, x:SE2State, u:nav.lib.VectorInput, dt:float):
+        return self.Q
+
+Q = np.eye(2) * 0.1**2
+process_model = WheeledRobotSE2(Q)
+
+
+
+
+
+

Define the Measurement Model

+

Finally, our measurement model remains largely unchanged. We just need to extract the position from an SE2State object now, as done below.

+
+
[10]:
+
+
+
class RangeToLandmarkSE2(nav.MeasurementModel):
+    def __init__(
+        self,
+        landmark_position: np.ndarray,
+        measurement_covariance: float,
+    ):
+        self.landmark_position = landmark_position
+        self.R = measurement_covariance
+
+    def evaluate(self, x: SE2State):
+        pos = x.value[0:2, 2]
+        return np.linalg.norm(pos - self.landmark_position)
+
+    def covariance(self, x: SE2State):
+        return self.R
+
+
+landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])
+meas_models = [RangeToLandmarkSE2(landmark,  0.1**2) for landmark in landmarks]
+
+
+
+
+
+

Run the Filter!

+

And that’s it! All remaining snippets are now literally copy-pasted from our previous approach with zero modifications. Using the abstraction framework in navlie, we can easily switch between different state representations and process/measurement models without having to change any of data generation or filtering code.

+
+
[ ]:
+
+
+
dg = nav.DataGenerator(
+    process_model=process_model,                  # process model to use
+    input_func=lambda t, x: np.array([0.5, 0.3]), # a callable that specifies the input values over time
+    input_covariance= Q,                          # numpy array or callable that specifies the input covariance over time
+    input_freq=50,                                # the frequency (Hz) at which the input is sampled (and the process model integrated)
+    meas_model_list=meas_models,                  # a list of measurement models to use
+    meas_freq_list=[10, 10, 10, 10]               # corresponding measurement frequencies (Hz)
+)
+
+state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)
+
+print(state_data[1])
+print(input_data[2])
+print(meas_data[3])
+
+
+
+
+
+
+
+
+SE2State(stamp=0.02, dof=3, state_id=None)
+    [[ 9.99950000e-01 -9.99983333e-03  5.99990000e-03]
+     [ 9.99983333e-03  9.99950000e-01  2.99997500e-05]
+     [ 0.00000000e+00  0.00000000e+00  1.00000000e+00]]
+VectorInput(stamp=0.04, state_id=None)
+    [0.52438924 0.40056502]
+Measurement(stamp=0.0, state_id=None) of PoseRangeToLandMark
+    2.299276237837416
+
+
+
+
[12]:
+
+
+
# First, define the filter
+kalman_filter = nav.ExtendedKalmanFilter(process_model)
+P0 = np.diag([0.1**2, 1**2, 1**2])  # Initial covariance
+x = nav.StateWithCovariance(x, P0)  # Estimate and covariance in one container
+
+meas_idx = 0
+y = meas_data[meas_idx]
+estimates = []
+for k in range(len(input_data) - 1):
+    u = input_data[k]
+
+    # Fuse any measurements that have occurred.
+    while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):
+        x = kalman_filter.correct(x, y, u)
+
+        # Load the next measurement
+        meas_idx += 1
+        if meas_idx < len(meas_data):
+            y = meas_data[meas_idx]
+
+    # Predict until the next input is available
+    dt = input_data[k + 1].stamp - x.state.stamp
+    x = kalman_filter.predict(x, u, dt)
+
+    estimates.append(x.copy())
+
+
+results = nav.GaussianResultList.from_estimates(estimates, state_data)
+
+import matplotlib.pyplot as plt
+fig, axs = nav.plot_error(results)
+axs[0].set_title("Estimation Errors")
+axs[0].set_ylabel("theta (rad)")
+axs[1].set_ylabel("x (m)")
+axs[2].set_ylabel("y (m)")
+axs[2].set_xlabel("Time (s)")
+
+fig, ax = nav.plot_nees(results)
+ax.set_title("NEES")
+ax.set_xlabel("Time (s)")
+plt.show()
+
+
+
+
+
+
+
+../_images/tutorial_lie_groups_12_0.png +
+
+
+
+
+
+../_images/tutorial_lie_groups_12_1.png +
+
+
+
+

Built-in Lie group states

+

While we implemented our own SE2State from scratch here for pedagogical purposes, navlie comes with many built-in Lie group states that you can use out of the box. Some of the built-in Lie group states include:

+
    +

  • nav.lib.SO2State: representing 2D rotations using, beloning to the group \(SO(2)\)

    • +

  • nav.lib.SO3State: representing 3D rotations using, beloning to the group \(SO(3)\)

    • +

  • nav.lib.SE2State: representing 2D poses using, beloning to the group \(SE(2)\)

    • +

  • nav.lib.SE3State: representing 3D poses using, beloning to the group \(SE(3)\)

    • +

  • nav.lib.SE23State: representing “extended” poses that also contain velocity information, belonging to the group \(SE_2(3)\)

    • +

  • nav.lib.SL3State: representing 3D homographies, belonging to the group \(SL(3)\)

    • +
+

Each of these classes stores the value as a square numpy array in the x.value property. Moreover, closed-form formulas for the exponential and logarithmic maps have been implemented for each of these states, which is faster than using scipy.linalg.expm and scipy.linalg.logm. These underlying operations have even been implemented in C++ for maximum speed.

+
+
+ + +
+ + + +
+ + +
+

previous

+

Toy Problem - Traditional Approach

+
+ + +
+

next

+

Jacobians in navlie

+
+ + +
+ +
+ + +
+
+ + +
+
+ +
+

+ © Copyright 2022.
+

+
+ +
+

+Created using Sphinx 7.1.2.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/_build/html/tutorial/lie_groups.ipynb b/_build/html/tutorial/lie_groups.ipynb new file mode 100644 index 00000000..75ce7373 --- /dev/null +++ b/_build/html/tutorial/lie_groups.ipynb @@ -0,0 +1,424 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Lie group approach\n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "Another way we could approach the same state estimation task is to instead use Lie group theory, which is becoming increasingly common practice in state estimation. Lie group theory can be very abstract, and the main references that navlie refer to are the following:\n", + "\n", + "1. [A micro Lie theory for state estimation in robotics](https://arxiv.org/abs/1812.01537)\n", + "2. [T.Barfoot, State Estimation for Robotics](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf)\n", + "\n", + "\n", + "## Define the State\n", + "Instead of representing the state using a vector, we will represent the state using an element of the *special Euclidean group* $SE(2)$, sometimes called *pose transformation matrices*. Elements of this group are 3x3 matrices of the form \n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab}(\\theta) & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2)\n", + "$$\n", + "\n", + "where $\\mathbf{r}_a = [x,y]^T$ again denotes the position of the robot and $\\mathbf{C}_{ab}(\\theta) \\in SO(2)$ is a rotation matrix (sometimes called a direction cosine matrix) with the form \n", + "\n", + "$$ \n", + "\\mathbf{C}_{ab}(\\theta) = \\begin{bmatrix} \\cos \\theta & - \\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{bmatrix}.\n", + "$$\n", + "\n", + "The rotation matrix transforms vectors resolved in one frame to another frame, i.e. $\\mathbf{r}_a = \\mathbf{C}_{ab} \\mathbf{r}_b$. Unlike vectors, elements of $SO(2)$ or $SE(2)$ cannot be added together to produce another valid element of $SE(2)$, but they can be multiplied together with the result still having the same form.\n", + "\n", + "$$\n", + "\\mathbf{T}_1 \\mathbf{T}_2 \\in SE(2)\n", + "$$\n", + "\n", + " To proceed further with our mathematical setup, we need to define a few very common operators seen in Lie group theory. The first two are the \"wedge\" $(\\cdot)^\\wedge$ and \"vee\" $(\\cdot)^\\vee$ operators, which for this specific group has the form\n", + "\n", + "$$ \n", + "\\begin{bmatrix} \\theta \\\\ x \\\\ y \\end{bmatrix}^\\wedge = \\begin{bmatrix} 0 & -\\theta & x \\\\ \\theta & 0 & y \\\\ 0 & 0 & 0 \\end{bmatrix}\n", + "$$\n", + "\n", + "and the $(\\cdot)^\\vee$ operator simply does the exact inverse of $(\\cdot)^\\wedge$. We can implement them as follows.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "%reset -f\n", + "import numpy as np\n", + "\n", + "# Helper functions for SE(2)\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def vee_se2(X):\n", + " return np.array([X[1, 0], X[0, 2], X[1, 2]])\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Two other fundamental relationships appearing in Lie group theory are the exponential (denoted $\\exp$) and logarithmic (denoted $\\log$) maps. While these have a deeper definition, for our case it suffices to think of them as simply the [matrix exponential](https://en.wikipedia.org/wiki/Matrix_exponential) and [matrix logarithm](https://en.wikipedia.org/wiki/Logarithm_of_a_matrix). Using the wedge and vee operators for $SE(2)$ defined above, we can convert a 3x1 vector to an $SE(2)$ element and back as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "An element of SE2:\n", + "[[ 0.99500417 -0.09983342 0.18467933]\n", + " [ 0.09983342 0.99500417 0.30949192]\n", + " [ 0. 0. 1. ]]\n", + "\n", + "The original vector 'representing' it:\n", + "[0.1 0.2 0.3]\n" + ] + } + ], + "source": [ + "from scipy.linalg import expm, logm\n", + "\n", + "T = expm(wedge_se2(np.array([0.1, 0.2, 0.3])))\n", + "print(\"An element of SE2:\")\n", + "print(T)\n", + "\n", + "x = vee_se2(logm(T))\n", + "print(\"\\nThe original vector 'representing' it:\")\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have the tools we need to abstract-ify our problem a little bit. As commonly seen in the literature, we can define the so-called \"oplus\" and \"ominus\" operators as follows (sometimes called \"boxplus\" $\\boxplus$ and \"boxminus\" $\\boxminus$):\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbf{T}_2 &= \\mathbf{T}_1 \\oplus \\boldsymbol{\\xi} := \\mathbf{T}_1 \\exp(\\boldsymbol{\\xi}^\\wedge) \\\\\n", + "\\boldsymbol{\\varepsilon} &= \\mathbf{T}_2 \\ominus \\mathbf{T}_1 := \\log(\\mathbf{T}_2^{-1} \\mathbf{T}_1)^\\vee\n", + "\\end{aligned}\n", + "$$ \n", + "\n", + "Here, both $\\boldsymbol{\\varepsilon}, \\boldsymbol{\\xi} \\in \\mathbb{R}^3$ are 3x1 vectors. The $\\oplus: SE(2) \\times \\mathbb{R}^3 \\to SE(2)$ operator \"adds\" a vector to an $SE(2)$ element to produce another $SE(2)$ element, and the $\\ominus:SE(2) \\times SE(2) \\to \\mathbb{R}^3$ operator \"subtracts\" two $SE(2)$ elements to produce a vector that represents the \"difference\" between them. \n", + "\n", + "\n", + "With this context, lets implement an $SE(2)$ state inside navlie's framework. To define a custom state, you must subclass the `nav.State` abstract class and you *must* implement the `plus`, `minus`, and `copy` methods. These methods play exactly the role of $\\oplus$ and $\\ominus$ described above, while the `copy` method is used to create a deep copy of that state object. In addition, state objects must hold an integer property named `dof` that specifies the *degrees of freedom* associated with that state. For $SE(2)$, this is 3." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.0, dof=3, state_id=None)\n", + " [[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n" + ] + } + ], + "source": [ + "import navlie as nav\n", + "\n", + "class SE2State(nav.State):\n", + " def __init__(self, value :np.ndarray, stamp: float):\n", + " super().__init__(value=value, dof=3, stamp=stamp)\n", + "\n", + " def plus(self, dx: np.ndarray):\n", + " new_value = self.value @ expm(wedge_se2(dx))\n", + " return SE2State(new_value, self.stamp)\n", + "\n", + " def minus(self, other: \"SE2State\"):\n", + " other_inv = np.linalg.inv(other.value)\n", + " return vee_se2(logm(other_inv @ self.value))\n", + " \n", + " def copy(self):\n", + " return SE2State(self.value.copy(), self.stamp)\n", + "\n", + "x = SE2State(np.eye(3), 0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Process Model\n", + "\n", + "Now, we must adapt the process model to work with our new `SE2State`. It is well known that the rotational kinematics can be written directly in terms of rotation matrices using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{C}}_{ab} = \\mathbf{C}_{ab}\\begin{bmatrix}0 & -\\omega \\\\ \\omega & 0 \\end{bmatrix} \n", + "$$\n", + "\n", + "and that the translational kinematics can be written in vector form using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{r}}_a = \\mathbf{C}_{ab} \\begin{bmatrix} v \\\\ 0 \\end{bmatrix} .\n", + "$$\n", + "\n", + "By stacking these into matrices it follows that \n", + "$$ \n", + "\\dot{\\mathbf{T}} = \\mathbf{T} \\boldsymbol{\\varpi}^\\wedge\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\varpi} = [\\omega, v, 0]^T$. This equation is now a linear, matrix-valued ODE, and can be integrated exactly over a short duration $\\Delta t = t_{k+1} - t_k$ using the matrix exponential. This gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}_k^\\wedge \\Delta t)\n", + "$$\n", + "\n", + "which we can implement as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " vel = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(vel * dt))\n", + " return x_next\n", + " \n", + " def input_covariance(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Measurement Model\n", + "\n", + "Finally, our measurement model remains largely unchanged. We just need to extract the position from an `SE2State` object now, as done below." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: SE2State):\n", + " return self.R\n", + " \n", + "\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmarkSE2(landmark, 0.1**2) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run the Filter!\n", + "\n", + "And that's it! All remaining snippets are now _literally_ copy-pasted from our previous approach with zero modifications. Using the abstraction framework in navlie, we can easily switch between different state representations and process/measurement models without having to change any of data generation or filtering code. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.02, dof=3, state_id=None)\n", + " [[ 9.99950000e-01 -9.99983333e-03 5.99990000e-03]\n", + " [ 9.99983333e-03 9.99950000e-01 2.99997500e-05]\n", + " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00]]\n", + "VectorInput(stamp=0.04, state_id=None)\n", + " [0.52438924 0.40056502]\n", + "Measurement(stamp=0.0, state_id=None) of PoseRangeToLandMark\n", + " 2.299276237837416\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.5, 0.3]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[1])\n", + "print(input_data[2])\n", + "print(meas_data[3])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Built-in Lie group states \n", + "While we implemented our own `SE2State` from scratch here for pedagogical purposes, navlie comes with many built-in Lie group states that you can use out of the box. Some of the built-in Lie group states include:\n", + "\n", + "- `nav.lib.SO2State`: representing 2D rotations using, beloning to the group $SO(2)$\n", + "- `nav.lib.SO3State`: representing 3D rotations using, beloning to the group $SO(3)$\n", + "- `nav.lib.SE2State`: representing 2D poses using, beloning to the group $SE(2)$\n", + "- `nav.lib.SE3State`: representing 3D poses using, beloning to the group $SE(3)$\n", + "- `nav.lib.SE23State`: representing \"extended\" poses that also contain velocity information, belonging to the group $SE_2(3)$\n", + "- `nav.lib.SL3State`: representing 3D homographies, belonging to the group $SL(3)$\n", + "\n", + "Each of these classes stores the value as a square numpy array in the `x.value` property. Moreover, closed-form formulas for the exponential and logarithmic maps have been implemented for each of these states, which is faster than using `scipy.linalg.expm` and `scipy.linalg.logm`. These underlying operations have even been implemented in C++ for maximum speed. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/_build/html/tutorial/traditional.html b/_build/html/tutorial/traditional.html new file mode 100644 index 00000000..2b3da45c --- /dev/null +++ b/_build/html/tutorial/traditional.html @@ -0,0 +1,537 @@ + + + + + + + + Toy Problem - Traditional Approach — navlie 0.1.0 documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ On this page +
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+

Toy Problem - Traditional Approach

+

In this tutorial, we’ll simulate a simple 2D localization problem as per the figure below. We’ll assume that we have a robot following a simple body-frame-velocity model, which has access to noisy measurements of its forward velocity \(v\) and angular velocity \(\omega\). In addition, this robot will have a time-of-flight sensor that gives it range measurements to a few known landmarks in the environment.

+

Toy Problem

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+

Define the State

+

The first step is to define the state of the robot. We’ll start with a more traditional approach and define the state of the robot to be a vector of the form \(\mathbf{x} = [\theta, x, y ]^T\), where \(x\) and \(y\) are the robot’s position in the world and \(\theta\) is its orientation. We’ll also define the control inputs to be \(\mathbf{u} = [\omega, v]^T\), the robot’s forward and angular velocity. The process (motion) model of the robot is then given by:

+
+\[\begin{split}\begin{aligned} + \dot{\theta} &= \omega,\\ + \dot{x} &= v \cos(\theta), \\ + \dot{y} &= v \sin(\theta). +\end{aligned}\end{split}\]
+

However, this is in continuous time, and we need to discretize it to use it in a filter. For now, we’ll use the simple Euler discretization method, which gives us the following discrete-time process model:

+
+\[\begin{split}\begin{aligned} + \theta_{k+1} &= \theta_k + \omega_k \Delta t, \\ + x_{k+1} &= x_k + v_k \cos(\theta_k) \Delta t, \\ + y_{k+1} &= y_k + v_k \sin(\theta_k) \Delta t. +\end{aligned}\end{split}\]
+

Lets now code up our state and process model using navlie’s framework. Since our state is just a regular 3x1 vector, we can use a standard type from the built-in library: navlie.lib.VectorState

+
+
[2]:
+
+
+
import numpy as np
+np.random.seed(0)
+import navlie as nav
+from navlie.lib import VectorState
+
+x = VectorState([0, 0, 0], stamp=0.0)
+print(x)
+
+
+
+
+
+
+
+
+VectorState(stamp=0.0, dof=3, state_id=None)
+    [0. 0. 0.]
+
+
+

The VectorState is a subclass of the abstract State class in navlie, which is one of the core primitive types. The value of the state is stored as a numpy array, and can be accessed directly through x.value.

+
+
+

Define the Process Model

+

For the process model, we’ll choose to define our own from scratch here. Process models in navlie must inherit from the abstract navlie.ProcessModel class and implement the evaluate and either the input_covariance or covariance methods.

+
+
[3]:
+
+
+
from navlie.lib import VectorInput
+
+Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation
+
+class WheeledRobot(nav.ProcessModel):
+    def __init__(self, input_covariance):
+        self.Q = input_covariance
+
+    def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:
+        x_next = x.copy()
+        x_next.value[0] += u.value[0] * dt
+        x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])
+        x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])
+        return x_next
+
+    def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:
+        return self.Q
+
+process_model = WheeledRobot(Q) # instantiate it
+
+
+
+

The methods in navlie process models must always accept the arguments shown above: a State object, an Input object, and a float dt. The evaluate method must always return a valid (i.e. subclass of a) State object, and the input_covariance method must always return a square numpy array. There are more optional methods that can be implemented for performance reasons, but we will cover those later.

+
+
+

Define the Measurement Model(s)

+

Moving on to the measurement model, if \(\mathbf{r}_a = [x,y]^T\) denotes the position vector of the robot resolved in the world frame, and \(\mathbf{\ell}^{(i)}_{a} \in \mathbb{R}^2\) is the 2 x 1 position vector of landmark \(i\), then the measurement model for each landmark is simply

+
+\[y_i = ||\mathbf{r}_a - \mathbf{\ell}^{(i)}_{a}||\]
+

In navlie, measurement models must be implemented in a similar way to process models: inherit from the navlie.MeasurementModel abstract class, and then implement the evaluate and covariance methods. Here’s an example for this problem:

+
+
[23]:
+
+
+
class RangeToLandmark(nav.MeasurementModel):
+    def __init__(self, landmark_position: np.ndarray):
+        self.landmark_position = landmark_position
+
+    def evaluate(self, x: VectorState) -> np.ndarray:
+        return np.linalg.norm(x.value[1:] - self.landmark_position)
+
+    def covariance(self, x: VectorState) -> np.ndarray:
+        return 0.1**2
+
+landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])
+meas_models = [RangeToLandmark(landmark) for landmark in landmarks]
+
+
+
+
+
+

(Simulation only) Generate fake data

+

The next step is to generate some fake data for our simulation (although navlie is also compatible with real data). To do this, we will use the DataGenerator class which is used as follows

+
+
[24]:
+
+
+
dg = nav.DataGenerator(
+    process_model=process_model,                  # process model to use
+    input_func=lambda t, x: np.array([0.3, 0.5]), # a callable that specifies the input values over time
+    input_covariance= Q,                          # numpy array or callable that specifies the input covariance over time
+    input_freq=50,                                # the frequency (Hz) at which the input is sampled (and the process model integrated)
+    meas_model_list=meas_models,                  # a list of measurement models to use
+    meas_freq_list=[10, 10, 10, 10]               # corresponding measurement frequencies (Hz)
+)
+
+state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)
+
+print(state_data[0])
+print(input_data[0])
+print(meas_data[0])
+
+
+
+
+
+
+
+
+VectorState(stamp=0.0, dof=3, state_id=None)
+    [0. 0. 0.]
+VectorInput(stamp=0.0, state_id=None)
+    [0.4867558  0.40227221]
+Measurement(stamp=0.0, state_id=None) of RangeToLandmark
+    1.5906187969698615
+
+
+

The output of the DataGenerator.generate method is three lists: a list of ground-truth State objects, a list of Input objects, and a list of Measurement objects, with the input/measurement lists possibly being corrupted by random noise if the noise=True flag is set. Each item in these lists correspond to different points in time. We can plot the trajectory as follows

+
+
[25]:
+
+
+
import matplotlib.pyplot as plt
+
+# Plot the state trajectory
+pos = np.array([state.value[1:] for state in state_data])
+plt.plot(pos[:, 0], pos[:, 1])
+plt.scatter(landmarks[:, 0], landmarks[:, 1])
+# add labels
+for i, landmark in enumerate(landmarks):
+    plt.annotate(f"Landmark {i}", landmark)
+plt.xlabel("x")
+plt.ylabel("y")
+plt.title("Simulated Trajectory")
+plt.axis("equal")
+
+
+# Plot the input data
+plt.figure()
+u_array = np.array([u.value for u in input_data])
+u_stamps = np.array([u.stamp for u in input_data])
+plt.plot(u_stamps, u_array[:, 0], label="omega")
+plt.plot(u_stamps, u_array[:, 1], label="v")
+plt.xlabel("Time (s)")
+plt.ylabel("Input")
+plt.title("Input Data")
+plt.legend()
+plt.show()
+
+
+
+
+
+
+
+../_images/tutorial_traditional_9_0.png +
+
+
+
+
+
+../_images/tutorial_traditional_9_1.png +
+
+
+
+

Run a filter!

+

Finally, lets run an extended Kalman filter on this data to get a state estimate that uses only the noisy measurements. In the below filter, we instantiate the ExtendedKalmanFilter to use on our data, and looping over the input measurements while also calling the correction step whenever a measurement occurs.

+
+
[26]:
+
+
+
# First, define the filter
+kalman_filter = nav.ExtendedKalmanFilter(process_model)
+
+# You can try other filters too!
+# kalman_filter = nav.UnscentedKalmanFilter(process_model)
+# kalman_filter = nav.IteratedKalmanFIlter(process_model)
+
+P0 = np.diag([0.1**2, 1**2, 1**2])  # Initial covariance
+x = nav.StateWithCovariance(x, P0)  # Estimate and covariance in one container
+
+meas_idx = 0
+y = meas_data[meas_idx]
+estimates = []
+for k in range(len(input_data) - 1):
+    u = input_data[k]
+
+    # Fuse any measurements that have occurred.
+    while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):
+        x = kalman_filter.correct(x, y, u)
+
+        # Load the next measurement
+        meas_idx += 1
+        if meas_idx < len(meas_data):
+            y = meas_data[meas_idx]
+
+    # Predict until the next input is available
+    dt = input_data[k + 1].stamp - x.state.stamp
+    x = kalman_filter.predict(x, u, dt)
+
+    estimates.append(x.copy())
+
+
+
+

The filters in navlie are all designed to be stateless: this means that the actual state estimate is stored externally to the filter objects, in this case in a container called StateWithCovariance. Although this adds a slight burden on the user, it has the advantage of being more transparent, and also providing the ability to combine different filters in the same loop! For example, you could use an EKF for the prediction, but a UKF for +the correction, or even to use different filters for different measurement models!

+

Once estimates have been obtained, we will often be interested in evaluating the performance. The GaussianResultList object is a useful container for evaluating the quality of the state estimates when ground truth data is available. It calculates useful metrics such as raw error, Mahalanobis distance, and normalized estimation error squared (NEES).

+
+
[27]:
+
+
+
results = nav.GaussianResultList.from_estimates(estimates, state_data)
+# results.nees
+# results.three_sigma
+# results.error
+# results.md # mahalanobis distance
+# # and more...
+
+# Some plotting functions that work directly with GaussianResultList
+fig, axs = nav.plot_error(results)
+axs[0].set_title("Estimation Errors")
+axs[0].set_ylabel("theta (rad)")
+axs[1].set_ylabel("x (m)")
+axs[2].set_ylabel("y (m)")
+axs[2].set_xlabel("Time (s)")
+
+fig, ax = nav.plot_nees(results)
+ax.set_title("NEES")
+ax.set_xlabel("Time (s)")
+plt.show()
+
+
+
+
+
+
+
+../_images/tutorial_traditional_13_0.png +
+
+
+
+
+
+../_images/tutorial_traditional_13_1.png +
+
+

As a final note, GaussianResultList will invoke the State.minus method of the state objects to calculate the error. As we will see next, this allows us to implement a custom measure of error, when it might not make sense to directly subtract two of our state objects.

+
+
+ + +
+ + + +
+ + +
+

previous

+

Getting Started

+
+ + +
+

next

+

Toy Problem - Lie group approach

+
+ + +
+ +
+ + +
+
+ + +
+
+ +
+

+ © Copyright 2022.
+

+
+ +
+

+Created using Sphinx 7.1.2.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/_build/html/tutorial/traditional.ipynb b/_build/html/tutorial/traditional.ipynb new file mode 100644 index 00000000..4db74a60 --- /dev/null +++ b/_build/html/tutorial/traditional.ipynb @@ -0,0 +1,392 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Traditional Approach\n", + "\n", + "In this tutorial, we'll simulate a simple 2D localization problem as per the figure below. We'll assume that we have a robot following a simple body-frame-velocity model, which has access to noisy measurements of its forward velocity $v$ and angular velocity $\\omega$. In addition, this robot will have a time-of-flight sensor that gives it range measurements to a few known landmarks in the environment. \n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "\n", + "## Define the State\n", + "The first step is to define the state of the robot. We'll start with a more traditional approach and define the state of the robot to be a vector of the form $\\mathbf{x} = [\\theta, x, y ]^T$, where $x$ and $y$ are the robot's position in the world and $\\theta$ is its orientation. We'll also define the control inputs to be $\\mathbf{u} = [\\omega, v]^T$, the robot's forward and angular velocity. The process (motion) model of the robot is then given by:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\dot{\\theta} &= \\omega,\\\\\n", + " \\dot{x} &= v \\cos(\\theta), \\\\\n", + " \\dot{y} &= v \\sin(\\theta). \n", + "\\end{aligned}\n", + "$$\n", + "\n", + "However, this is in continuous time, and we need to discretize it to use it in a filter. For now, we'll use the simple Euler discretization method, which gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t, \\\\\n", + " x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t, \\\\\n", + " y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t.\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Lets now code up our state and process model using navlie's framework. Since our state is just a regular 3x1 vector, we can use a standard type from the built-in library: [navlie.lib.VectorState](../_autosummary/navlie.lib.states.VectorState.rst)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "np.random.seed(0)\n", + "import navlie as nav\n", + "from navlie.lib import VectorState\n", + "\n", + "x = VectorState([0, 0, 0], stamp=0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `VectorState` is a subclass of the abstract [State](../_autosummary/navlie.types.State.rst) class in navlie, which is one of the core primitive types. The value of the state is stored as a numpy array, and can be accessed directly through `x.value`. \n", + "\n", + "\n", + "## Define the Process Model\n", + "For the process model, we'll choose to define our own from scratch here. Process models in navlie *must* inherit from the abstract [navlie.ProcessModel](../_autosummary/navlie.types.ProcessModel.rst) class and implement the `evaluate` and either the `input_covariance` or `covariance` methods." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "from navlie.lib import VectorInput\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The methods in navlie process models must always accept the arguments shown above: a `State` object, an `Input` object, and a float `dt`. The `evaluate` method must always return a valid (i.e. subclass of a) `State` object, and the `input_covariance` method must always return a square numpy array. There are more optional methods that can be implemented for performance reasons, but we will cover those later.\n", + "\n", + "## Define the Measurement Model(s)\n", + "Moving on to the measurement model, if $\\mathbf{r}_a = [x,y]^T$ denotes the position vector of the robot resolved in the world frame, and $\\mathbf{\\ell}^{(i)}_{a} \\in \\mathbb{R}^2$ is the 2 x 1 position vector of landmark $i$, then the measurement model for each landmark is simply \n", + "\n", + "$$ \n", + "y_i = ||\\mathbf{r}_a - \\mathbf{\\ell}^{(i)}_{a}||\n", + "$$\n", + "\n", + "In navlie, measurement models must be implemented in a similar way to process models: inherit from the [navlie.MeasurementModel](../_autosummary/navlie.types.MeasurementModel.rst) abstract class, and then implement the `evaluate` and `covariance` methods. Here's an example for this problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmark(landmark) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## (Simulation only) Generate fake data\n", + "\n", + "The next step is to generate some fake data for our simulation (although navlie is also compatible with real data). To do this, we will use the [DataGenerator](../_autosummary/navlie.datagen.DataGenerator.rst) class which is used as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n", + "VectorInput(stamp=0.0, state_id=None)\n", + " [0.4867558 0.40227221]\n", + "Measurement(stamp=0.0, state_id=None) of RangeToLandmark\n", + " 1.5906187969698615\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.3, 0.5]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[0])\n", + "print(input_data[0])\n", + "print(meas_data[0])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output of the `DataGenerator.generate` method is three lists: a list of ground-truth `State` objects, a list of `Input` objects, and a list of [Measurement](../_autosummary/navlie.types.Measurement.rst) objects, with the input/measurement lists possibly being corrupted by random noise if the `noise=True` flag is set. Each item in these lists correspond to different points in time. We can plot the trajectory as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Plot the state trajectory\n", + "pos = np.array([state.value[1:] for state in state_data])\n", + "plt.plot(pos[:, 0], pos[:, 1])\n", + "plt.scatter(landmarks[:, 0], landmarks[:, 1])\n", + "# add labels\n", + "for i, landmark in enumerate(landmarks):\n", + " plt.annotate(f\"Landmark {i}\", landmark)\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "plt.title(\"Simulated Trajectory\")\n", + "plt.axis(\"equal\")\n", + "\n", + "\n", + "# Plot the input data\n", + "plt.figure()\n", + "u_array = np.array([u.value for u in input_data])\n", + "u_stamps = np.array([u.stamp for u in input_data])\n", + "plt.plot(u_stamps, u_array[:, 0], label=\"omega\")\n", + "plt.plot(u_stamps, u_array[:, 1], label=\"v\")\n", + "plt.xlabel(\"Time (s)\")\n", + "plt.ylabel(\"Input\")\n", + "plt.title(\"Input Data\")\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run a filter!\n", + "\n", + "Finally, lets run an extended Kalman filter on this data to get a state estimate that uses only the noisy measurements. In the below filter, we instantiate the [ExtendedKalmanFilter](../_autosummary/navlie.filters.ExtendedKalmanFilter.rst) to use on our data, and looping over the input measurements while also calling the correction step whenever a measurement occurs." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "\n", + "# You can try other filters too!\n", + "# kalman_filter = nav.UnscentedKalmanFilter(process_model)\n", + "# kalman_filter = nav.IteratedKalmanFIlter(process_model)\n", + "\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filters in navlie are all designed to be *stateless*: this means that the actual state estimate is stored externally to the filter objects, in this case in a container called [StateWithCovariance](../_autosummary/navlie.types.StateWithCovariance.rst). Although this adds a slight burden on the user, it has the advantage of being more transparent, and also providing the ability to combine different filters in the same loop! For example, you could use an EKF for the prediction, but a UKF for the correction, or even to use different filters for different measurement models!\n", + "\n", + "\n", + "Once estimates have been obtained, we will often be interested in evaluating the performance. The [GaussianResultList](../_autosummary/navlie.utils.GaussianResultList.rst) object is a useful container for evaluating the quality of the state estimates when ground truth data is available. It calculates useful metrics such as raw error, Mahalanobis distance, and normalized estimation error squared (NEES). " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "# results.nees \n", + "# results.three_sigma\n", + "# results.error\n", + "# results.md # mahalanobis distance\n", + "# # and more...\n", + "\n", + "# Some plotting functions that work directly with GaussianResultList\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a final note, `GaussianResultList` will invoke the `State.minus` method of the state objects to calculate the error. As we will see next, this allows us to implement a custom measure of error, when it might not make sense to directly subtract two of our state objects." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/index.html b/index.html new file mode 100644 index 00000000..0f0d91ff --- /dev/null +++ b/index.html @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/make.bat b/make.bat new file mode 100644 index 00000000..6247f7e2 --- /dev/null +++ b/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=source +set BUILDDIR=build + +if "%1" == "" goto help + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.http://sphinx-doc.org/ + exit /b 1 +) + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% + +:end +popd diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 00000000..6d9dc705 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,5 @@ +sphinx==7.1.2 +pandoc +nbsphinx +ipykernel +pydata-sphinx-theme==0.7.2 diff --git a/source/_autosummary/navlie.batch.estimator.BatchEstimator.rst b/source/_autosummary/navlie.batch.estimator.BatchEstimator.rst new file mode 100644 index 00000000..b4222adc --- /dev/null +++ b/source/_autosummary/navlie.batch.estimator.BatchEstimator.rst @@ -0,0 +1,10 @@ +navlie.batch.estimator.BatchEstimator +===================================== + +.. currentmodule:: navlie.batch.estimator + +.. autoclass:: BatchEstimator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.estimator.rst b/source/_autosummary/navlie.batch.estimator.rst new file mode 100644 index 00000000..29b2582d --- /dev/null +++ b/source/_autosummary/navlie.batch.estimator.rst @@ -0,0 +1,31 @@ +navlie.batch.estimator +====================== + +.. automodule:: navlie.batch.estimator + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + BatchEstimator + + + + + + + + + diff --git a/source/_autosummary/navlie.batch.gaussian_mixtures.GaussianMixtureResidual.rst b/source/_autosummary/navlie.batch.gaussian_mixtures.GaussianMixtureResidual.rst new file mode 100644 index 00000000..4cf8538f --- /dev/null +++ b/source/_autosummary/navlie.batch.gaussian_mixtures.GaussianMixtureResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.GaussianMixtureResidual +======================================================= + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: GaussianMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.gaussian_mixtures.HessianSumMixtureResidual.rst b/source/_autosummary/navlie.batch.gaussian_mixtures.HessianSumMixtureResidual.rst new file mode 100644 index 00000000..dacea608 --- /dev/null +++ b/source/_autosummary/navlie.batch.gaussian_mixtures.HessianSumMixtureResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.HessianSumMixtureResidual +========================================================= + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: HessianSumMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.gaussian_mixtures.MaxMixtureResidual.rst b/source/_autosummary/navlie.batch.gaussian_mixtures.MaxMixtureResidual.rst new file mode 100644 index 00000000..feb7ccc0 --- /dev/null +++ b/source/_autosummary/navlie.batch.gaussian_mixtures.MaxMixtureResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.MaxMixtureResidual +================================================== + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: MaxMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.gaussian_mixtures.MaxSumMixtureResidual.rst b/source/_autosummary/navlie.batch.gaussian_mixtures.MaxSumMixtureResidual.rst new file mode 100644 index 00000000..49b7a8d7 --- /dev/null +++ b/source/_autosummary/navlie.batch.gaussian_mixtures.MaxSumMixtureResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.MaxSumMixtureResidual +===================================================== + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: MaxSumMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.gaussian_mixtures.SumMixtureResidual.rst b/source/_autosummary/navlie.batch.gaussian_mixtures.SumMixtureResidual.rst new file mode 100644 index 00000000..be782443 --- /dev/null +++ b/source/_autosummary/navlie.batch.gaussian_mixtures.SumMixtureResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.gaussian\_mixtures.SumMixtureResidual +================================================== + +.. currentmodule:: navlie.batch.gaussian_mixtures + +.. autoclass:: SumMixtureResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.gaussian_mixtures.rst b/source/_autosummary/navlie.batch.gaussian_mixtures.rst new file mode 100644 index 00000000..91df23dd --- /dev/null +++ b/source/_autosummary/navlie.batch.gaussian_mixtures.rst @@ -0,0 +1,35 @@ +navlie.batch.gaussian\_mixtures +=============================== + +.. automodule:: navlie.batch.gaussian_mixtures + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + GaussianMixtureResidual + HessianSumMixtureResidual + MaxMixtureResidual + MaxSumMixtureResidual + SumMixtureResidual + + + + + + + + + diff --git a/source/_autosummary/navlie.batch.losses.CauchyLoss.rst b/source/_autosummary/navlie.batch.losses.CauchyLoss.rst new file mode 100644 index 00000000..8a2b1e42 --- /dev/null +++ b/source/_autosummary/navlie.batch.losses.CauchyLoss.rst @@ -0,0 +1,10 @@ +navlie.batch.losses.CauchyLoss +============================== + +.. currentmodule:: navlie.batch.losses + +.. autoclass:: CauchyLoss + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.losses.L2Loss.rst b/source/_autosummary/navlie.batch.losses.L2Loss.rst new file mode 100644 index 00000000..dbe005c2 --- /dev/null +++ b/source/_autosummary/navlie.batch.losses.L2Loss.rst @@ -0,0 +1,10 @@ +navlie.batch.losses.L2Loss +========================== + +.. currentmodule:: navlie.batch.losses + +.. autoclass:: L2Loss + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.losses.LossFunction.rst b/source/_autosummary/navlie.batch.losses.LossFunction.rst new file mode 100644 index 00000000..b275f496 --- /dev/null +++ b/source/_autosummary/navlie.batch.losses.LossFunction.rst @@ -0,0 +1,10 @@ +navlie.batch.losses.LossFunction +================================ + +.. currentmodule:: navlie.batch.losses + +.. autoclass:: LossFunction + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.losses.rst b/source/_autosummary/navlie.batch.losses.rst new file mode 100644 index 00000000..fc889ee2 --- /dev/null +++ b/source/_autosummary/navlie.batch.losses.rst @@ -0,0 +1,33 @@ +navlie.batch.losses +=================== + +.. automodule:: navlie.batch.losses + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + CauchyLoss + L2Loss + LossFunction + + + + + + + + + diff --git a/source/_autosummary/navlie.batch.problem.OptimizationSummary.rst b/source/_autosummary/navlie.batch.problem.OptimizationSummary.rst new file mode 100644 index 00000000..bcb8ee19 --- /dev/null +++ b/source/_autosummary/navlie.batch.problem.OptimizationSummary.rst @@ -0,0 +1,10 @@ +navlie.batch.problem.OptimizationSummary +======================================== + +.. currentmodule:: navlie.batch.problem + +.. autoclass:: OptimizationSummary + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.problem.Problem.rst b/source/_autosummary/navlie.batch.problem.Problem.rst new file mode 100644 index 00000000..40846284 --- /dev/null +++ b/source/_autosummary/navlie.batch.problem.Problem.rst @@ -0,0 +1,10 @@ +navlie.batch.problem.Problem +============================ + +.. currentmodule:: navlie.batch.problem + +.. autoclass:: Problem + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.problem.rst b/source/_autosummary/navlie.batch.problem.rst new file mode 100644 index 00000000..c85847bb --- /dev/null +++ b/source/_autosummary/navlie.batch.problem.rst @@ -0,0 +1,32 @@ +navlie.batch.problem +==================== + +.. automodule:: navlie.batch.problem + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + OptimizationSummary + Problem + + + + + + + + + diff --git a/source/_autosummary/navlie.batch.residuals.MeasurementResidual.rst b/source/_autosummary/navlie.batch.residuals.MeasurementResidual.rst new file mode 100644 index 00000000..b288b24c --- /dev/null +++ b/source/_autosummary/navlie.batch.residuals.MeasurementResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.residuals.MeasurementResidual +========================================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: MeasurementResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.residuals.PriorResidual.rst b/source/_autosummary/navlie.batch.residuals.PriorResidual.rst new file mode 100644 index 00000000..4976a042 --- /dev/null +++ b/source/_autosummary/navlie.batch.residuals.PriorResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.residuals.PriorResidual +==================================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: PriorResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.residuals.ProcessResidual.rst b/source/_autosummary/navlie.batch.residuals.ProcessResidual.rst new file mode 100644 index 00000000..33b29685 --- /dev/null +++ b/source/_autosummary/navlie.batch.residuals.ProcessResidual.rst @@ -0,0 +1,10 @@ +navlie.batch.residuals.ProcessResidual +====================================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: ProcessResidual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.residuals.Residual.rst b/source/_autosummary/navlie.batch.residuals.Residual.rst new file mode 100644 index 00000000..2752872c --- /dev/null +++ b/source/_autosummary/navlie.batch.residuals.Residual.rst @@ -0,0 +1,10 @@ +navlie.batch.residuals.Residual +=============================== + +.. currentmodule:: navlie.batch.residuals + +.. autoclass:: Residual + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.batch.residuals.rst b/source/_autosummary/navlie.batch.residuals.rst new file mode 100644 index 00000000..d9198a9f --- /dev/null +++ b/source/_autosummary/navlie.batch.residuals.rst @@ -0,0 +1,34 @@ +navlie.batch.residuals +====================== + +.. automodule:: navlie.batch.residuals + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + MeasurementResidual + PriorResidual + ProcessResidual + Residual + + + + + + + + + diff --git a/source/_autosummary/navlie.batch.rst b/source/_autosummary/navlie.batch.rst new file mode 100644 index 00000000..d327bc0e --- /dev/null +++ b/source/_autosummary/navlie.batch.rst @@ -0,0 +1,36 @@ +navlie.batch +============ + +.. automodule:: navlie.batch + + + + + + + + + + + + + + + + + + + +.. rubric:: Modules + +.. autosummary:: + :toctree: + :template: custom-module-template.rst + :recursive: + + navlie.batch.estimator + navlie.batch.gaussian_mixtures + navlie.batch.losses + navlie.batch.problem + navlie.batch.residuals + diff --git a/source/_autosummary/navlie.composite.CompositeInput.rst b/source/_autosummary/navlie.composite.CompositeInput.rst new file mode 100644 index 00000000..49444858 --- /dev/null +++ b/source/_autosummary/navlie.composite.CompositeInput.rst @@ -0,0 +1,10 @@ +navlie.composite.CompositeInput +=============================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeInput + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.composite.CompositeMeasurement.rst b/source/_autosummary/navlie.composite.CompositeMeasurement.rst new file mode 100644 index 00000000..3aa7b2c7 --- /dev/null +++ b/source/_autosummary/navlie.composite.CompositeMeasurement.rst @@ -0,0 +1,10 @@ +navlie.composite.CompositeMeasurement +===================================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeMeasurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.composite.CompositeMeasurementModel.rst b/source/_autosummary/navlie.composite.CompositeMeasurementModel.rst new file mode 100644 index 00000000..3d086bbb --- /dev/null +++ b/source/_autosummary/navlie.composite.CompositeMeasurementModel.rst @@ -0,0 +1,10 @@ +navlie.composite.CompositeMeasurementModel +========================================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeMeasurementModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.composite.CompositeProcessModel.rst b/source/_autosummary/navlie.composite.CompositeProcessModel.rst new file mode 100644 index 00000000..8ba205b7 --- /dev/null +++ b/source/_autosummary/navlie.composite.CompositeProcessModel.rst @@ -0,0 +1,10 @@ +navlie.composite.CompositeProcessModel +====================================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeProcessModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.composite.CompositeState.rst b/source/_autosummary/navlie.composite.CompositeState.rst new file mode 100644 index 00000000..a2124b82 --- /dev/null +++ b/source/_autosummary/navlie.composite.CompositeState.rst @@ -0,0 +1,10 @@ +navlie.composite.CompositeState +=============================== + +.. currentmodule:: navlie.composite + +.. autoclass:: CompositeState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.composite.rst b/source/_autosummary/navlie.composite.rst new file mode 100644 index 00000000..6d49c4aa --- /dev/null +++ b/source/_autosummary/navlie.composite.rst @@ -0,0 +1,35 @@ +navlie.composite +================ + +.. automodule:: navlie.composite + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + CompositeInput + CompositeMeasurement + CompositeMeasurementModel + CompositeProcessModel + CompositeState + + + + + + + + + diff --git a/source/_autosummary/navlie.datagen.DataGenerator.rst b/source/_autosummary/navlie.datagen.DataGenerator.rst new file mode 100644 index 00000000..0d12bc00 --- /dev/null +++ b/source/_autosummary/navlie.datagen.DataGenerator.rst @@ -0,0 +1,10 @@ +navlie.datagen.DataGenerator +============================ + +.. currentmodule:: navlie.datagen + +.. autoclass:: DataGenerator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.datagen.generate_measurement.rst b/source/_autosummary/navlie.datagen.generate_measurement.rst new file mode 100644 index 00000000..ed9151b3 --- /dev/null +++ b/source/_autosummary/navlie.datagen.generate_measurement.rst @@ -0,0 +1,6 @@ +navlie.datagen.generate\_measurement +==================================== + +.. currentmodule:: navlie.datagen + +.. autofunction:: generate_measurement \ No newline at end of file diff --git a/source/_autosummary/navlie.datagen.rst b/source/_autosummary/navlie.datagen.rst new file mode 100644 index 00000000..0fadd626 --- /dev/null +++ b/source/_autosummary/navlie.datagen.rst @@ -0,0 +1,38 @@ +navlie.datagen +============== + +.. automodule:: navlie.datagen + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + generate_measurement + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + DataGenerator + + + + + + + + + diff --git a/source/_autosummary/navlie.filters.CubatureKalmanFilter.rst b/source/_autosummary/navlie.filters.CubatureKalmanFilter.rst new file mode 100644 index 00000000..0e4deac2 --- /dev/null +++ b/source/_autosummary/navlie.filters.CubatureKalmanFilter.rst @@ -0,0 +1,10 @@ +navlie.filters.CubatureKalmanFilter +=================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: CubatureKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.ExtendedKalmanFilter.rst b/source/_autosummary/navlie.filters.ExtendedKalmanFilter.rst new file mode 100644 index 00000000..04abc897 --- /dev/null +++ b/source/_autosummary/navlie.filters.ExtendedKalmanFilter.rst @@ -0,0 +1,10 @@ +navlie.filters.ExtendedKalmanFilter +=================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: ExtendedKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.GaussHermiteKalmanFilter.rst b/source/_autosummary/navlie.filters.GaussHermiteKalmanFilter.rst new file mode 100644 index 00000000..5a7fbbb5 --- /dev/null +++ b/source/_autosummary/navlie.filters.GaussHermiteKalmanFilter.rst @@ -0,0 +1,10 @@ +navlie.filters.GaussHermiteKalmanFilter +======================================= + +.. currentmodule:: navlie.filters + +.. autoclass:: GaussHermiteKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.IteratedKalmanFilter.rst b/source/_autosummary/navlie.filters.IteratedKalmanFilter.rst new file mode 100644 index 00000000..7f5c0fae --- /dev/null +++ b/source/_autosummary/navlie.filters.IteratedKalmanFilter.rst @@ -0,0 +1,10 @@ +navlie.filters.IteratedKalmanFilter +=================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: IteratedKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.SigmaPointKalmanFilter.rst b/source/_autosummary/navlie.filters.SigmaPointKalmanFilter.rst new file mode 100644 index 00000000..b5561363 --- /dev/null +++ b/source/_autosummary/navlie.filters.SigmaPointKalmanFilter.rst @@ -0,0 +1,10 @@ +navlie.filters.SigmaPointKalmanFilter +===================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: SigmaPointKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.UnscentedKalmanFilter.rst b/source/_autosummary/navlie.filters.UnscentedKalmanFilter.rst new file mode 100644 index 00000000..48cfcfd7 --- /dev/null +++ b/source/_autosummary/navlie.filters.UnscentedKalmanFilter.rst @@ -0,0 +1,10 @@ +navlie.filters.UnscentedKalmanFilter +==================================== + +.. currentmodule:: navlie.filters + +.. autoclass:: UnscentedKalmanFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.check_outlier.rst b/source/_autosummary/navlie.filters.check_outlier.rst new file mode 100644 index 00000000..8c57017a --- /dev/null +++ b/source/_autosummary/navlie.filters.check_outlier.rst @@ -0,0 +1,6 @@ +navlie.filters.check\_outlier +============================= + +.. currentmodule:: navlie.filters + +.. autofunction:: check_outlier \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.generate_sigmapoints.rst b/source/_autosummary/navlie.filters.generate_sigmapoints.rst new file mode 100644 index 00000000..0e3d73b3 --- /dev/null +++ b/source/_autosummary/navlie.filters.generate_sigmapoints.rst @@ -0,0 +1,6 @@ +navlie.filters.generate\_sigmapoints +==================================== + +.. currentmodule:: navlie.filters + +.. autofunction:: generate_sigmapoints \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.mean_state.rst b/source/_autosummary/navlie.filters.mean_state.rst new file mode 100644 index 00000000..768de0f1 --- /dev/null +++ b/source/_autosummary/navlie.filters.mean_state.rst @@ -0,0 +1,6 @@ +navlie.filters.mean\_state +========================== + +.. currentmodule:: navlie.filters + +.. autofunction:: mean_state \ No newline at end of file diff --git a/source/_autosummary/navlie.filters.rst b/source/_autosummary/navlie.filters.rst new file mode 100644 index 00000000..31deba7f --- /dev/null +++ b/source/_autosummary/navlie.filters.rst @@ -0,0 +1,46 @@ +navlie.filters +============== + +.. automodule:: navlie.filters + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + check_outlier + generate_sigmapoints + mean_state + run_filter + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + CubatureKalmanFilter + ExtendedKalmanFilter + GaussHermiteKalmanFilter + IteratedKalmanFilter + SigmaPointKalmanFilter + UnscentedKalmanFilter + + + + + + + + + diff --git a/source/_autosummary/navlie.filters.run_filter.rst b/source/_autosummary/navlie.filters.run_filter.rst new file mode 100644 index 00000000..3f92b237 --- /dev/null +++ b/source/_autosummary/navlie.filters.run_filter.rst @@ -0,0 +1,6 @@ +navlie.filters.run\_filter +========================== + +.. currentmodule:: navlie.filters + +.. autofunction:: run_filter \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.IMMResult.rst b/source/_autosummary/navlie.imm.IMMResult.rst new file mode 100644 index 00000000..c73bc08b --- /dev/null +++ b/source/_autosummary/navlie.imm.IMMResult.rst @@ -0,0 +1,10 @@ +navlie.imm.IMMResult +==================== + +.. currentmodule:: navlie.imm + +.. autoclass:: IMMResult + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.IMMResultList.rst b/source/_autosummary/navlie.imm.IMMResultList.rst new file mode 100644 index 00000000..bfc03531 --- /dev/null +++ b/source/_autosummary/navlie.imm.IMMResultList.rst @@ -0,0 +1,10 @@ +navlie.imm.IMMResultList +======================== + +.. currentmodule:: navlie.imm + +.. autoclass:: IMMResultList + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.IMMState.rst b/source/_autosummary/navlie.imm.IMMState.rst new file mode 100644 index 00000000..31721ab9 --- /dev/null +++ b/source/_autosummary/navlie.imm.IMMState.rst @@ -0,0 +1,10 @@ +navlie.imm.IMMState +=================== + +.. currentmodule:: navlie.imm + +.. autoclass:: IMMState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.InteractingModelFilter.rst b/source/_autosummary/navlie.imm.InteractingModelFilter.rst new file mode 100644 index 00000000..d60023ce --- /dev/null +++ b/source/_autosummary/navlie.imm.InteractingModelFilter.rst @@ -0,0 +1,10 @@ +navlie.imm.InteractingModelFilter +================================= + +.. currentmodule:: navlie.imm + +.. autoclass:: InteractingModelFilter + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.gaussian_mixing.rst b/source/_autosummary/navlie.imm.gaussian_mixing.rst new file mode 100644 index 00000000..ceab06be --- /dev/null +++ b/source/_autosummary/navlie.imm.gaussian_mixing.rst @@ -0,0 +1,6 @@ +navlie.imm.gaussian\_mixing +=========================== + +.. currentmodule:: navlie.imm + +.. autofunction:: gaussian_mixing \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.gaussian_mixing_vectorspace.rst b/source/_autosummary/navlie.imm.gaussian_mixing_vectorspace.rst new file mode 100644 index 00000000..ae5a3089 --- /dev/null +++ b/source/_autosummary/navlie.imm.gaussian_mixing_vectorspace.rst @@ -0,0 +1,6 @@ +navlie.imm.gaussian\_mixing\_vectorspace +======================================== + +.. currentmodule:: navlie.imm + +.. autofunction:: gaussian_mixing_vectorspace \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.reparametrize_gaussians_about_X_par.rst b/source/_autosummary/navlie.imm.reparametrize_gaussians_about_X_par.rst new file mode 100644 index 00000000..d41719d5 --- /dev/null +++ b/source/_autosummary/navlie.imm.reparametrize_gaussians_about_X_par.rst @@ -0,0 +1,6 @@ +navlie.imm.reparametrize\_gaussians\_about\_X\_par +================================================== + +.. currentmodule:: navlie.imm + +.. autofunction:: reparametrize_gaussians_about_X_par \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.rst b/source/_autosummary/navlie.imm.rst new file mode 100644 index 00000000..c7b7615e --- /dev/null +++ b/source/_autosummary/navlie.imm.rst @@ -0,0 +1,45 @@ +navlie.imm +========== + +.. automodule:: navlie.imm + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + gaussian_mixing + gaussian_mixing_vectorspace + reparametrize_gaussians_about_X_par + run_imm_filter + update_X + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + IMMResult + IMMResultList + IMMState + InteractingModelFilter + + + + + + + + + diff --git a/source/_autosummary/navlie.imm.run_imm_filter.rst b/source/_autosummary/navlie.imm.run_imm_filter.rst new file mode 100644 index 00000000..664f1bb1 --- /dev/null +++ b/source/_autosummary/navlie.imm.run_imm_filter.rst @@ -0,0 +1,6 @@ +navlie.imm.run\_imm\_filter +=========================== + +.. currentmodule:: navlie.imm + +.. autofunction:: run_imm_filter \ No newline at end of file diff --git a/source/_autosummary/navlie.imm.update_X.rst b/source/_autosummary/navlie.imm.update_X.rst new file mode 100644 index 00000000..a3430fed --- /dev/null +++ b/source/_autosummary/navlie.imm.update_X.rst @@ -0,0 +1,6 @@ +navlie.imm.update\_X +==================== + +.. currentmodule:: navlie.imm + +.. autofunction:: update_X \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.camera.PinholeCamera.rst b/source/_autosummary/navlie.lib.camera.PinholeCamera.rst new file mode 100644 index 00000000..f6f84b08 --- /dev/null +++ b/source/_autosummary/navlie.lib.camera.PinholeCamera.rst @@ -0,0 +1,10 @@ +navlie.lib.camera.PinholeCamera +=============================== + +.. currentmodule:: navlie.lib.camera + +.. autoclass:: PinholeCamera + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.camera.PoseMatrix.rst b/source/_autosummary/navlie.lib.camera.PoseMatrix.rst new file mode 100644 index 00000000..24f8028b --- /dev/null +++ b/source/_autosummary/navlie.lib.camera.PoseMatrix.rst @@ -0,0 +1,10 @@ +navlie.lib.camera.PoseMatrix +============================ + +.. currentmodule:: navlie.lib.camera + +.. autoclass:: PoseMatrix + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.camera.rst b/source/_autosummary/navlie.lib.camera.rst new file mode 100644 index 00000000..1c25fb39 --- /dev/null +++ b/source/_autosummary/navlie.lib.camera.rst @@ -0,0 +1,32 @@ +navlie.lib.camera +================= + +.. automodule:: navlie.lib.camera + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + PinholeCamera + PoseMatrix + + + + + + + + + diff --git a/source/_autosummary/navlie.lib.datasets.SimulatedInertialGPSDataset.rst b/source/_autosummary/navlie.lib.datasets.SimulatedInertialGPSDataset.rst new file mode 100644 index 00000000..08f43c62 --- /dev/null +++ b/source/_autosummary/navlie.lib.datasets.SimulatedInertialGPSDataset.rst @@ -0,0 +1,10 @@ +navlie.lib.datasets.SimulatedInertialGPSDataset +=============================================== + +.. currentmodule:: navlie.lib.datasets + +.. autoclass:: SimulatedInertialGPSDataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.rst b/source/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.rst new file mode 100644 index 00000000..3b935bb7 --- /dev/null +++ b/source/_autosummary/navlie.lib.datasets.SimulatedInertialLandmarkDataset.rst @@ -0,0 +1,10 @@ +navlie.lib.datasets.SimulatedInertialLandmarkDataset +==================================================== + +.. currentmodule:: navlie.lib.datasets + +.. autoclass:: SimulatedInertialLandmarkDataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.datasets.SimulatedPoseRangingDataset.rst b/source/_autosummary/navlie.lib.datasets.SimulatedPoseRangingDataset.rst new file mode 100644 index 00000000..621f9f1c --- /dev/null +++ b/source/_autosummary/navlie.lib.datasets.SimulatedPoseRangingDataset.rst @@ -0,0 +1,10 @@ +navlie.lib.datasets.SimulatedPoseRangingDataset +=============================================== + +.. currentmodule:: navlie.lib.datasets + +.. autoclass:: SimulatedPoseRangingDataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.datasets.generate_landmark_positions.rst b/source/_autosummary/navlie.lib.datasets.generate_landmark_positions.rst new file mode 100644 index 00000000..2538be3a --- /dev/null +++ b/source/_autosummary/navlie.lib.datasets.generate_landmark_positions.rst @@ -0,0 +1,6 @@ +navlie.lib.datasets.generate\_landmark\_positions +================================================= + +.. currentmodule:: navlie.lib.datasets + +.. autofunction:: generate_landmark_positions \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.datasets.rst b/source/_autosummary/navlie.lib.datasets.rst new file mode 100644 index 00000000..cbfb9b06 --- /dev/null +++ b/source/_autosummary/navlie.lib.datasets.rst @@ -0,0 +1,40 @@ +navlie.lib.datasets +=================== + +.. automodule:: navlie.lib.datasets + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + generate_landmark_positions + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + SimulatedInertialGPSDataset + SimulatedInertialLandmarkDataset + SimulatedPoseRangingDataset + + + + + + + + + diff --git a/source/_autosummary/navlie.lib.imu.G_matrix.rst b/source/_autosummary/navlie.lib.imu.G_matrix.rst new file mode 100644 index 00000000..23ce529c --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.G_matrix.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.G\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: G_matrix \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.G_matrix_inv.rst b/source/_autosummary/navlie.lib.imu.G_matrix_inv.rst new file mode 100644 index 00000000..83190a0e --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.G_matrix_inv.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.G\_matrix\_inv +============================= + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: G_matrix_inv \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.IMU.rst b/source/_autosummary/navlie.lib.imu.IMU.rst new file mode 100644 index 00000000..dd7e48d0 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.IMU.rst @@ -0,0 +1,10 @@ +navlie.lib.imu.IMU +================== + +.. currentmodule:: navlie.lib.imu + +.. autoclass:: IMU + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.IMUKinematics.rst b/source/_autosummary/navlie.lib.imu.IMUKinematics.rst new file mode 100644 index 00000000..aab31572 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.IMUKinematics.rst @@ -0,0 +1,10 @@ +navlie.lib.imu.IMUKinematics +============================ + +.. currentmodule:: navlie.lib.imu + +.. autoclass:: IMUKinematics + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.IMUState.rst b/source/_autosummary/navlie.lib.imu.IMUState.rst new file mode 100644 index 00000000..fde4052b --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.IMUState.rst @@ -0,0 +1,10 @@ +navlie.lib.imu.IMUState +======================= + +.. currentmodule:: navlie.lib.imu + +.. autoclass:: IMUState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.L_matrix.rst b/source/_autosummary/navlie.lib.imu.L_matrix.rst new file mode 100644 index 00000000..b1acfeb2 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.L_matrix.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.L\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: L_matrix \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.M_matrix.rst b/source/_autosummary/navlie.lib.imu.M_matrix.rst new file mode 100644 index 00000000..e6339ca9 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.M_matrix.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.M\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: M_matrix \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.N_matrix.rst b/source/_autosummary/navlie.lib.imu.N_matrix.rst new file mode 100644 index 00000000..ebecf6b7 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.N_matrix.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.N\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: N_matrix \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.U_matrix.rst b/source/_autosummary/navlie.lib.imu.U_matrix.rst new file mode 100644 index 00000000..6c6c3737 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.U_matrix.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.U\_matrix +======================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: U_matrix \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.U_matrix_inv.rst b/source/_autosummary/navlie.lib.imu.U_matrix_inv.rst new file mode 100644 index 00000000..28d7140c --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.U_matrix_inv.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.U\_matrix\_inv +============================= + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: U_matrix_inv \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.U_tilde_matrix.rst b/source/_autosummary/navlie.lib.imu.U_tilde_matrix.rst new file mode 100644 index 00000000..58b61c9f --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.U_tilde_matrix.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.U\_tilde\_matrix +=============================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: U_tilde_matrix \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.adjoint_IE3.rst b/source/_autosummary/navlie.lib.imu.adjoint_IE3.rst new file mode 100644 index 00000000..4b0bff12 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.adjoint_IE3.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.adjoint\_IE3 +=========================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: adjoint_IE3 \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.delta_matrix.rst b/source/_autosummary/navlie.lib.imu.delta_matrix.rst new file mode 100644 index 00000000..b91120ac --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.delta_matrix.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.delta\_matrix +============================ + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: delta_matrix \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.get_unbiased_imu.rst b/source/_autosummary/navlie.lib.imu.get_unbiased_imu.rst new file mode 100644 index 00000000..9b35ce2f --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.get_unbiased_imu.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.get\_unbiased\_imu +================================= + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: get_unbiased_imu \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.inverse_IE3.rst b/source/_autosummary/navlie.lib.imu.inverse_IE3.rst new file mode 100644 index 00000000..e1857eca --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.inverse_IE3.rst @@ -0,0 +1,6 @@ +navlie.lib.imu.inverse\_IE3 +=========================== + +.. currentmodule:: navlie.lib.imu + +.. autofunction:: inverse_IE3 \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.imu.rst b/source/_autosummary/navlie.lib.imu.rst new file mode 100644 index 00000000..7ded5990 --- /dev/null +++ b/source/_autosummary/navlie.lib.imu.rst @@ -0,0 +1,51 @@ +navlie.lib.imu +============== + +.. automodule:: navlie.lib.imu + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + G_matrix + G_matrix_inv + L_matrix + M_matrix + N_matrix + U_matrix + U_matrix_inv + U_tilde_matrix + adjoint_IE3 + delta_matrix + get_unbiased_imu + inverse_IE3 + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + IMU + IMUKinematics + IMUState + + + + + + + + + diff --git a/source/_autosummary/navlie.lib.models.AbsolutePosition.rst b/source/_autosummary/navlie.lib.models.AbsolutePosition.rst new file mode 100644 index 00000000..071b4177 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.AbsolutePosition.rst @@ -0,0 +1,10 @@ +navlie.lib.models.AbsolutePosition +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: AbsolutePosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.AbsoluteVelocity.rst b/source/_autosummary/navlie.lib.models.AbsoluteVelocity.rst new file mode 100644 index 00000000..a7dd329f --- /dev/null +++ b/source/_autosummary/navlie.lib.models.AbsoluteVelocity.rst @@ -0,0 +1,10 @@ +navlie.lib.models.AbsoluteVelocity +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: AbsoluteVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.Altitude.rst b/source/_autosummary/navlie.lib.models.Altitude.rst new file mode 100644 index 00000000..fa3777b6 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.Altitude.rst @@ -0,0 +1,10 @@ +navlie.lib.models.Altitude +========================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: Altitude + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.BodyFrameVelocity.rst b/source/_autosummary/navlie.lib.models.BodyFrameVelocity.rst new file mode 100644 index 00000000..2938a897 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.BodyFrameVelocity.rst @@ -0,0 +1,10 @@ +navlie.lib.models.BodyFrameVelocity +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: BodyFrameVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.CameraProjection.rst b/source/_autosummary/navlie.lib.models.CameraProjection.rst new file mode 100644 index 00000000..b157a313 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.CameraProjection.rst @@ -0,0 +1,10 @@ +navlie.lib.models.CameraProjection +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: CameraProjection + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.DoubleIntegrator.rst b/source/_autosummary/navlie.lib.models.DoubleIntegrator.rst new file mode 100644 index 00000000..04e207b3 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.DoubleIntegrator.rst @@ -0,0 +1,10 @@ +navlie.lib.models.DoubleIntegrator +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: DoubleIntegrator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.DoubleIntegratorWithBias.rst b/source/_autosummary/navlie.lib.models.DoubleIntegratorWithBias.rst new file mode 100644 index 00000000..613e08bc --- /dev/null +++ b/source/_autosummary/navlie.lib.models.DoubleIntegratorWithBias.rst @@ -0,0 +1,10 @@ +navlie.lib.models.DoubleIntegratorWithBias +========================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: DoubleIntegratorWithBias + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.GlobalPosition.rst b/source/_autosummary/navlie.lib.models.GlobalPosition.rst new file mode 100644 index 00000000..2a84bea5 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.GlobalPosition.rst @@ -0,0 +1,10 @@ +navlie.lib.models.GlobalPosition +================================ + +.. currentmodule:: navlie.lib.models + +.. autoclass:: GlobalPosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.Gravitometer.rst b/source/_autosummary/navlie.lib.models.Gravitometer.rst new file mode 100644 index 00000000..85266c50 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.Gravitometer.rst @@ -0,0 +1,10 @@ +navlie.lib.models.Gravitometer +============================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: Gravitometer + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.InvariantMeasurement.rst b/source/_autosummary/navlie.lib.models.InvariantMeasurement.rst new file mode 100644 index 00000000..8636519d --- /dev/null +++ b/source/_autosummary/navlie.lib.models.InvariantMeasurement.rst @@ -0,0 +1,10 @@ +navlie.lib.models.InvariantMeasurement +====================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: InvariantMeasurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.InvariantPointRelativePosition.rst b/source/_autosummary/navlie.lib.models.InvariantPointRelativePosition.rst new file mode 100644 index 00000000..4b018ecc --- /dev/null +++ b/source/_autosummary/navlie.lib.models.InvariantPointRelativePosition.rst @@ -0,0 +1,10 @@ +navlie.lib.models.InvariantPointRelativePosition +================================================ + +.. currentmodule:: navlie.lib.models + +.. autoclass:: InvariantPointRelativePosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.LinearMeasurement.rst b/source/_autosummary/navlie.lib.models.LinearMeasurement.rst new file mode 100644 index 00000000..5ad7f33b --- /dev/null +++ b/source/_autosummary/navlie.lib.models.LinearMeasurement.rst @@ -0,0 +1,10 @@ +navlie.lib.models.LinearMeasurement +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: LinearMeasurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.Magnetometer.rst b/source/_autosummary/navlie.lib.models.Magnetometer.rst new file mode 100644 index 00000000..3217a8ea --- /dev/null +++ b/source/_autosummary/navlie.lib.models.Magnetometer.rst @@ -0,0 +1,10 @@ +navlie.lib.models.Magnetometer +============================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: Magnetometer + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.OneDimensionalPositionVelocityRange.rst b/source/_autosummary/navlie.lib.models.OneDimensionalPositionVelocityRange.rst new file mode 100644 index 00000000..cb6007ef --- /dev/null +++ b/source/_autosummary/navlie.lib.models.OneDimensionalPositionVelocityRange.rst @@ -0,0 +1,10 @@ +navlie.lib.models.OneDimensionalPositionVelocityRange +===================================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: OneDimensionalPositionVelocityRange + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.PointRelativePosition.rst b/source/_autosummary/navlie.lib.models.PointRelativePosition.rst new file mode 100644 index 00000000..ae77f493 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.PointRelativePosition.rst @@ -0,0 +1,10 @@ +navlie.lib.models.PointRelativePosition +======================================= + +.. currentmodule:: navlie.lib.models + +.. autoclass:: PointRelativePosition + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.PointRelativePositionSLAM.rst b/source/_autosummary/navlie.lib.models.PointRelativePositionSLAM.rst new file mode 100644 index 00000000..35be905e --- /dev/null +++ b/source/_autosummary/navlie.lib.models.PointRelativePositionSLAM.rst @@ -0,0 +1,10 @@ +navlie.lib.models.PointRelativePositionSLAM +=========================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: PointRelativePositionSLAM + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.RangePointToAnchor.rst b/source/_autosummary/navlie.lib.models.RangePointToAnchor.rst new file mode 100644 index 00000000..f2862bcd --- /dev/null +++ b/source/_autosummary/navlie.lib.models.RangePointToAnchor.rst @@ -0,0 +1,10 @@ +navlie.lib.models.RangePointToAnchor +==================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangePointToAnchor + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.RangePoseToAnchor.rst b/source/_autosummary/navlie.lib.models.RangePoseToAnchor.rst new file mode 100644 index 00000000..96f5b7e9 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.RangePoseToAnchor.rst @@ -0,0 +1,10 @@ +navlie.lib.models.RangePoseToAnchor +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangePoseToAnchor + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.RangePoseToPose.rst b/source/_autosummary/navlie.lib.models.RangePoseToPose.rst new file mode 100644 index 00000000..e23e49f4 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.RangePoseToPose.rst @@ -0,0 +1,10 @@ +navlie.lib.models.RangePoseToPose +================================= + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangePoseToPose + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.RangeRelativePose.rst b/source/_autosummary/navlie.lib.models.RangeRelativePose.rst new file mode 100644 index 00000000..ddc3abf1 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.RangeRelativePose.rst @@ -0,0 +1,10 @@ +navlie.lib.models.RangeRelativePose +=================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RangeRelativePose + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.RelativeBodyFrameVelocity.rst b/source/_autosummary/navlie.lib.models.RelativeBodyFrameVelocity.rst new file mode 100644 index 00000000..47176d46 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.RelativeBodyFrameVelocity.rst @@ -0,0 +1,10 @@ +navlie.lib.models.RelativeBodyFrameVelocity +=========================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: RelativeBodyFrameVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.SingleIntegrator.rst b/source/_autosummary/navlie.lib.models.SingleIntegrator.rst new file mode 100644 index 00000000..2a62fd56 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.SingleIntegrator.rst @@ -0,0 +1,10 @@ +navlie.lib.models.SingleIntegrator +================================== + +.. currentmodule:: navlie.lib.models + +.. autoclass:: SingleIntegrator + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.models.rst b/source/_autosummary/navlie.lib.models.rst new file mode 100644 index 00000000..a4499773 --- /dev/null +++ b/source/_autosummary/navlie.lib.models.rst @@ -0,0 +1,52 @@ +navlie.lib.models +================= + +.. automodule:: navlie.lib.models + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + AbsolutePosition + AbsoluteVelocity + Altitude + BodyFrameVelocity + CameraProjection + DoubleIntegrator + DoubleIntegratorWithBias + GlobalPosition + Gravitometer + InvariantMeasurement + InvariantPointRelativePosition + LinearMeasurement + Magnetometer + OneDimensionalPositionVelocityRange + PointRelativePosition + PointRelativePositionSLAM + RangePointToAnchor + RangePoseToAnchor + RangePoseToPose + RangeRelativePose + RelativeBodyFrameVelocity + SingleIntegrator + + + + + + + + + diff --git a/source/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.rst b/source/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.rst new file mode 100644 index 00000000..ed38e157 --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.AngularVelocityIncrement.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.AngularVelocityIncrement +================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: AngularVelocityIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.rst b/source/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.rst new file mode 100644 index 00000000..4e80763d --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.BodyVelocityIncrement.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.BodyVelocityIncrement +=============================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: BodyVelocityIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.IMUIncrement.rst b/source/_autosummary/navlie.lib.preintegration.IMUIncrement.rst new file mode 100644 index 00000000..3981994d --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.IMUIncrement.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.IMUIncrement +====================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: IMUIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.LinearIncrement.rst b/source/_autosummary/navlie.lib.preintegration.LinearIncrement.rst new file mode 100644 index 00000000..c5da1061 --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.LinearIncrement.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.LinearIncrement +========================================= + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: LinearIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.PreintegratedAngularVelocity.rst b/source/_autosummary/navlie.lib.preintegration.PreintegratedAngularVelocity.rst new file mode 100644 index 00000000..fb60ace4 --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.PreintegratedAngularVelocity.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedAngularVelocity +====================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedAngularVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.rst b/source/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.rst new file mode 100644 index 00000000..894991a5 --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.PreintegratedBodyVelocity.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedBodyVelocity +=================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedBodyVelocity + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.PreintegratedIMUKinematics.rst b/source/_autosummary/navlie.lib.preintegration.PreintegratedIMUKinematics.rst new file mode 100644 index 00000000..1a954882 --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.PreintegratedIMUKinematics.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedIMUKinematics +==================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedIMUKinematics + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.rst b/source/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.rst new file mode 100644 index 00000000..082f830d --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.PreintegratedLinearModel.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedLinearModel +================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedLinearModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.rst b/source/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.rst new file mode 100644 index 00000000..71d21557 --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.PreintegratedWheelOdometry.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.PreintegratedWheelOdometry +==================================================== + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: PreintegratedWheelOdometry + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.RelativeMotionIncrement.rst b/source/_autosummary/navlie.lib.preintegration.RelativeMotionIncrement.rst new file mode 100644 index 00000000..f8d40c93 --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.RelativeMotionIncrement.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.RelativeMotionIncrement +================================================= + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: RelativeMotionIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.rst b/source/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.rst new file mode 100644 index 00000000..5eaa4b5d --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.WheelOdometryIncrement.rst @@ -0,0 +1,10 @@ +navlie.lib.preintegration.WheelOdometryIncrement +================================================ + +.. currentmodule:: navlie.lib.preintegration + +.. autoclass:: WheelOdometryIncrement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.preintegration.rst b/source/_autosummary/navlie.lib.preintegration.rst new file mode 100644 index 00000000..90c46d0c --- /dev/null +++ b/source/_autosummary/navlie.lib.preintegration.rst @@ -0,0 +1,41 @@ +navlie.lib.preintegration +========================= + +.. automodule:: navlie.lib.preintegration + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + AngularVelocityIncrement + BodyVelocityIncrement + IMUIncrement + LinearIncrement + PreintegratedAngularVelocity + PreintegratedBodyVelocity + PreintegratedIMUKinematics + PreintegratedLinearModel + PreintegratedWheelOdometry + RelativeMotionIncrement + WheelOdometryIncrement + + + + + + + + + diff --git a/source/_autosummary/navlie.lib.rst b/source/_autosummary/navlie.lib.rst new file mode 100644 index 00000000..33cf70de --- /dev/null +++ b/source/_autosummary/navlie.lib.rst @@ -0,0 +1,37 @@ +navlie.lib +========== + +.. automodule:: navlie.lib + + + + + + + + + + + + + + + + + + + +.. rubric:: Modules + +.. autosummary:: + :toctree: + :template: custom-module-template.rst + :recursive: + + navlie.lib.camera + navlie.lib.datasets + navlie.lib.imu + navlie.lib.models + navlie.lib.preintegration + navlie.lib.states + diff --git a/source/_autosummary/navlie.lib.states.MatrixLieGroupState.rst b/source/_autosummary/navlie.lib.states.MatrixLieGroupState.rst new file mode 100644 index 00000000..b7bd6ed7 --- /dev/null +++ b/source/_autosummary/navlie.lib.states.MatrixLieGroupState.rst @@ -0,0 +1,10 @@ +navlie.lib.states.MatrixLieGroupState +===================================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: MatrixLieGroupState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.SE23State.rst b/source/_autosummary/navlie.lib.states.SE23State.rst new file mode 100644 index 00000000..3a2acab9 --- /dev/null +++ b/source/_autosummary/navlie.lib.states.SE23State.rst @@ -0,0 +1,10 @@ +navlie.lib.states.SE23State +=========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SE23State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.SE2State.rst b/source/_autosummary/navlie.lib.states.SE2State.rst new file mode 100644 index 00000000..26d31deb --- /dev/null +++ b/source/_autosummary/navlie.lib.states.SE2State.rst @@ -0,0 +1,10 @@ +navlie.lib.states.SE2State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SE2State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.SE3State.rst b/source/_autosummary/navlie.lib.states.SE3State.rst new file mode 100644 index 00000000..928977a9 --- /dev/null +++ b/source/_autosummary/navlie.lib.states.SE3State.rst @@ -0,0 +1,10 @@ +navlie.lib.states.SE3State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SE3State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.SL3State.rst b/source/_autosummary/navlie.lib.states.SL3State.rst new file mode 100644 index 00000000..dfe1fc10 --- /dev/null +++ b/source/_autosummary/navlie.lib.states.SL3State.rst @@ -0,0 +1,10 @@ +navlie.lib.states.SL3State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SL3State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.SO2State.rst b/source/_autosummary/navlie.lib.states.SO2State.rst new file mode 100644 index 00000000..9f2678f9 --- /dev/null +++ b/source/_autosummary/navlie.lib.states.SO2State.rst @@ -0,0 +1,10 @@ +navlie.lib.states.SO2State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SO2State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.SO3State.rst b/source/_autosummary/navlie.lib.states.SO3State.rst new file mode 100644 index 00000000..c5fd87ce --- /dev/null +++ b/source/_autosummary/navlie.lib.states.SO3State.rst @@ -0,0 +1,10 @@ +navlie.lib.states.SO3State +========================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: SO3State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.StampedValue.rst b/source/_autosummary/navlie.lib.states.StampedValue.rst new file mode 100644 index 00000000..83bad4eb --- /dev/null +++ b/source/_autosummary/navlie.lib.states.StampedValue.rst @@ -0,0 +1,10 @@ +navlie.lib.states.StampedValue +============================== + +.. currentmodule:: navlie.lib.states + +.. autoclass:: StampedValue + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.VectorInput.rst b/source/_autosummary/navlie.lib.states.VectorInput.rst new file mode 100644 index 00000000..0023f248 --- /dev/null +++ b/source/_autosummary/navlie.lib.states.VectorInput.rst @@ -0,0 +1,10 @@ +navlie.lib.states.VectorInput +============================= + +.. currentmodule:: navlie.lib.states + +.. autoclass:: VectorInput + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.VectorState.rst b/source/_autosummary/navlie.lib.states.VectorState.rst new file mode 100644 index 00000000..e91253a0 --- /dev/null +++ b/source/_autosummary/navlie.lib.states.VectorState.rst @@ -0,0 +1,10 @@ +navlie.lib.states.VectorState +============================= + +.. currentmodule:: navlie.lib.states + +.. autoclass:: VectorState + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.lib.states.rst b/source/_autosummary/navlie.lib.states.rst new file mode 100644 index 00000000..24b7ca9b --- /dev/null +++ b/source/_autosummary/navlie.lib.states.rst @@ -0,0 +1,40 @@ +navlie.lib.states +================= + +.. automodule:: navlie.lib.states + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + MatrixLieGroupState + SE23State + SE2State + SE3State + SL3State + SO2State + SO3State + StampedValue + VectorInput + VectorState + + + + + + + + + diff --git a/source/_autosummary/navlie.types.Dataset.rst b/source/_autosummary/navlie.types.Dataset.rst new file mode 100644 index 00000000..d691044d --- /dev/null +++ b/source/_autosummary/navlie.types.Dataset.rst @@ -0,0 +1,10 @@ +navlie.types.Dataset +==================== + +.. currentmodule:: navlie.types + +.. autoclass:: Dataset + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.types.Input.rst b/source/_autosummary/navlie.types.Input.rst new file mode 100644 index 00000000..e1cd1004 --- /dev/null +++ b/source/_autosummary/navlie.types.Input.rst @@ -0,0 +1,10 @@ +navlie.types.Input +================== + +.. currentmodule:: navlie.types + +.. autoclass:: Input + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.types.Measurement.rst b/source/_autosummary/navlie.types.Measurement.rst new file mode 100644 index 00000000..327432f7 --- /dev/null +++ b/source/_autosummary/navlie.types.Measurement.rst @@ -0,0 +1,10 @@ +navlie.types.Measurement +======================== + +.. currentmodule:: navlie.types + +.. autoclass:: Measurement + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.types.MeasurementModel.rst b/source/_autosummary/navlie.types.MeasurementModel.rst new file mode 100644 index 00000000..f90ca7b8 --- /dev/null +++ b/source/_autosummary/navlie.types.MeasurementModel.rst @@ -0,0 +1,10 @@ +navlie.types.MeasurementModel +============================= + +.. currentmodule:: navlie.types + +.. autoclass:: MeasurementModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.types.ProcessModel.rst b/source/_autosummary/navlie.types.ProcessModel.rst new file mode 100644 index 00000000..9619b0e5 --- /dev/null +++ b/source/_autosummary/navlie.types.ProcessModel.rst @@ -0,0 +1,10 @@ +navlie.types.ProcessModel +========================= + +.. currentmodule:: navlie.types + +.. autoclass:: ProcessModel + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.types.State.rst b/source/_autosummary/navlie.types.State.rst new file mode 100644 index 00000000..81afa6ff --- /dev/null +++ b/source/_autosummary/navlie.types.State.rst @@ -0,0 +1,10 @@ +navlie.types.State +================== + +.. currentmodule:: navlie.types + +.. autoclass:: State + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.types.StateWithCovariance.rst b/source/_autosummary/navlie.types.StateWithCovariance.rst new file mode 100644 index 00000000..c0f962b0 --- /dev/null +++ b/source/_autosummary/navlie.types.StateWithCovariance.rst @@ -0,0 +1,10 @@ +navlie.types.StateWithCovariance +================================ + +.. currentmodule:: navlie.types + +.. autoclass:: StateWithCovariance + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.types.rst b/source/_autosummary/navlie.types.rst new file mode 100644 index 00000000..da1b20d1 --- /dev/null +++ b/source/_autosummary/navlie.types.rst @@ -0,0 +1,37 @@ +navlie.types +============ + +.. automodule:: navlie.types + + + + + + + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + Dataset + Input + Measurement + MeasurementModel + ProcessModel + State + StateWithCovariance + + + + + + + + + diff --git a/source/_autosummary/navlie.utils.GaussianResult.rst b/source/_autosummary/navlie.utils.GaussianResult.rst new file mode 100644 index 00000000..a920d1d2 --- /dev/null +++ b/source/_autosummary/navlie.utils.GaussianResult.rst @@ -0,0 +1,10 @@ +navlie.utils.GaussianResult +=========================== + +.. currentmodule:: navlie.utils + +.. autoclass:: GaussianResult + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.GaussianResultList.rst b/source/_autosummary/navlie.utils.GaussianResultList.rst new file mode 100644 index 00000000..2aee2fed --- /dev/null +++ b/source/_autosummary/navlie.utils.GaussianResultList.rst @@ -0,0 +1,10 @@ +navlie.utils.GaussianResultList +=============================== + +.. currentmodule:: navlie.utils + +.. autoclass:: GaussianResultList + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.MonteCarloResult.rst b/source/_autosummary/navlie.utils.MonteCarloResult.rst new file mode 100644 index 00000000..81755eb5 --- /dev/null +++ b/source/_autosummary/navlie.utils.MonteCarloResult.rst @@ -0,0 +1,10 @@ +navlie.utils.MonteCarloResult +============================= + +.. currentmodule:: navlie.utils + +.. autoclass:: MonteCarloResult + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.associate_stamps.rst b/source/_autosummary/navlie.utils.associate_stamps.rst new file mode 100644 index 00000000..2174fc69 --- /dev/null +++ b/source/_autosummary/navlie.utils.associate_stamps.rst @@ -0,0 +1,6 @@ +navlie.utils.associate\_stamps +============================== + +.. currentmodule:: navlie.utils + +.. autofunction:: associate_stamps \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.find_nearest_stamp_idx.rst b/source/_autosummary/navlie.utils.find_nearest_stamp_idx.rst new file mode 100644 index 00000000..1615cc7f --- /dev/null +++ b/source/_autosummary/navlie.utils.find_nearest_stamp_idx.rst @@ -0,0 +1,6 @@ +navlie.utils.find\_nearest\_stamp\_idx +====================================== + +.. currentmodule:: navlie.utils + +.. autofunction:: find_nearest_stamp_idx \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.jacobian.rst b/source/_autosummary/navlie.utils.jacobian.rst new file mode 100644 index 00000000..1b02c953 --- /dev/null +++ b/source/_autosummary/navlie.utils.jacobian.rst @@ -0,0 +1,6 @@ +navlie.utils.jacobian +===================== + +.. currentmodule:: navlie.utils + +.. autofunction:: jacobian \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.monte_carlo.rst b/source/_autosummary/navlie.utils.monte_carlo.rst new file mode 100644 index 00000000..17886c27 --- /dev/null +++ b/source/_autosummary/navlie.utils.monte_carlo.rst @@ -0,0 +1,6 @@ +navlie.utils.monte\_carlo +========================= + +.. currentmodule:: navlie.utils + +.. autofunction:: monte_carlo \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.plot_error.rst b/source/_autosummary/navlie.utils.plot_error.rst new file mode 100644 index 00000000..da67b0b7 --- /dev/null +++ b/source/_autosummary/navlie.utils.plot_error.rst @@ -0,0 +1,6 @@ +navlie.utils.plot\_error +======================== + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_error \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.plot_meas.rst b/source/_autosummary/navlie.utils.plot_meas.rst new file mode 100644 index 00000000..7a2608b1 --- /dev/null +++ b/source/_autosummary/navlie.utils.plot_meas.rst @@ -0,0 +1,6 @@ +navlie.utils.plot\_meas +======================= + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_meas \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.plot_meas_by_model.rst b/source/_autosummary/navlie.utils.plot_meas_by_model.rst new file mode 100644 index 00000000..57a6b919 --- /dev/null +++ b/source/_autosummary/navlie.utils.plot_meas_by_model.rst @@ -0,0 +1,6 @@ +navlie.utils.plot\_meas\_by\_model +================================== + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_meas_by_model \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.plot_nees.rst b/source/_autosummary/navlie.utils.plot_nees.rst new file mode 100644 index 00000000..5ca9c13a --- /dev/null +++ b/source/_autosummary/navlie.utils.plot_nees.rst @@ -0,0 +1,6 @@ +navlie.utils.plot\_nees +======================= + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_nees \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.plot_poses.rst b/source/_autosummary/navlie.utils.plot_poses.rst new file mode 100644 index 00000000..b7ae0d81 --- /dev/null +++ b/source/_autosummary/navlie.utils.plot_poses.rst @@ -0,0 +1,6 @@ +navlie.utils.plot\_poses +======================== + +.. currentmodule:: navlie.utils + +.. autofunction:: plot_poses \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.randvec.rst b/source/_autosummary/navlie.utils.randvec.rst new file mode 100644 index 00000000..37d661e7 --- /dev/null +++ b/source/_autosummary/navlie.utils.randvec.rst @@ -0,0 +1,6 @@ +navlie.utils.randvec +==================== + +.. currentmodule:: navlie.utils + +.. autofunction:: randvec \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.rst b/source/_autosummary/navlie.utils.rst new file mode 100644 index 00000000..d1c57608 --- /dev/null +++ b/source/_autosummary/navlie.utils.rst @@ -0,0 +1,53 @@ +navlie.utils +============ + +.. automodule:: navlie.utils + + + + + + + + .. rubric:: Functions + + .. autosummary:: + :toctree: + + associate_stamps + find_nearest_stamp_idx + jacobian + monte_carlo + plot_error + plot_meas + plot_meas_by_model + plot_nees + plot_poses + randvec + schedule_sequential_measurements + set_axes_equal + state_interp + van_loans + + + + + + .. rubric:: Classes + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + + GaussianResult + GaussianResultList + MonteCarloResult + + + + + + + + + diff --git a/source/_autosummary/navlie.utils.schedule_sequential_measurements.rst b/source/_autosummary/navlie.utils.schedule_sequential_measurements.rst new file mode 100644 index 00000000..1e2d5b81 --- /dev/null +++ b/source/_autosummary/navlie.utils.schedule_sequential_measurements.rst @@ -0,0 +1,6 @@ +navlie.utils.schedule\_sequential\_measurements +=============================================== + +.. currentmodule:: navlie.utils + +.. autofunction:: schedule_sequential_measurements \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.set_axes_equal.rst b/source/_autosummary/navlie.utils.set_axes_equal.rst new file mode 100644 index 00000000..1c458ce9 --- /dev/null +++ b/source/_autosummary/navlie.utils.set_axes_equal.rst @@ -0,0 +1,6 @@ +navlie.utils.set\_axes\_equal +============================= + +.. currentmodule:: navlie.utils + +.. autofunction:: set_axes_equal \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.state_interp.rst b/source/_autosummary/navlie.utils.state_interp.rst new file mode 100644 index 00000000..6cdbdbe2 --- /dev/null +++ b/source/_autosummary/navlie.utils.state_interp.rst @@ -0,0 +1,6 @@ +navlie.utils.state\_interp +========================== + +.. currentmodule:: navlie.utils + +.. autofunction:: state_interp \ No newline at end of file diff --git a/source/_autosummary/navlie.utils.van_loans.rst b/source/_autosummary/navlie.utils.van_loans.rst new file mode 100644 index 00000000..2538562c --- /dev/null +++ b/source/_autosummary/navlie.utils.van_loans.rst @@ -0,0 +1,6 @@ +navlie.utils.van\_loans +======================= + +.. currentmodule:: navlie.utils + +.. autofunction:: van_loans \ No newline at end of file diff --git a/source/_static/imu.pdf b/source/_static/imu.pdf new file mode 100644 index 00000000..ed99dc63 Binary files /dev/null and b/source/_static/imu.pdf differ diff --git a/source/_templates/custom-class-template.rst b/source/_templates/custom-class-template.rst new file mode 100644 index 00000000..a6a62727 --- /dev/null +++ b/source/_templates/custom-class-template.rst @@ -0,0 +1,9 @@ +{{ fullname | escape | underline}} + +.. currentmodule:: {{ module }} + +.. autoclass:: {{ objname }} + :members: + :show-inheritance: + :inherited-members: + :undoc-members: \ No newline at end of file diff --git a/source/_templates/custom-module-template.rst b/source/_templates/custom-module-template.rst new file mode 100644 index 00000000..66b15cd1 --- /dev/null +++ b/source/_templates/custom-module-template.rst @@ -0,0 +1,66 @@ +{{ fullname | escape | underline}} + +.. automodule:: {{ fullname }} + + {% block attributes %} + {% if attributes %} + .. rubric:: Module Attributes + + .. autosummary:: + :toctree: + {% for item in attributes %} + {{ item }} + {%- endfor %} + {% endif %} + {% endblock %} + + {% block functions %} + {% if functions %} + .. rubric:: {{ _('Functions') }} + + .. autosummary:: + :toctree: + {% for item in functions %} + {{ item }} + {%- endfor %} + {% endif %} + {% endblock %} + + {% block classes %} + {% if classes %} + .. rubric:: {{ _('Classes') }} + + .. autosummary:: + :toctree: + :template: custom-class-template.rst + {% for item in classes %} + {{ item }} + {%- endfor %} + {% endif %} + {% endblock %} + + {% block exceptions %} + {% if exceptions %} + .. rubric:: {{ _('Exceptions') }} + + .. autosummary:: + :toctree: + {% for item in exceptions %} + {{ item }} + {%- endfor %} + {% endif %} + {% endblock %} + +{% block modules %} +{% if modules %} +.. rubric:: Modules + +.. autosummary:: + :toctree: + :template: custom-module-template.rst + :recursive: +{% for item in modules %} + {{ item }} +{%- endfor %} +{% endif %} +{% endblock %} \ No newline at end of file diff --git a/source/_templates/package.rst b/source/_templates/package.rst new file mode 100644 index 00000000..eef128ef --- /dev/null +++ b/source/_templates/package.rst @@ -0,0 +1,15 @@ +{{ name | escape | underline}} + +{% block modules %} +{% if modules %} +.. rubric:: Modules + +.. autosummary:: + :toctree: + :template: custom-module-template.rst + :recursive: +{% for item in modules %} + {{ item }} +{%- endfor %} +{% endif %} +{% endblock %} \ No newline at end of file diff --git a/source/api.rst b/source/api.rst new file mode 100644 index 00000000..4870a37d --- /dev/null +++ b/source/api.rst @@ -0,0 +1,17 @@ +API Documentation +------------------ +Below is a list of all the modules in the navlie package. Click on any of the links to see the documentation for that module. Alternatively, you can use the search box at the top of the page to search for a particular class/function/module. + +.. autosummary:: + :toctree: _autosummary + :recursive: + :template: custom-module-template.rst + + navlie.composite + navlie.datagen + navlie.filters + navlie.imm + navlie.types + navlie.utils + navlie.batch + navlie.lib \ No newline at end of file diff --git a/source/conf.py b/source/conf.py new file mode 100644 index 00000000..d6321eaa --- /dev/null +++ b/source/conf.py @@ -0,0 +1,75 @@ +# Configuration file for the Sphinx documentation builder. +# +# This file only contains a selection of the most common options. For a full +# list see the documentation: +# https://www.sphinx-doc.org/en/master/usage/configuration.html + +# -- Path setup -------------------------------------------------------------- + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +# +# import os +# import sys +# sys.path.insert(0, os.path.abspath('.')) + + +# -- Project information ----------------------------------------------------- + +project = "navlie" +copyright = "2022" +author = "Charles C. Cossette" + +# The full version, including alpha/beta/rc tags +release = "0.1.0" + + +# -- General configuration --------------------------------------------------- + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = [ + "sphinx.ext.autodoc", + "sphinx.ext.napoleon", + "sphinx.ext.mathjax", + "sphinx.ext.autosummary", + "sphinx.ext.intersphinx", + "sphinx.ext.githubpages", + "nbsphinx", +] +autodoc_default_options = { + "member-order": "bysource", + "exclude-members": "__weakref__", +} +autosummary_generate = True +autoclass_content = "both" + +intersphinx_mapping = { + "python": ("https://docs.python.org/3/", None), + "numpy": ("https://numpy.org/doc/stable/", None), + "scipy": ("https://docs.scipy.org/doc/scipy/", None), + "matplotlib": ("https://matplotlib.org/stable/", None), +} + +# Add any paths that contain templates here, relative to this directory. +templates_path = ["_templates"] + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +# This pattern also affects html_static_path and html_extra_path. +exclude_patterns = [] + + +# -- Options for HTML output ------------------------------------------------- + +# The theme to use for HTML and HTML Help pages. See the documentation for +# a list of builtin themes. +# +html_theme = "pydata_sphinx_theme" + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +# html_static_path = ['_static'] diff --git a/source/figs.pptx b/source/figs.pptx new file mode 100644 index 00000000..699b6041 Binary files /dev/null and b/source/figs.pptx differ diff --git a/source/fun_figs.png b/source/fun_figs.png new file mode 100644 index 00000000..b351c5aa Binary files /dev/null and b/source/fun_figs.png differ diff --git a/source/fun_figs.py b/source/fun_figs.py new file mode 100644 index 00000000..55099f02 --- /dev/null +++ b/source/fun_figs.py @@ -0,0 +1,177 @@ +# %% +import navlie as nav +import numpy as np +import matplotlib.pyplot as plt +import seaborn as sns + +sns.set_style("whitegrid") + + +# %% Banana distribution plot +def banana_plot(ax=None): + N = 500 + x0 = nav.lib.SE2State([0.3, 3, 4], direction="right") + covariance = np.diag([0.2**2, 0.05**2, 0.05**2]) + process_model = nav.lib.BodyFrameVelocity(np.zeros(3)) + + dx_samples = nav.randvec(covariance, N).T + x0_samples = [x0.plus(dx) for dx in dx_samples] + + # Monte-carlo the trajectory forward in time + dt = 0.1 + T = 10 + stamps = np.arange(0, T, dt) + + if ax is None: + fig, ax = plt.subplots(figsize=(8, 8)) + + final_states = [] + for sample in x0_samples: + x_traj = [sample.copy()] + u = nav.lib.VectorInput([0.1, 0.3, 0]) + x = sample + for _ in stamps: + x = process_model.evaluate(x, u, dt) + x_traj.append(x.copy()) + + # plot the trajectory + traj_pos = np.array([x.position for x in x_traj]) + + # random greyscale color + color = np.random.uniform(0.3, 0.9) + ax.plot( + traj_pos[:, 0], + traj_pos[:, 1], + color=(color, color, color), + zorder=1, + ) + + # save the final state + final_states.append(x_traj[-1]) + + final_positions = np.array([x.position for x in final_states]) + ax.scatter( + final_positions[:, 0], final_positions[:, 1], color="C0", zorder=2 + ) + + # Propagate the mean with EKF + kf = nav.ExtendedKalmanFilter(process_model) + x0_hat = nav.StateWithCovariance(x0, covariance) + + x_hat_traj = [x0_hat] + for t in stamps: + u.stamp = t + x_hat_traj.append(kf.predict(x_hat_traj[-1], u, dt)) + + mean_traj = np.array([x.state.position for x in x_hat_traj]) + ax.plot(mean_traj[:, 0], mean_traj[:, 1], color="r", zorder=3, linewidth=3) + ax.set_aspect("equal") + + +# banana_plot() + + +# %% +def pose3d_plot(ax=None): + N = 500 + x0 = nav.lib.SE3State([0.3, 3, 4, 0, 0, 0], direction="right") + process_model = nav.lib.BodyFrameVelocity(np.zeros(6)) + + dt = 0.1 + T = 20 + stamps = np.arange(0, T, dt) + + x_traj = [x0.copy()] + u = nav.lib.VectorInput([0.1, 0.3, 0, 1, 0, 0]) + x = x0.copy() + for _ in stamps: + x = process_model.evaluate(x, u, dt) + x_traj.append(x.copy()) + + fig, ax = nav.plot_poses(x_traj, ax=ax) + + +# pose3d_plot() + + +# %% +def three_sigma_plot(axs=None): + dataset = nav.lib.datasets.SimulatedPoseRangingDataset() + + estimates = nav.run_filter( + nav.ExtendedKalmanFilter(dataset.process_model), + dataset.get_ground_truth()[0], + np.diag([0.1**2, 0.1**2, 0.1**2, 0.1**2, 0.1**2, 0.1**2]), + dataset.get_input_data(), + dataset.get_measurement_data(), + ) + + results = nav.GaussianResultList.from_estimates( + estimates, dataset.get_ground_truth() + ) + + fig, axs = nav.plot_error(results[:, :3], axs=axs) + axs[2].set_xlabel("Time (s)") + + +# three_sigma_plot() + + +if __name__ == "__main__": + # Make one large figure which has all the plots. This will be a 1x3 grid, with the + # last plot itself being a three vertically stacked plots. + + # The following values where chosen by trial and error + # top=0.975, + # bottom=0.097, + # left=0.025, + # right=0.992, + # hspace=0.2, + # wspace=0.117 + + # which will be used here: + + fig = plt.figure(figsize=(20, 6)) + gs = fig.add_gridspec(1, 3, width_ratios=[1, 1, 1]) + ax1 = fig.add_subplot(gs[0]) + ax2 = fig.add_subplot(gs[1], projection="3d") + + # The last plot is a 3x1 grid + gs2 = gs[2].subgridspec(3, 1, hspace=0.1) + ax3 = fig.add_subplot(gs2[0]) + ax4 = fig.add_subplot(gs2[1]) + ax5 = fig.add_subplot(gs2[2]) + + # Remove tick labels for ax3 and ax4 + ax3.set_xticklabels([]) + ax4.set_xticklabels([]) + + # Remove all tick labels for ax2 + ax2.set_xticklabels([]) + ax2.set_yticklabels([]) + ax2.set_zticklabels([]) + + banana_plot(ax1) + pose3d_plot(ax2) + three_sigma_plot(np.array([ax3, ax4, ax5])) + + # Set spacing to the above values + fig.subplots_adjust( + top=0.975, + bottom=0.097, + left=0.025, + right=0.992, + hspace=0.2, + wspace=0.117, + ) + + # Save the figure with transparent background, next to this file + import os + + fig.savefig( + os.path.join(os.path.dirname(__file__), "fun_figs.png"), + transparent=True, + ) + + plt.show() +# %% diff --git a/source/index.rst b/source/index.rst new file mode 100644 index 00000000..fbb725ee --- /dev/null +++ b/source/index.rst @@ -0,0 +1,62 @@ +.. navlie documentation master file, created by + sphinx-quickstart on Wed Aug 24 15:11:06 2022. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. toctree:: + :maxdepth: 1 + :hidden: + + Home + Tutorial + API + + +Welcome to navlie! +------------------ + +.. make a row of three figures stacked side by side +.. image:: ./fun_figs.png + :width: 100% + :align: center + +navlie is a state estimation package specifically designed for both traditional and Lie-group-based estimation problems! + +The core idea behind this project is to use abstraction in such a way that both traditional and Lie-group-based problems fall under the exact same interface. Using this, a single estimator implementation can operate on a variety of state definitions, such as the usual vector space, and any Lie group. We allow the user to define their custom state, process model, and measurement models, after which they will have a variety of algorithms available to them, including: + +- Extended Kalman Filter +- Iterated Extended Kalman Filter +- Sigmapoint Kalman Filters (Unscented, Spherical Cubature, Gauss-Hermite) +- Interacting Multiple Model Filter +- Batch MAP Estimation + +In addition, navlie contains + +- A large collection of common process and measurement models +- Out-of-the-box on-manifold numerical Jacobians using finite differencing +- Various utils for plotting, error, and consistency evaluation +- Monte Carlo experiment executor with result aggregation +- A preintegration module for linear, wheel odometry, and IMU process models + +By implementing a few classes, the user can model a large variety of problems. The following diagram summarizes the abstraction + +.. image:: ./system_diagram.png + :width: 100% + :align: center + + +Installation +^^^^^^^^^^^^ + +Clone this repo, change to its directory, and execute + +.. code-block:: bash + + git clone git@github.com:decargroup/navlie.git + cd navlie && pip install -e . + +This command should automatically install all dependencies, including our package `pymlg `_ for back-end Lie group mathematical operations. + +Examples +^^^^^^^^ +A more in-depth `tutorial `_ can be found on this website, but there are also many examples found in the `examples/` folder. Simply run these as python3 scripts. \ No newline at end of file diff --git a/source/system_diagram.png b/source/system_diagram.png new file mode 100644 index 00000000..022d65dd Binary files /dev/null and b/source/system_diagram.png differ diff --git a/source/toy_problem.png b/source/toy_problem.png new file mode 100644 index 00000000..3fec2618 Binary files /dev/null and b/source/toy_problem.png differ diff --git a/source/tutorial.rst b/source/tutorial.rst new file mode 100644 index 00000000..bdcf0772 --- /dev/null +++ b/source/tutorial.rst @@ -0,0 +1,27 @@ + +Getting Started +--------------- + +Welcome to the navlie tutorial! The following few pages will go through a toy localization problem, where we will be running state estimation algorithms using navlie's framework. The first step is to install this package. This should be done by directly cloning the git repo and performing a local pip install: + +.. code-block:: bash + + git clone git@github.com:decargroup/navlie.git + cd navlie && pip install -e . + +All the dependencies should get installed by this command and the package should now be ready to use. Use the column on the left to go to next page of the tutorial. + + +.. note:: + + Although this package is currently registed with PyPi, installation via ``pip install navlie`` will not work. We're still figuring out how to set this up properly. Sorry! Feel free to help. + + +.. toctree:: + :hidden: + + 1. Getting Started + 2. Toy Problem - Traditional <./tutorial/traditional.ipynb> + 3. Toy Problem - Lie groups <./tutorial/lie_groups.ipynb> + 4. Specifying Jacobians <./tutorial/jacobians.ipynb> + 4. Composite States <./tutorial/composite.ipynb> \ No newline at end of file diff --git a/source/tutorial/composite.ipynb b/source/tutorial/composite.ipynb new file mode 100644 index 00000000..8a00bfdb --- /dev/null +++ b/source/tutorial/composite.ipynb @@ -0,0 +1,406 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Composite States\n", + "\n", + "The [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) is a class that allows you to arbitarily combine multiple states, potentially of different types, into a new state that can be used with the navlie framework.\n", + "\n", + "Let's consider the previous example where we used the following $SE(2)$ pose transformation matrix to represent the state:\n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab} & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2).\n", + "$$\n", + "\n", + "Suppose we now also want to estimate a wheel odometry bias $\\mathbf{b} \\in \\mathbb{R}^2$ in addition to the robot's pose. Our state is now \n", + "\n", + "$$\n", + "\\mathbf{x} = (\\mathbf{T}, \\mathbf{b}) \\in SE(2) \\times \\mathbb{R}^2.\n", + "$$\n", + "\n", + "This can be implemented easily using the [CompositeState](../_autosummary/navlie.composite.CompositeState.rst) class in one of two ways: either directly or by inheritance. We'll show the former approach first." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [0.1 2. ]\n" + ] + } + ], + "source": [ + "import navlie as nav \n", + "import numpy as np\n", + "\n", + "# Define the pose and bias as their own states\n", + "T = nav.lib.SE2State(value = [0.1, 2.0, 3.0], stamp = 0.0, state_id=\"pose\")\n", + "b = nav.lib.VectorState(value = [0.1, 2.0], stamp = 0.0, state_id=\"bias\")\n", + "\n", + "# Combine into a composite state, and its ready to use!\n", + "x = nav.CompositeState([T, b], stamp=0.0)\n", + "\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``CompositeState`` class is a subclass of the ``State`` class, but who's ``value`` is a list of states, referred to as the *substates*. A convenience of this class is that the composite state's ``plus``, ``minus``, and ``copy`` methods have already been implemented for you based on the implementations in the substates. Note that the order in which the states are listed is important, and will correspond to the order of the components in the vectors involved in the ``plus`` and ``minus`` operations. This can be demonstrated with the following example." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Result after plus():\n", + "CompositeState(stamp=0.0, state_id=None) with substates:\n", + " SE2State(stamp=0.0, state_id=pose, direction=right)\n", + " [[ 0.45359612 -0.89120736 1.80531705]\n", + " [ 0.89120736 0.45359612 6.55185711]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.0, dof=2, state_id=bias)\n", + " [4.1 7. ]\n", + "\n", + "Result after minus():\n", + "[[1.]\n", + " [2.]\n", + " [3.]\n", + " [4.]\n", + " [5.]]\n" + ] + } + ], + "source": [ + "# plus() and minus() have been defined for you. Here, the first three elements\n", + "# of the vector to be added correspond to the pose (since it has 3 DOF), and the\n", + "# last two to the bias.\n", + "x_temp = x.plus(np.array([1,2,3,4,5]))\n", + "print(\"\\nResult after plus():\")\n", + "print(x_temp)\n", + "\n", + "dx = x_temp.minus(x)\n", + "print(\"\\nResult after minus():\")\n", + "print(dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we must write a process model that works with this state. We'll use the same process model as before, but now we'll also include the wheel odometry bias in the state. The bias process model will be modelled as a random walk of the form \n", + "\n", + "$$\n", + "\\mathbf{b}_{k+1} = \\mathbf{b}_k + \\Delta t \\mathbf{w}^\\mathrm{bias}_k,\n", + "$$\n", + "\n", + "where $\\mathbf{w}^{\\mathrm{bias}}_k \\sim \\mathcal{N}(0, \\mathbf{Q}^{\\mathrm{bias}})$ represents random error associated with this otherwise constant process model, which allows the bias to slowly vary. The process model for the composite state is then" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.linalg import expm\n", + "\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "class WheeledRobotWithBias(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " pose = x.value[0]\n", + " bias = x.value[1]\n", + " vel = np.array([u.value[0] - bias.value[0], u.value[1] - bias.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value[0].value = pose.value @ expm(wedge_se2(vel * dt))\n", + "\n", + " # Largely data generation and jacobian purposes, we also update the bias\n", + " # state with an input, even if the input here is always zero in the\n", + " # nominal case.\n", + " x_next.value[1].value = bias.value + u.value[2:4]*dt\n", + " return x_next\n", + " \n", + " def input_covariance(self, x: nav.CompositeState, u: nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(4) * 0.1**2\n", + "process_model = WheeledRobotWithBias(Q)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'd like to use the same measurement model as before, which was just a series of range measurements to known landmarks:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: nav.lib.SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: nav.lib.SE2State):\n", + " return self.R\n", + " \n", + "R = 0.1**2\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The problem is that this was made for an ``SE2State`` instead of our new composite state, and specifically the line `pos = x.value[0:2, 2]` is going to throw an error when we feed in a composite state. This is easy to change, but then that means we have to make a similar change for all sorts of different state definitions. An alternative is to use the [CompositeMeasurementModel](../_autosummary/navlie.composite.CompositeMeasurementModel.rst), which is just a lightweight wrapper around one measurement model that \"assigns\" the model to a specific substate, referenced to by its `state_id` field. It is used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RangeToLandmarkSE2(of substate pose)\n", + "Jacobian:\n", + "[[0. 0.46544123 0.88507893 0. 0. ]]\n" + ] + } + ], + "source": [ + "meas_models = []\n", + "for lm in landmarks:\n", + " meas_models.append(\n", + " nav.CompositeMeasurementModel(RangeToLandmarkSE2(lm, R), \"pose\")\n", + " )\n", + "\n", + "print(meas_models[0])\n", + "print(\"Jacobian:\")\n", + "print(meas_models[0].jacobian(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This does mean that the `state_id` of each substate must be unique, but this is a good practice anyway. The `CompositeMeasurementModel` will then automatically handle the extraction of the relevant substate from the composite state and pass it to the measurement model, as well as handle the corresponding Jacobian accordingly. This is a good way to avoid having to write a lot of boilerplate code for different state definitions. Notice in the above example that the Jacobian has two extra zeros at the end, which correspond to the bias state that has no effect on the measurement. This is automatically handled by the `CompositeMeasurementModel`.\n", + "\n", + "With our problem now set up, we can run a filter on it with the same snippet as usual!" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, \n", + " input_func=lambda t, x: np.array([0.5, 0.3, 0.0, 0.0]), \n", + " input_covariance= Q, \n", + " input_freq=50, \n", + " meas_model_list=meas_models, \n", + " meas_freq_list=[10, 10, 10, 10] \n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2, 0.1**2, 0.1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0,0].set_title(\"Pose Estimation Errors\")\n", + "axs[0,0].set_ylabel(\"theta (rad)\")\n", + "axs[1,0].set_ylabel(\"x (m)\")\n", + "axs[2,0].set_ylabel(\"y (m)\")\n", + "axs[2,0].set_xlabel(\"Time (s)\")\n", + "axs[0, 1].set_title(\"Bias Estimation Errors\")\n", + "axs[0, 1].set_ylabel(\"ang. vel. (rad/s)\")\n", + "axs[1, 1].set_ylabel(\"forward vel. (m/s)\")\n", + "axs[1, 1].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Inheriting from `CompositeState`\n", + "\n", + "The previous example showed how to use the `CompositeState` class directly, but it's also possible to inherit from it. This is useful if you want to add some extra methods or attributes to the composite state, or if you are going to frequently be using the same composite state. Here's an example of how you would do it:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "WheeledRobotState(stamp=0.1, state_id=None) with substates:\n", + " SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n", + " VectorState(stamp=0.1, dof=2, state_id=bias)\n", + " [0.1 2. ]\n", + "SE2State(stamp=0.1, state_id=pose, direction=right)\n", + " [[ 0.99500417 -0.09983342 1.84679329]\n", + " [ 0.09983342 0.99500417 3.09491919]\n", + " [ 0. 0. 1. ]]\n" + ] + } + ], + "source": [ + "class WheeledRobotState(nav.CompositeState):\n", + " def __init__(self, pose_values: np.ndarray, bias_values: np.ndarray, stamp: float):\n", + " pose = nav.lib.SE2State(pose_values, stamp=stamp, state_id=\"pose\")\n", + " bias = nav.lib.VectorState(bias_values, stamp=stamp, state_id=\"bias\")\n", + " super().__init__([pose, bias], stamp=stamp)\n", + "\n", + " # Define any getter that you want for convenience! \n", + " @property\n", + " def pose(self):\n", + " return self.value[0]\n", + "\n", + " @property\n", + " def bias(self):\n", + " return self.value[1]\n", + "\n", + " def copy(self):\n", + " return WheeledRobotState(self.pose.copy(), self.bias.copy())\n", + " \n", + "x = WheeledRobotState([0.1, 2.0, 3.0], [0.1, 2.0], stamp = 0.1)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can end up looking a lot cleaner, and is potentially more flexible to work with since you can add methods and attributes to the composite state. For example, because of the getters we defined above, we can access the pose and bias more ergonomically with `x.pose` and `x.bias`." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/source/tutorial/jacobians.ipynb b/source/tutorial/jacobians.ipynb new file mode 100644 index 00000000..ce634985 --- /dev/null +++ b/source/tutorial/jacobians.ipynb @@ -0,0 +1,341 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Jacobians in navlie\n", + "\n", + "As you may know, many state estimation algorithm require access to process model and measurement model Jacobians, with respect to the state and sometimes other inputs. For states belonging to Lie groups, algorithms will require _Lie Jacobians_, which differ from traditional derivatives as they conform to the constraints of the group. The abstraction provided by the $\\oplus$ and $\\ominus$ operators (implemented with `State.plus` and `State.minus` respectively) allow for a generic definition of a derivative:\n", + "\n", + "$$\n", + "\\left.\\frac{D f(\\mathcal{X})}{D \\mathcal{X}}\\right|_{\\bar{\\mathcal{X}} }\\triangleq \\left.\\frac{\\partial f(\\bar{\\mathcal{X}} \\oplus \\delta \\mathbf{x}) \\ominus f(\\bar{\\mathcal{X}})}{\\partial \\delta \\mathbf{x}}\\right|_{\\delta \\mathbf{x} = \\mathbf{0}},\n", + "$$\n", + "\n", + "which can be shown to fall back to a traditional derivatives when $\\oplus$ and $\\ominus$ are defined to be regular addition/subtraction. This derivative definition is used universally throughout navlie, and roughly follows what is done in the [Micro Lie Theory paper](https://arxiv.org/pdf/1812.01537.pdf). In that reference, seperate definitions are given for \"left\" and \"right\" derivatives, whereas we have aggregated them into a single definition, with left and right derivatives naturally arising from the choice of $\\oplus$ and $\\ominus$ operators.\n", + "\n", + "If you dont want to worry about this, the good news is that navlie computes Lie Jacobians for you by default using finite difference. However, finite difference can have some drawbacks, such as being computationally expensive and less accurate than analytic derivatives. In this notebook, we will show you how to use analytic derivatives in navlie, which offer the maximum accuracy and speed.\n", + "\n", + "## Jacobians - Traditional Approach\n", + "Recall the traditional approach to the previous example. We had defined the state to be $\\mathbf{x} = [\\theta, x, y]^T$ and the process model to be\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t \\\\\n", + "x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t \\\\\n", + "y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where $\\omega_k$ is the angular velocity and $v_k$ is the linear velocity. Since the state is just a regular vector, Lie Jacobians fall back to regular Jacobians, and standard derivative techniques lead to the following expressions for the process model Jacobian with respect to the state\n", + "\n", + "$$\n", + "\\mathbf{F} := \\frac{\\partial f(\\mathbf{x}_k, \\mathbf{u}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 1 & 0 & 0 \\\\ -v_k \\sin(\\theta_k) \\Delta t & 1 & 0 \\\\ v_k \\cos(\\theta_k) \\Delta t & 0 & 1 \\end{bmatrix}\n", + "$$\n", + "\n", + "To implement this Jacobian in navlie, all we need to do is override the `jacobian()` method in our process model, and it will get used automatically by the estimation algorithms. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import navlie as nav\n", + "import numpy as np\n", + "\n", + "from navlie.lib import VectorInput, VectorState\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + " def jacobian(self, x:VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " F = np.eye(3)\n", + " F[1, 0] = -u.value[1] * dt * np.sin(x.value[0])\n", + " F[2, 0] = u.value[1] * dt * np.cos(x.value[0])\n", + " return F\n", + "\n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, lets just double check that we did everything correctly by comparing with finite difference. All process models inherit the `jacobian_fd()` method, which computes the Jacobian using finite difference. We can use this to compare with our analytic Jacobian." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682942 1. 0. ]\n", + " [ 0.01080605 0. 1. ]]\n", + "\n", + "Finite difference:\n", + "[[ 1. 0. 0. ]\n", + " [-0.01682943 1. 0. ]\n", + " [ 0.01080604 0. 1. ]]\n" + ] + } + ], + "source": [ + "x = VectorState([1,2,3]) \n", + "u = VectorInput([0.1, 0.2]) \n", + "dt = 0.1 \n", + "\n", + "print(\"Analyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Jacobians match almost perfectly, but differ slightly due to errors in finite difference. This is expected, as finite difference is only an approximation. Nevertheless, finite difference is generally sufficiently accurate for most applications.\n", + "\n", + "
\n", + "Note: The `jacobian` methods must *always* return a 2D array.\n", + "
\n", + "\n", + "\n", + "\n", + "Moving on to the measurement model, which was previously defined to be \n", + "\n", + "$$\n", + "\\mathbf{y}_k = || \\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)} || \n", + "$$ \n", + "\n", + "where $\\mathbf{r}_k$ is the robot's position and $\\boldsymbol{\\ell}^{(i)}$ is the $i$th landmark. The measurement model Jacobian with respect to the state is\n", + "\n", + "$$ \n", + "\\mathbf{G} := \\frac{\\partial g(\\mathbf{x}_k)}{\\partial \\mathbf{x}_k} = \\begin{bmatrix} 0 & \\frac{(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})^T}{||(\\mathbf{r}_k - \\boldsymbol{\\ell}^{(i)})||} \\end{bmatrix},\n", + "$$\n", + "\n", + "and we can implement this in navlie by again overriding the `jacobian()` method in our measurement model. Adding this to our measurement model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[0. 0.70710678 0.70710678]]\n", + "\n", + "Finite difference:\n", + "[[0. 0.70710696 0.70710696]]\n" + ] + } + ], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + " def jacobian(self, x: VectorState) -> np.ndarray:\n", + " G = np.zeros((1, 3))\n", + " r = x.value[1:]\n", + " G[0,1:] = (r - self.landmark_position) / np.linalg.norm(r - self.landmark_position)\n", + " return G\n", + " \n", + "meas_model = RangeToLandmark(np.array([1, 2]))\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(meas_model.jacobian(x))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(meas_model.jacobian_fd(x))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can again see that the results match nicely." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jacobians - Lie Group Approach \n", + "\n", + "Now, lets see how to implement analytical Jacobians when states belong to Lie groups. In the previous example the state was $\\mathbf{T} \\in SE(2)$ and the process model was\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t).\n", + "$$\n", + "\n", + "To derive the Jacobian, we can \"perturb\" both sides of the equation and manipulate. This is a common technique for deriving Lie Jacobians, and for computing matrix-vector derivatives in general. For more details, we recommend reading [State Estimation for Robotics by Tim Barfoot](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf).\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "\\mathbf{T}_{k+1} &= \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + "\\bar{\\mathbf{T}}_{k+1} \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\bar{\\mathbf{T}}_{k} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\underbrace{\\bar{\\mathbf{T}}_{k+1}^{-1} \\bar{\\mathbf{T}}_{k}}_{\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}} \\exp(\\delta \\boldsymbol{\\xi}_{k}^\\wedge) \\exp(\\boldsymbol{\\varpi}^\\wedge_k \\Delta t) \\\\\n", + " \\exp(\\delta \\boldsymbol{\\xi}_{k+1}^\\wedge) &= \\exp((\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1}) \\delta \\boldsymbol{\\xi}_{k})^\\wedge) \\\\\n", + " \\delta \\boldsymbol{\\xi}_{k+1} &= \\underbrace{\\mathbf{Ad}(\\exp(\\boldsymbol{\\varpi}^\\wedge \\Delta t)^{-1})}_{\\mathbf{F}} \\delta \\boldsymbol{\\xi}_{k}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "There, we used the _adjoint matrix_ $\\mathbf{Ad}(\\cdot)$, to invoke the identity $\\mathbf{X}^{-1} \\exp(\\boldsymbol{\\xi}^\\wedge) \\mathbf{X} = \\exp(\\mathbf{Ad}(\\mathbf{X}) \\boldsymbol{\\xi}^\\wedge)$, which is true for any $\\mathbf{X} \\in SE(2)$. The adjoint matrix for $SE(2)$ is given by \n", + "\n", + "$$ \n", + "\\mathbf{Ad}(\\mathbf{T}) = \\begin{bmatrix} 1 & \\mathbf{0} \\\\ - \\boldsymbol{\\Omega} \\mathbf{r} & \\mathbf{C} \\end{bmatrix}\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\Omega} = \\begin{bmatrix} 0 & -1 \\\\ 1 \n", + "&0 \\end{bmatrix}$.\n", + "\n", + "
\n", + "Note: in this Jacobian derivation, we perturbed the state $\\mathbf{T} = \\bar{\\mathbf{T}} \\exp(\\delta \\boldsymbol{\\xi}^\\wedge)$ \"on the right\" because that corresponds to what was implemented in the `plus()` method of our `SE2State` class. It is important to be consistent here for everything to work.\n", + "
\n", + "\n", + "Now, we can implement this Jacobian in navlie by overriding the `jacobian()` method in our process model. Adding this to our process model from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Analyical:\n", + "[[ 1. 0. 0. ]\n", + " [ 0.0394695 0.92106099 0.38941834]\n", + " [ 0.19470917 -0.38941834 0.92106099]]\n", + "\n", + "Finite difference:\n", + "[[ 1.00000000e+00 -1.10747782e-11 -1.10747782e-11]\n", + " [ 3.94695038e-02 9.21060995e-01 3.89418343e-01]\n", + " [ 1.94709171e-01 -3.89418342e-01 9.21060994e-01]]\n" + ] + } + ], + "source": [ + "from navlie.lib import SE2State, VectorInput\n", + "from scipy.linalg import expm\n", + "\n", + "\n", + "def wedge_se2(x:np):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def adjoint_se2(T:np.ndarray):\n", + " C = T[:2, :2]\n", + " r = T[:2, 2]\n", + " Omega = np.array([[0, -1], [1, 0]])\n", + " Ad = np.zeros((3,3))\n", + " Ad[0,0] = 1\n", + " Ad[1:,1:] = C\n", + " Ad[1:,0] = - Omega @ r\n", + " return Ad\n", + "\n", + "\n", + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(u * dt))\n", + " return x_next\n", + " def input_covariance(self, x:SE2State, u:VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + " def jacobian(self, x:SE2State, u:VectorInput, dt:float):\n", + " u = np.array([u.value[0], u.value[1], 0])\n", + " return adjoint_se2(expm(-wedge_se2(u * dt)))\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)\n", + "x = SE2State(expm(wedge_se2(np.array([1,2,3]))))\n", + "u = VectorInput([4, 2])\n", + "dt = 0.1\n", + "\n", + "print(\"\\nAnalyical:\")\n", + "print(process_model.jacobian(x, u, dt))\n", + "\n", + "print(\"\\nFinite difference:\")\n", + "print(process_model.jacobian_fd(x, u, dt))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that when using Lie groups, our Jacobian no longer has dependence on the state itself. This can be a tangible advantage when the state estimate has high uncertainty, where using a traditional approach can result in excessive linearization errors when the state estimate is far from the true value." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/source/tutorial/lie_groups.ipynb b/source/tutorial/lie_groups.ipynb new file mode 100644 index 00000000..fd96344d --- /dev/null +++ b/source/tutorial/lie_groups.ipynb @@ -0,0 +1,425 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Lie group approach\n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "Another way we could approach the same state estimation task is to instead use Lie group theory, which is becoming increasingly common practice in state estimation. Lie group theory can be very abstract, and the main references that navlie refer to are the following:\n", + "\n", + "1. [A micro Lie theory for state estimation in robotics](https://arxiv.org/abs/1812.01537)\n", + "2. [T.Barfoot, State Estimation for Robotics](http://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser17.pdf)\n", + "\n", + "\n", + "## Define the State\n", + "Instead of representing the state using a vector, we will represent the state using an element of the *special Euclidean group* $SE(2)$, sometimes called *pose transformation matrices*. Elements of this group are 3x3 matrices of the form \n", + "\n", + "$$ \n", + "\\mathbf{T} = \\begin{bmatrix} \\mathbf{C}_{ab}(\\theta) & \\mathbf{r}_a \\\\ \\mathbf{0} & 1 \\end{bmatrix} \\in SE(2)\n", + "$$\n", + "\n", + "where $\\mathbf{r}_a = [x,y]^T$ again denotes the position of the robot and $\\mathbf{C}_{ab}(\\theta) \\in SO(2)$ is a rotation matrix (sometimes called a direction cosine matrix) with the form \n", + "\n", + "$$ \n", + "\\mathbf{C}_{ab}(\\theta) = \\begin{bmatrix} \\cos \\theta & - \\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{bmatrix}.\n", + "$$\n", + "\n", + "The rotation matrix transforms vectors resolved in one frame to another frame, i.e. $\\mathbf{r}_a = \\mathbf{C}_{ab} \\mathbf{r}_b$. Unlike vectors, elements of $SO(2)$ or $SE(2)$ cannot be added together to produce another valid element of $SE(2)$, but they can be multiplied together with the result still having the same form.\n", + "\n", + "$$\n", + "\\mathbf{T}_1 \\mathbf{T}_2 \\in SE(2)\n", + "$$\n", + "\n", + " To proceed further with our mathematical setup, we need to define a few very common operators seen in Lie group theory. The first two are the \"wedge\" $(\\cdot)^\\wedge$ and \"vee\" $(\\cdot)^\\vee$ operators, which for this specific group has the form\n", + "\n", + "$$ \n", + "\\begin{bmatrix} \\theta \\\\ x \\\\ y \\end{bmatrix}^\\wedge = \\begin{bmatrix} 0 & -\\theta & x \\\\ \\theta & 0 & y \\\\ 0 & 0 & 0 \\end{bmatrix}\n", + "$$\n", + "\n", + "and the $(\\cdot)^\\vee$ operator simply does the exact inverse of $(\\cdot)^\\wedge$. We can implement them as follows.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "%reset -f\n", + "import numpy as np\n", + "\n", + "# Helper functions for SE(2)\n", + "def wedge_se2(x):\n", + " return np.array([[ 0, -x[0], x[1]],\n", + " [x[0], 0, x[2]], \n", + " [ 0, 0, 0]])\n", + "\n", + "def vee_se2(X):\n", + " return np.array([X[1, 0], X[0, 2], X[1, 2]])\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Two other fundamental relationships appearing in Lie group theory are the exponential (denoted $\\exp$) and logarithmic (denoted $\\log$) maps. While these have a deeper definition, for our case it suffices to think of them as simply the [matrix exponential](https://en.wikipedia.org/wiki/Matrix_exponential) and [matrix logarithm](https://en.wikipedia.org/wiki/Logarithm_of_a_matrix). Using the wedge and vee operators for $SE(2)$ defined above, we can convert a 3x1 vector to an $SE(2)$ element and back as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "An element of SE2:\n", + "[[ 0.99500417 -0.09983342 0.18467933]\n", + " [ 0.09983342 0.99500417 0.30949192]\n", + " [ 0. 0. 1. ]]\n", + "\n", + "The original vector 'representing' it:\n", + "[0.1 0.2 0.3]\n" + ] + } + ], + "source": [ + "from scipy.linalg import expm, logm\n", + "\n", + "T = expm(wedge_se2(np.array([0.1, 0.2, 0.3])))\n", + "print(\"An element of SE2:\")\n", + "print(T)\n", + "\n", + "x = vee_se2(logm(T))\n", + "print(\"\\nThe original vector 'representing' it:\")\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have the tools we need to abstract-ify our problem a little bit. As commonly seen in the literature, we can define the so-called \"oplus\" and \"ominus\" operators as follows (sometimes called \"boxplus\" $\\boxplus$ and \"boxminus\" $\\boxminus$):\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbf{T}_2 &= \\mathbf{T}_1 \\oplus \\boldsymbol{\\xi} := \\mathbf{T}_1 \\exp(\\boldsymbol{\\xi}^\\wedge) \\\\\n", + "\\boldsymbol{\\varepsilon} &= \\mathbf{T}_2 \\ominus \\mathbf{T}_1 := \\log(\\mathbf{T}_2^{-1} \\mathbf{T}_1)^\\vee\n", + "\\end{aligned}\n", + "$$ \n", + "\n", + "Here, both $\\boldsymbol{\\varepsilon}, \\boldsymbol{\\xi} \\in \\mathbb{R}^3$ are 3x1 vectors. The $\\oplus: SE(2) \\times \\mathbb{R}^3 \\to SE(2)$ operator \"adds\" a vector to an $SE(2)$ element to produce another $SE(2)$ element, and the $\\ominus:SE(2) \\times SE(2) \\to \\mathbb{R}^3$ operator \"subtracts\" two $SE(2)$ elements to produce a vector that represents the \"difference\" between them. \n", + "\n", + "\n", + "With this context, lets implement an $SE(2)$ state inside navlie's framework. To define a custom state, you must subclass the `nav.State` abstract class and you *must* implement the `plus`, `minus`, and `copy` methods. These methods play exactly the role of $\\oplus$ and $\\ominus$ described above, while the `copy` method is used to create a deep copy of that state object. In addition, state objects must hold an integer property named `dof` that specifies the *degrees of freedom* associated with that state. For $SE(2)$, this is 3." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.0, dof=3, state_id=None)\n", + " [[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n" + ] + } + ], + "source": [ + "import navlie as nav\n", + "\n", + "class SE2State(nav.State):\n", + " def __init__(self, value :np.ndarray, stamp: float):\n", + " super().__init__(value=value, dof=3, stamp=stamp)\n", + "\n", + " def plus(self, dx: np.ndarray):\n", + " new_value = self.value @ expm(wedge_se2(dx))\n", + " return SE2State(new_value, self.stamp)\n", + "\n", + " def minus(self, other: \"SE2State\"):\n", + " other_inv = np.linalg.inv(other.value)\n", + " return vee_se2(logm(other_inv @ self.value))\n", + " \n", + " def copy(self):\n", + " return SE2State(self.value.copy(), self.stamp)\n", + "\n", + "x = SE2State(np.eye(3), 0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Process Model\n", + "\n", + "Now, we must adapt the process model to work with our new `SE2State`. It is well known that the rotational kinematics can be written directly in terms of rotation matrices using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{C}}_{ab} = \\mathbf{C}_{ab}\\begin{bmatrix}0 & -\\omega \\\\ \\omega & 0 \\end{bmatrix} \n", + "$$\n", + "\n", + "and that the translational kinematics can be written in vector form using \n", + "\n", + "$$ \n", + "\\dot{\\mathbf{r}}_a = \\mathbf{C}_{ab} \\begin{bmatrix} v \\\\ 0 \\end{bmatrix} .\n", + "$$\n", + "\n", + "By stacking these into matrices it follows that \n", + "$$ \n", + "\\dot{\\mathbf{T}} = \\mathbf{T} \\boldsymbol{\\varpi}^\\wedge\n", + "$$\n", + "\n", + "where $\\boldsymbol{\\varpi} = [\\omega, v, 0]^T$. This equation is now a linear, matrix-valued ODE, and can be integrated exactly over a short duration $\\Delta t = t_{k+1} - t_k$ using the matrix exponential. This gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\mathbf{T}_{k+1} = \\mathbf{T}_k \\exp(\\boldsymbol{\\varpi}_k^\\wedge \\Delta t)\n", + "$$\n", + "\n", + "which we can implement as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "class WheeledRobotSE2(nav.ProcessModel):\n", + " def __init__(self, input_covariance_matrix):\n", + " self.Q = input_covariance_matrix\n", + "\n", + " def evaluate(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " vel = np.array([u.value[0], u.value[1], 0])\n", + " x_next = x.copy()\n", + " x_next.value = x.value @ expm(wedge_se2(vel * dt))\n", + " return x_next\n", + " \n", + " def input_covariance(self, x:SE2State, u:nav.lib.VectorInput, dt:float):\n", + " return self.Q\n", + "\n", + "Q = np.eye(2) * 0.1**2\n", + "process_model = WheeledRobotSE2(Q)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the Measurement Model\n", + "\n", + "Finally, our measurement model remains largely unchanged. We just need to extract the position from an `SE2State` object now, as done below." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmarkSE2(nav.MeasurementModel):\n", + " def __init__(\n", + " self,\n", + " landmark_position: np.ndarray,\n", + " measurement_covariance: float,\n", + " ):\n", + " self.landmark_position = landmark_position\n", + " self.R = measurement_covariance\n", + "\n", + " def evaluate(self, x: SE2State):\n", + " pos = x.value[0:2, 2]\n", + " return np.linalg.norm(pos - self.landmark_position)\n", + "\n", + " def covariance(self, x: SE2State):\n", + " return self.R\n", + " \n", + "\n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmarkSE2(landmark, 0.1**2) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run the Filter!\n", + "\n", + "And that's it! All remaining snippets are now _literally_ copy-pasted from our previous approach with zero modifications. Using the abstraction framework in navlie, we can easily switch between different state representations and process/measurement models without having to change any of data generation or filtering code. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SE2State(stamp=0.02, dof=3, state_id=None)\n", + " [[ 9.99950000e-01 -9.99983333e-03 5.99990000e-03]\n", + " [ 9.99983333e-03 9.99950000e-01 2.99997500e-05]\n", + " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00]]\n", + "VectorInput(stamp=0.04, state_id=None)\n", + " [0.52438924 0.40056502]\n", + "Measurement(stamp=0.0, state_id=None) of PoseRangeToLandMark\n", + " 2.299276237837416\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.5, 0.3]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[1])\n", + "print(input_data[2])\n", + "print(meas_data[3])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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cNIt2mD+0USBPPN4OIxPKExf2QWH7LCSaJVjtjsbqmiDGaZIC3MkL8EbuS1NEnQHpBHi8htLbDEwo15zREV/fPlwW4MILRRAkTVKAqxq4SYpLgRHtsMAVvd93vC5iVtbZAABJFnf/9wTFBi7GoSAYmqQAZxqgxSQ08MagpMoKwGARU8lG+MAXGzBv/WGDI2OTPSeqAACdW6a6tSWaJVAq8qEIgqNJCnCXDVyKS40vVjDyQqmut+OzNcWY9sn6xulUGKhTFinTEt0DmFhqWbaQecFLy/DoN1si1zlBTNMkBbiT80IRNB5GBR34Qgfxgp15oUhGboSyWYX5gm86XIH3V+yPWN8EsU2TFOB2zoQCxGcCpcbmUFkNrnlnFSpqbB730Xuh8J8L22eFq2sRx+rQjjcepoHfOedP7D4Rfy8vQXhpkgKc1SA0K14BQn6Hntd/3YOlu0rw1Z/FHvfRz4B4AZfuIV9KLGJ3OGGWiGEucOaZsmx3Cf4+Z32EeyaIdZqoAJf/N0vxXEa3cclOSQAAVNTaPe6j18B5gZ7iIWNhLGJ3UsMgHgBItLgewVqr598q3qGU4tedJ8VsOECapAC3O7WRcWLQhJ7fdp0EAFjMntcZ9JGYZoNQ83jAanca5kEBtL7h/PU7m5hXytfrD+O6d1djzupDjd2VmKJBTwwhJIsQ8gUhZDshZBshZGioOhZOHJwXCiA08FBzuLwWG4srAMieJZ7QL2KauQ3xFNtid3oW4Imcb3h+c5ebYXUT08aPlMvFPQ6dqmnknsQWDTU0vgBgAaV0CiEkAUCKrwOiAQcXiQkIG3ioOV3rWrj0lh5WH4nJe2nEU1pZm50aLmACWg2cz0rY1CpFsaEQT/c9EgQtwAkhmQBGAbgeACilVgDW0HQrvPxv5QEAnAlF6OAhpc7mMPxbj34Rk/8YTwLM5nQauhACOhs491sZ1c90Oql7ArA4gc3UhPwOjIaYUPIBnATwHiHkT0LI24QQt1AzQshUQsgaQsiakydPNuDrQoPN4cRcpZiuRXihhAVeEJV7cSPUh5bz0YjxpInZHFR1F9TDa+C1Vtfvpn+BHSqrQaeHvncvBB0nsPeSWI8KjIYIcDOAAQBeo5T2B1ANYLp+J0rpm5TSIkppUYsWLRrwdaFh53GXr60I5AkP9TaXKeBUjedJmV6A80md4kkDZ26ERiRxGnhJVb36t76K0S7FR/ybDUfC0MPGh3kkCfkdGA2xgRcDKKaUrlI+fwEDAe4Lm82G4uJi1NXV+d45BNhsDrw1qQ0AuR7hVd3bYO+uHYY+ugLvJCUloV27drBYLJrtvNmkotazBq5/gcarDdjmoB49bHg5fbSijtuuvX42PuPpd+Fx2cAbtx+xRtACnFJ6jBByiBDSnVK6A8BYAFsDPU9xcTHS09ORl5cXESFaUWuFVCqvdGcmW1BRa0P33EyhjQcIpRSlpaUoLi5Gfn6+po3XpL3ZwPXwWmd8mVCcSPCwiNmpRSr+MqAd5q0/rDEh6ZNbsQXfePpdeEicX1+4aKjj7d8BfEwI2QigEMC/Aj1BXV0dcnJyIqYB8xqPNxc3gXcIIcjJyTGcOfHPoNFinCds8WpCcTo9auAWk4T/XlqAzi3S3I7hkeJcwIknMTga5EZIKV0PoKihnYik+YIXDMJq0jA83TeHRpPUCqKRXZtj6a4STBnYzu04ltgJAAKQ+1GPNzdChv6ntOt+AObEEk8vNh7hRhgc8Rn65gWjAZJgMaOwsFD9N3PmzLD3o7y8HK+++mrAxz366KP4z3/+Y7g9JSUFJ06cULelpbm0OpPJZHiNY8aMQffu3dXtU6ZMAQDs2LEDY8aMQWFhIXr27ImpU6f63Uf+N9YLorevK8L+mRPxn0sK3I7r3jpd7qtE4ioS0eYlkIehTyvgJqiVj844CnAyQuhUgRE/GYP8xEgDT05Oxvr16yPaDybAb7vttpCds3nz5vjvf/+Lp59+2q3N2zV+/PHHKCrSTqTuvPNO3H333Zg8eTIAYNOmTX73Q2tCcUmcvJwUjZat5+6zu6F3bga+/vOwGpkXD9gcfghwXbN+5sJs4o4411CFM0FgNGkNnLeB6/1PKyoq0L17d+zYsQMAcMUVV+Ctt94CIGu2d999N3r37o2xY8eC+bfv2bMH48ePx8CBAzFy5Ehs374dAHD8+HFcdNFFKCgoQEFBAVasWIHp06djz549KCwsxP333w8AePbZZzFo0CD069cPjzzyiNqXp556Ct26dcOIESPU/hhx44034tNPP0VZWVlDfiIAwNGjR9GuncvM0bdvX7+P5YUMEzw9WqfjpSsGeD0uwSzh/H65kAiJq6m03UE9uhEy9Bq4fu2AKR4nKuPnxcYTRxOuiBJdGvhddwGh1oQLC4Hnn1c/8nKBPTO1tbXo2acfEkwSJIngwQcfxGWXXYaXX34Z119/PaZNm4ZTp07h5ptvBgBUV1ejqKgIzz33HB5//HE89thjePnllzF16lS8/vrr6Nq1K1atWoXbbrsNixcvxp133onRo0fjq6++gsPhQFVVFWbOnInNmzerWvHChQuxa9curF69GpRSTJo0Cb/99htSU1PxySefYP369bDb7RgwYAAGDhxoeKlpaWm48cYb8cILL+Cxxx7TtNXW1qKwsFD9zK4RAK666iokJycDAM455xw8++yzuPvuu3HWWWdh2LBhOPfcc3HDDTcgKyvLr5/cyITy6lUD0Em3UOcJk0TiytZrczhh8RDIw2CaZ4JJLnKs995hM5lDZbXYebwS3Vqlh6ezjUQ8mcwiSXQJ8AhhMUlon52MOiXgJCk5GZ/9uBRZyQnokONK53LOOefg888/x+23344NGzao2yVJUoXf1VdfjYsvvhhVVVVYsWIFLrnkEnW/+no5MGPx4sX48MMPAci26MzMTJw6dUrTp4ULF2LhwoXo378/AKCqqgq7du1CZWUlLrroIqSkyP2aNGmS12u78847UVhYiPvuu0+zPVATyg033IBx48ZhwYIFmDdvHt544w1s2LABiYmJXr8f0D6Mh8trAbhrmN6QJBJXpgKbg8LiUwOX/09PMqO02ooaqwNbj5zGgdJqnNe3jeaFNvnl5dj2xPhwdjnisJd+PL24I0F0CXBOUw4XlMrCJC3JgjqbLGDZo6W3OzqdTmzbtg0pKSk4deqUxqTAQwiB0+lEVlZW0LZ0SikefPBB3HLLLZrtzwf4m2RlZeHKK6/EK6+8ElQ/eHJzc3HjjTfixhtvRJ8+fbB582aP2j+P0TMYiAA3kfhaxLT7YwNXfh8mwKvq7Zjw4lIAwP6ZE2Hjfo96u/++9bECu7poNZ0dLq/Fhyv244HxPaIqZqTJ2cAdlLos37r7oJcZzz33HHr27InZs2fjhhtugM0mRxU6nU588cUXAIDZs2djxIgRyMjIQH5+Pj7//HMAskBmWvvYsWPx2muvyd/vcKCiogLp6emorHSF9Y8bNw7vvvsuqqrkCuaHDx/GiRMnMGrUKHz99deora1FZWUlvv32W5/XeM899+CNN96A3R58StIFCxao13vs2DGUlpaibdu2fh1r9BB6yOVkiCnONHCrl0hMBpMJGclyVGtNvfbeOZx8kBPw09bjoe1kI8PGTLTe9Ue/2YI3ftuL3/eWNnZXNDQpAV5Tb0dlnQ11Og2mtrYWl44biQvOGobCwkJMnz4dO3bswNtvv43//ve/GDlyJEaNGoUnn3wSAJCamorVq1ejT58+WLx4Mf7v//4PgGyKeOedd1BQUIDevXtj3rx5AIAXXngBS5YsQd++fTFw4EBs3boVOTk5GD58OPr06YP7778f5557Lq688koMHToUffv2xZQpU1BZWYkBAwbgsssuQ0FBAc477zwMGjTI53U2b94cF110kWrCYdfIuxFOn+7KenDVVVep288++2wAskmnT58+KCgowLhx4/Dss8+idevWfv3ORtPggEwohMSNu9ysn3aipKreDz9wlwYOANVcYiur3em2qHnzh2tC3NPGhb2vozWZVapSIepYRXQtIkeXCSXMVNYba6THK2pwpLwWyQkmdG3pWhzatm2b+vesWbM0x+g/A0B+fj4WLFjgtr1Vq1aqMOeZPXu25vO0adMwbdo0t/1mzJiBGTNmGPad8eijj7r1j++jw2E87f7ll18Mt+uPDwSjZzAgE4oUP7bQFxftAgA/TCjy/8kWE8wSQTU3Vj/946ChBk8p9ZrpMJZgJrNofXGzxGv1ds8d/OyPQ2iTlYSRXSOXtC/273wA+Hy5x4fMaHSMzB9N2YQCwGNNTAZ7wUmEIDXRrBHgD8/bgi1HKtyO+fcP29Htnz9okoDFKtFuA2f98mb+fuDLjbjmndUR6pFMkxLgeiHC7oU6ffPzPMxOLTDG0AYesAklOh/kYEnwcxFTIgSpCSZUWx3o1SYDgOxD/9HvB92O+WDFfgDuqWdjkWi3gbMh7c847vHwD6iJUEm8JiXARfKqyNBwE0ocauA+piDs5zFJBEkWE2ptDuSkJQAA2mQmGR7DzEz6dAWxCHtf61/cJVX1WH+oPPId0qH2yo9hXGdz4qXFu8PZHZUmJcA9E/sPQDTBBMvg/GbqNn39S29IJL4CeQDAYvZvEVOSCCQlF8zSXSUAPCf2YlGutmg1HAcAW7zUp9Gd/PJyXPjK8oj1o6LGpimswXCZUPwbx6/9siek/fKEEOBwie84U/oaBYeTYtZPOwEAT/+ln7qdBGgDjzcTSqt0Yy2awWyrJiK/7E7XuQph+PLMiAcNnF2ifubFAsEixYAnf0LRkz/jUFmNZjvrlr9qyLVDO4a2Yx5oYgLcw0CP/fEfNRworVb/5l3nmroJpWsr72kEJE4DJ0RbycjXwl482cAdjfwyYjO/v328VrOd9c/fYczcQcNNkxLgbGj0bC0vDrHXaXyJisaFr8bDu84FakKJA6uAhowki9d2poEnmiWYJKLxN/ZlTooPAS7/z7+4+VlYpP3D9bMal5+6n8dHaAbZpAQ4k9QmRTPUixQqRHmD4Qc+L8ADyRJqktzTGsQ6uVnJXtvZImd6kgUSISipchWD9iULIiUswgkT0PzLasUeV9RjpNdE9OHyTAP3180xUjOJJiXA2U/qLriBj995HeePHoLevXtr8o/k5eWhb9++KCwsVBM+nTx5EiNGjECfPn3w9ddfq/tOnjwZR46Ev2r4iy++iJ49e+Kqq67yut+wYcO8tgdbVMIb/INmDtaEQgicNHqj8gIh2WLC1FGdfAbbMKUiPdGs8TXu0zYDdh8adjz5gXt6GR3U2aTDjV6AB7pO9vayfThVbfW9YwNpUgLcHfkmbd+yBV/O/gAff7cIS39fg++++w67d7vcgJYsWYL169djzRo5fHnOnDm49dZbsXr1alXYf/vtt+jfvz9yc3PD3utXX30VP/30Ez7++GOv+61YscJrezgEOK85WzjXuUDy/0gSq/8Ysm41CpRS1NsdSPQjUpIJ6bQks3r9yRYTaqwOrDtYrn42PDbWfyjwkZiua0myuH638c8vjWh/3BQO5uboRYJnp1gwprsrCnPUs0vC0TUNTVyAy+zauR19+xchOTkFJpMJo0ePxty5cz3ub7FYUFNTg/r6ephMJtjtdjz//PN44IEHvH7Phx9+iH79+qGgoADXXHMNADlkvU+fPujTp49G89+/fz969uyJm2++Gb1798a5556L2tpa3Hrrrdi7dy/OO+88PPfcc16/j5VU83Quo6ISDUVrQnE9BIFkcGOml1i37W45chpO6juIB3AVcEhLNKvCIy3JjL0nXYvCN4/qZHjsvPWHQ9DbxoXJbV4B4EWlNcJjQV+Aw2VC8XwMBZCXk6p+rqyzhz2gJ+pyoYwZM8Zt26WXXorbbrsNNTU1mDBhglv79ddfj+uvvx4lJSVqTUcGn+tDdQXSvV279+yFJx97BOWnytAqheD7779XzSWEEJx77rkghOCWW27B1KlTceWVV+LKK6/Em2++iaeffhqvvvoqrrnmGjVntxFbtmzBk08+iRUrVqB58+YoKyvD2rVr8d5772HVqlWglGLIkCEYPXq0mhN8165dmDNnDt566y1ceuml+PLLL/H6669jwYIFWLJkCZo3b+7PT+rxXPqiEqGAN6HwQjuQUlkpSuKgWqtDzUERi/zlNXkGVGvznf6VvazSkyzqgi+vgQIw9E8GgPeW78cjF/RuSFcbHVVAcnLa1oimIUknwNksx9s6mdNJ3dZ69p6sRp+2mSHvH6OJaeDUMBqza/ceuOG2abj1qotx8aTzUVhYCJNJFhzLli3DunXr8MMPP+CVV17Bb7/9hszMTMyfPx9r1qzBgAED8O2332LKlCm4+eabMWXKFKxcudLtOxYvXoxLLrlEFbrNmjXDsmXLcNFFFyE1NRVpaWm4+OKLsXSpa6qYn5+vVtEZOHAg9u/fH/SVh/Jc3uCn88HWN0xNYBn5IhOOHC5Y4iNfqWQBlwBPSzSrQkAfvVlrjb884Hp4DdzWiKahWqsDlFI8++N27DhWiT0n5PQZXjVw6m568ZXErKFEnQbuKTseAKSkpHhtb968udd2CmhWMNmfZdVWXHz5Nbj48muQl5OKmU88ohZvYDmwW7ZsiYsuugirV6/GqFGj1HM88cQTmDFjBubMmYMRI0ZgypQpuPjii/Hjjz96v1A/4KvfmEwm1NYGH9QQynN5IxTeIymJ8suzJk4Elj8ulNcPy8O6A+XIa57C5UXR7nPTyHx89adsLom3snN8RZ7NhyvQOzfDTQN3OqmbZhwu2mUno8bqwCtL9uDDlQfU9QdvC+tOSt3umb40XqhpYhq4cSSVw0lRWiIXJj548ADmzp2LK6+8EtXV1WrRherqajVHNmPXrl0oLi7GmDFjUFNTA0mSQAgxFI5nnXUWPv/8c5SWyq5RZWVlGDlyJL7++mvU1NSguroaX331FUaOHBn6i/aAvqhEKAhFVGBqoqxXVHLRiKHm0W+24Kq3fw/b+Xn8mYiM79MGO54cj3bZKarpSa+B9851TcXjSXgDLgG+obgC57+0DHNWH3JbA+n00Pdh70euknemY06qet8q6+ycicebAHefdfpjPmsITU6Aa+B+63unXouLzjoDl0+5GK+88gqysrJw/PhxjBgxAgUFBRg8eDAmTpyI8eNdtQhnzJiBp556CoBctf61117DoEGDDHN69+7dGzNmzMDo0aNRUFCAe+65BwMGDMD111+PwYMHY8iQIbjppptU+7e/TJgwIWjXRX1RiYaeD3AJlveu9114whNtFZ/p4lPhC6N+f8V+LN8dmeoq/uqM7OHnE1sx/n5WlxD3KrrQy8WdxysNFy7DvbDNzDYOp1PTJzauvb03ndTdBh5uAR51JpRwYbU7cbKy3qM/8vtzfwAAtMtOQbNUOQtcp06dNMWM9Xz22Wfq3y1btvTptnfdddfhuuuu02y75557cM8997jtm5eXh82bN6uf+SLFvP36++89ayUs7a23c+mLSng7nz8wG3j7ZrIQvvecbujTLrBFnA7NUkAIsK+k2vfOcQgT3LwAv2RgewCyWSXOlG8A7v7VZokYzuZqbY6w2pWZO6fDqXUZdKiLmJ5hNvDPbx2Kw6dqcden61EvNPDQcKBMFgb8TTES5SIas2GU18jBC4lm2Wb497FdcWb3lgGdI8liQqv0pLBq4JEk0LVclkiJt/eyQKDvp4306A8ey+htyyYTUbXtHq1dVbLCbVNmLw0npaCcss9emv7YwAflNUP/DlkAhAklZPi7thYHwX+Nyt6SaqQmmNAu23vouC8SzFJE7LzhjGJkD/H4Pv7VEmXsUXy/9550FQ5hArxH6wzcOCIPAPwKEIoV9AEyFknSeOYw6qzhNqHI539/xX7s5xKzuUwo7mPS4aS4//MNsDupOsNn7q+1Ye5v/IyAECEEeMNwOCksZiloF0KGbCoI/82ot4dPQ+raMg1tMpPQhauzGgiVdS43Sj4Uny1ujuoWudqL4Ub/rpYIYFW04RROgIdbo+XNNgu2HOP659kGfrCsBp+vLQbgWsdQBXhT0MAjkfPCX3EiTCj+Y3TfHE4aUOZBT0hKPpRwc/x0+KqM2x00oAhUb/DRnEyYt87wnmM8ltAPJQelrvQCiS6TUThfuJRSTRwDP469JbPic4fzxamBGHAjJISYCCF/EkK+C+b4pKQklJaWhl+I+/kcCQ3cPyilKC0tRVKSVog4aWh8dUmENPCpH671vVOQ2J3ULSQ7WPi0BOxZSU8yY3JhLjrmeI4AjhX0z7/dSTF3nezzzgK7gPB6oehNdvw4ViMxDYbkpsOugtNM47aYCCQSfgEeCi+UaQC2AcgI5uB27dqhuLgYJ0+eDEFXPHP8dJ2ab2JbpWyfrbU6UKrLGFabZEZZsgXHT9fBLBHkpCW6nUsgk5SUpAY8MUKpgUdiZsbbOUONw0n9isL0B94kxWSYSSLKTMX9d3pk3mZ8sPIA9s+cGJLvDzf6a/hpy3HsVbyQUjkTitUevjGhTwrGj2PWvWd/3IEbh+cjOcE1K+CrJ7E0soQQmE1S2BONNUiAE0LaAZgI4CkA7r5wfmCxWJCfn9+QbvjFPS8sxbajpwFAHdQ/bjmGW77RamC3ju6M6ef1wHnT52v2FfiHwxlY4ipPRKqoQzifL5vDGTINnMfqYFqe5PF3+mDlgZB/bzjR34ectARVgPOLteHUwPXn9nTrvlh7CNcMzVM/V9e71ir4ghSyK2R0L2I+D+ABAFGfNk5vm5K3ae9Qglle+Y6HPNSNhWxCafh5ImVCCSeyBh64AP/yb6487hkGpbmYZ0NKggkSiY+86d6ugF/ADafXkN7v3JMpUK9V19S7zCT6ZG5Rq4ETQs4HcIJSupYQMsbLflMBTAWADh06BPt1DYbJ6pYZLpOI/v4kKgI83CvH8YzDSd1CwIPBk2kg1PA+xp6w2p1wUhpwZkSbk8IUxG8xsGM2ADmg6Ytbh+JEpTYLIRu36UnmiC32hhv9veY/8t44YdXAdVMZTzNJ/ayKT7rGC2xzBPLVNMSEMhzAJELIBABJADIIIR9RSq/md6KUvgngTQAoKipqtKHGtG0+iosFm7g+S7DanaqtXBA4Dqd7Qp9gMEnhE0x8Pot+fkSJjnv+N+wrqQ7YnOZwBm9C2fzYOJglgiSLCS113iZ3nt0VCWYJF/Vvh/WHymN+pgK4zyJ4UwTvKRTOvOB6U5Sne6d/KfOzAr6UWiRs4EGrSpTSByml7SileQAuB7BYL7xDTUWNDSeCdPtii0D8TRnWOQd3ju2qfrYoPzj/1oz1ogKRZv6mo2ogSkMIpx84LwTqbL7vb7Ah/XZH8F4oaYlmjxp/RpIFD4zvgQTF3z4uNHCn/rProlI0Xijhu1jmQnxBgVxVy1PaDf26ND+enDFmA48of/3gDwz+1yKvGcH07D5Rhbzp87FXyeerqdMoEdxzTjf1s0kicDqpJiVqvKQ0jTXCKZjqOY0pEL/iQMYdoLgRBmEDD4RIBTyFG338Ba+58tp5OG3g7Gsyk+UXhr+/q43zjOE9ZiJhAw+JAKeU/kIpPT8U5/LGmgOnAGjddnzxoxJNVamsFHuzSZokogQQCA08GEK5mBbOxTleCPijgavHBTgW7CFaD/D6HQ6Ksmqrx2o9sYJeztk8aLXhfB7Z9zD3QU/CV7+5nusTH/ZvlgjmrjuMy95wL/ASKmJKA2ecrvW/UktmskXz2WhKy+ygJiIvOvAmlFDkt24qhFLZCOcipk1jQvFfA68PUPuzh8mNkOeTPw4BAIqe/Dms+dPDjVsgD/fc8eMqnAKcdYF5n3hagNRvt9mdGJzXDJMLczV1S9ki6Kp9ZRpXw1ASkwK8otb/gaq3IxolAPropiGYf+cItcoJ/+YNRYWZpkIof6tw+oHzwkHv4eGNQMO4Hc7QhdL7QzjTAoQbvazkZzt3n9MNfZW6koG+RIOBvXQ9KW96xcLqcKJ5egJeuLy/RmHk14IOcuH2oSSmBDjz4Q7EhKJ/sz9xYR+3fTKSLOidm6kKcAcnOYQG7j+h/K3C6QfOC4d9JdWqSWVjcblXs019AOYWQJ6Ch7smIs9Vb6/C+kPl2HEstFWWIoH+d+dTCec3T8W824cDiIwJxaWBG3+Xfi3E5nD6vM9CgANIU4IaAtHA+Z86ySKhc4s0j/uyaTu/0i00cP8J5YJNpEwogJxS4dedJzHp5eX4aNVBj8cFqoHbHc6wa+C8o8Tx0/W48JXlGPf8b+q2WAny8TV0JInALJGImFA82cDP6iHntdfrKVa7U5NszIiTAcz0AiGmBHi6skCwPQANg7dXGVWk53Fp4PyiSWw8ANFAKIMWJKlhNvV3lu3DzR+uMWxjQmBMdzkd6+k6G65/bzUAYPdxz2MrkAVPIDJeKL4ER4zIb79e1haTFGY3QhmzBxv4ACW/u6EGbmCafZKb7ZdWWd3aQ0FMCXBW6uxgAAmIeI8DX8qQJBE4qPbNK0wo/uNK/9nwHGkSIVh74BRu/3hdUMc/8d1W/LT1uGEbE+DM5evjVQdVQect+VTgi5ihy0boiQQfRR1iZfRSKptK9PBC0GIiYXUjdDeh6JJbKR5FDr0N3IMGfvUZHbF/5kQkW0xhW2COKQHOHOsDkan8lMuTYz5DDn11amxf+vBagWfYi+/h83s2+FwlisYyf9PRBp9LD8tol6Ksqew+4ap8401j3nr0dECzDHuQofSBkJFk8doeKz7iFBQ5ioLGwz+zCWYprIuYvkwo7GW8Yo+2GLbV4fT6IpVI+F6kMVXUWE2qHsBDxE+5fGU5ZW6E/DGRKOsVL7DfKhRCi2WObChOp3t+cvZSr1Jcu37e5tLUvZkkHv56MywSweWD/cvp43A6NXm8G4Nol9+nqq3YdLgCTqexgsXfjiSLKawFHZiYNZmMNXD2cv9tpzb1tc1BvY4bOTVyKPvJnTs8pw0PbOoSiFahKWLsQ4JLkhzSK0Lpg4P9VuE2GwSCUWIy1k+jBUa9m6n+/vNltmqsdq+LU6GsyOMJX4uU0a6BX/fealz77mrU2hyGCha/bpVsMYW1QILTlwZuIKTZmpk3L5RwelTFlABnmncgWjGvrft6ltRITO6YK99apWpq0cyhshpc+sZK7DhWiRpr4/SX3ZdwL9wFglEqBG8v5bl/HtZ8PqUr+MEHZFz4ynIMeupnj+eKhBuhr0chyuW36pCw/lA5CAHaZHouE5dkMaE2jKktVBOKBzdCbYEHeWc2lryZUEgYi5PElgCn7H//fwx+wcGXDdwkSW5+4AA8JtA6WlGLvo/8iLs++dPv/oSLz9cWY/W+Mox7/jec/9KyRukDe/GFWgNviBnLSFizYrnJBsmi9p6s1jxses+TP/afUoXIzuNV8IbdGX43Ql/PQtTXeOW6t/tEFRbePUpzX/jnN9liCmuqZzWUXjLWwPl38StLdgNwLWx7M5WF0wYeUwKcPciBPM/8vr5MKCYCNxs4AEMt6sG5GzH034tRWW/H1+uP+N+hMNGxmasu4t4QZAMMhlDawHneW74v6GONvIj2Kb8PH/bMwwddGM2++EVPwLMZI5Q1MT3h61mI9iUc/gVUUmVFepJFU+OTf3knJZhQG6ArZyDoNfAj5bWadt6c85+FOwG4FASjCG/1uDDGNMSUAGc/QrAmFF8Jf4z8wAFjk8Cc1Yf87kMkiIbFVtUGHgITyqtXDVD//m1XSdDn0SegOlpRi+d+lh++tEQzcg2m7PxMbcKLS93aK+u1LmFGnhFOJwWlCHsyK/byuHhAW6/t0YpR8NfYni3Vv6lmBg1sOFQeNldCNlth9//3vWUAXMJZr/9tO3pa7Ys3U5mcmC3UvZWJDS+U998HduzA9asPoqzGivYbU4BdX/l16PC9pUg5eMq14UHP5oVLthxDaZUVXTc2wwNbXYtVafW/ALrSVg/8ult7sJfzRoJehyvwwC5udbwR+tO6ohYP/HkYXU4tBJo1rFL6BAAf7j6JzYcr0HVbut/3m8Huj/XY9/jkUAXO69samckWmCvr8cBa+eWbZfsFf19/BKdqZDv38M7NsXxPCTLqlgBKTgu3+wygvXJ9rI0++CugM8ccKKnGA5uPYsjBHGBRdkB9D4SX9pRg/aFy9N2diS5cdXSG5eFfAXNglYQiidFzdC+l6LXpGA6UVaPgcHPgmywAwBm/7sFgSrHp2m8wsGOzkPelpTI2BhxtiQd2nlC3pySYUWO1o+/xVnhgu8tjad/mzzG8S3M8sOoACo+3Ar4yru50+/L9yF+XCgz/F9CypeE+wUIi+YYuKiqia9YYR8d5ZfJkYMECWB0UFBQSIbD4OTW1O6nGjpbo5U1pd1I4Kcvj63rLJ5gktxjOep1m5+28kUAOQHL1qTH644QSlSZJIanKQyG7aBECv+83O45p3iwk3ywRmAhR+wjI91W+58x2L8HulIMy5MpCxDAOgF1fPXceT+ODfW+4YCPboRvnDKO+RROeniP23JolCWxCx/Y1ERIW0xQbG2wcMAgIKKjbdhMhkJTwfr6feqwOuUqVefMmoHv3oPpGCFlLKS3Sb48NDXzePADA+P/8gr0l1TijUzN8MnWoX4c+PX8r3lrqsqF6K4v1wsIdeGXJbvz74r74x5eb1O1LHzgT7XUaZXelar0/540Eb/26BzN/2K5+boz+rNhVgqvfWYXPbx2KQXkN15AIgHOeXYIDpTW4+owOePLCvn4dt+VwhbqQOyS/GVbtK8M/xvfA38Z0VvsIAFsfH4cn52/DbCX/yaxLC3DPZxvw0IQe+Nf32z2e/+1rizC2Z0t0f/B7AN7Hxz8n9sRNI41t7aGAyYwXFu7AS4vdZwt/PnwOsg0CZKIFT8/R8fJavLN0H6af1wMmxYTB9r39zM64f1yPkPdlc3E5Jr28HP+5pAD3fb5B3T62R0ss2n4Csy4tgMNJcf8XGwEAN43Ix0UD2mLii8vw+tUDMb5Pa8PzjvrXIozu1gJPBym8vREzNvDNhyuwVyltFUhwpMMpJ7HyhySLCU7qbtOMdl9aILyVSvyFaSeh9Lw4UCovKH70+0E3lz5PMJMIwC98y//zLpZmSaudMlcwb8IbgFvZvROVdR5//0j5xHtaoI/+kWtM26xk/N8FvQzd84y8h0IBu6XNUi04p1crdXtrZZ2kss6uGduZyRb1vntfxBR+4BrXuEADeXwl/GGwZ0D/MEbB+qBPoiHgSPUDD5PQ8teFrLretR9bJHP57cr/Ty7MRYJZ0vTVX1OH3enE37gcLX95bSXumG2csyXQSvbB4qnvsaB8+MvD5/cC4Dv/S7CwMUJA0E/JPw64Xhj1dodmgfu/P+3EHbNlF2Lvi5hEuBHyGNn6POGk7qHUnmAPgd5zIRYegmjwQnH5gTfusOKDbU4rqYeZ2xebJUxTilnz0XWetNhnpvTD9PNcU/Yaq8MtUdbCrcdxgYH/faQEuKchHgND12+uGNweALDtaHjynbOfihCtjGFjhK3H8BxWXA19vfubvAY+OF+2qQ7okBWgHzhVBXMHH54R7O2q18CNfvusFO9JhCJNFMhv1ec6XJGY/r6keDPJXl1FeaaBM41Jo4F7kILJFhNuHd0Zv94/BoBnc9UmAy8Qb1PrUOJJSYl2N8JAYM/nV7po2VChauC6gtosSMfuoB6DAb0JcElC2GxZMSPAUxNM6Ns2E5nJFr+TWVFK8dHvB1FabcWmR8/FwrtHed2fPQT6qbrRQ6BPfdkY4etHK2rx+95SXP7mSrz+656If7+ecNjAlz5wJnd+/+67p5zRlFI15S17yfAvG0+zYCbk2XUFkhEvUhV5PP3m8SO+fUdSNxS1JiYB/jo8H5MKcrHhkXPVGaWnyFpCgKGdcjyeN5zFSWLDCwXyQCTEFWzjD4e5SKp0H2k3Adc0tE6Xb8Ho6/TRjst3l2oWPiLBuc/9hsq66MnTwu6LJYQmFN67w9/77qmKUr3dCZvOzMNHjXoyobDt7JhAMuJFKo+Op3dmtJv/mqclqKmDfaEXnj9uOYaijtnISUsMSV/Y8CIgyEyx4MUr+gNwveRtijugnjHdWniN8iYI3ww5ZjRwSuUfIpC3WaCeGWyAfLDygGaw6L/P4aRudTmNps+BsnJPKfKmz8eGQ+V+7R8twpvZnJkJxRRiE8rtZ3YGEIgAN97v+01HVQ2cTYuZdv33s7p4WcTU5sgIpDZmy4zQCBdfeNJOo8G05o222SkY3a2FX/vywrOi1oZb/rcWN3mouhQMLhOKdrvLhOI0zL/ua5YlFjGhPEKEQCIE249V4oAfVXl4bwR/4N+iDifFG9cMBOAuwCvrbBq7eOuMJBw+pc2bEAxLdsjRX0/O39rgc0WKdQdPofcjP2LRtuNhS2bVt20WAP/rkzqUF4k+s92c1Qc5O7089C8oyAUATCrI1by05985Qv2b3Wv2IOsXuY3Ib56Knm0yMKxzc7/63FA8mlCiXAO32eWc6T3bZOCqId7zrPPPJ1uc3h7CBU1+EZPHZUKhGNo5B89O6adp9+kVI9wI5YFI4JqS3vnJep/HBFK9HnB3xWJajf63r9aZWDKSzUHZwBdsPqrJJ52XI9vVs1OiN/BCD5stTJ+7STUthFqAs/P56//PXiT3j9MGTjRLTVCFLztnfvNU7J85EV1bpWu0WH7BW80THYAG7nBS9GhtHFodDnq1yTDcHuXyW63o/sO0kXjqIv8CtQBXoqlQFh13cm6EPJ1ayM9l5xapIITgkqL2uHZoR7Xdl5uyRMKXjjBmBDggvxkvKWoHAEj2IzjnmQXeAzL06OUO+6x/e+oXUYNJc1lRY8OtH63TFN71J7dwtME02ZOV9Xhh0S55W4jdCJlJRv+wrj9UjtX7ytz2dzjlQgopCbILX/tmyQCAY6frVQ3caNrL339+zYQlOWLXZXV4vtdl1VY4nfJiaSQLWxS0zwLgXo+0ojY8tRhDhVz4OfDx8i8l6jgnNYQmKmYD1922Md1b4uvbh+PqM1xC+x/jXW6lvp5X2Qbe5DVw+YeYXNgWXVumqQWOPVFvd2BDcWB2ab0rFtPI9HZEpuGd1aMlHrmgV1CJ5n/YLNd6LD7lSl3qrVJMtLF4+3GMeHoxKriox/IaWViE2gbuqUr4ha8sx6VvrHTb36Z4CyQqSZzaZskCfMOhctgccpvRb8y2saZhnWXPAn2aUW8a+IAnfsIXa4sjUpGeJ8liwr5/T8DNurD9FXuCz+QYCaz24MrOsZlfKN152egyWk8obJ+lMeHw48eXr384vVBiR4CDqj+gRIjP6fQHK/arf799rVsOGEP0N4593HuySrVPAy5BMrkwFzcMz0dSEKWeps+Vc63wK/BWLllPtDNv/REUn6rF+kPuL8lQa56eSlwxKmq0WqZDqQbPTDppia6HvKzGitQE4weOvcBbpsu2c5ZDhH0ruy7eBm6UxnXj4XJ1FhBJCCFus0j+2hvCv3/Yhts+XhuSc/HU2x3qizYYQlngwelhEdMIfownexhPDELCZ8qKHQFOXYl7/MktwNzDhnfJwdl+uvfpZ3JMoN/z2Qbc8N4f6nZ95Y5gTCitM5LU/jFsdlcgQUOIhPxn12704gq5AFdt4K57vrG4XP17n25BmxVSYJpR55ap6N5KtkdvPlzhZmZgsPMzz5H+ilmifbaswUsSASFaDfyCfrlutm6zJKkZ6iKNxI1JIHQC7o1f9+L7Tcd87xgglXV2ZCQF780cyhqZTKT4M3r5l3OKDw1cHxgUSmJLgCu/GfHDLaeV8hA+eF5Pv79Dr4F7cs1SK88o7dmpFpT5mWiJ0SJd7l+7LNdiGTOhNLQMVriS/fAwdyojG2uoNU9miijm/Ponvbxc/XvNfq0d3KHYVUd3a4EXLi/Eved0x0tXyj69G4srkOpBgLPZUEvl3vx1RD5+unsU+nfIVvehVFvYOCPZ7KZMUConu2qM4s5syGYq+cxrQxBgFq46lFa7E/V2J9IbIMCNKi4FA6UUb/wmB8P5o0Dx+/jSwOVhIEwo6uqwXOHC/QeZ+uEa3PSBvCjIhKyvH5dHf+P0zx8TsOzcTNvJzUxGSZU1IG2AedN8usZV2eejVQcAuC+S+ktuZhJuGdUpIsEb7Hc9UamtF2qSSINnEHqYV85nf8i/lf53fnL+NvVvq92J//1+ADaHE4QQTC5siwSzhG6t0lVba52HQJwBHbOQYJZw+5ldAMjjoWsr754kPVpnGJp2gl2cayjsGUm0SLCYiGFR50Dxx20yGNgz4OmF6g+hysJ5tKIOy3eXAgh8BuvLBi5bDILtmXeCHmGEkPaEkCWEkK2EkC2EkGmh7Jjxl7LvNv5BFm49jp+3yUmG1JwXAUxjedvzxH5t3ARRjdUBq92JaUoRY7Z/G2WR7FiFcfFjI3iPCvZCYIuA/ioVFxbmaj4TJcF8JBJbsZfE8dPaMnXh0Do7tUjTmCn4hV89s5WXoFGQExsTh8qMffZbpidh55PnaTRub7x7fRFSE81uL1yKyNTDNGL1PlkIHSitQZLZ5FaUORj469t9InR+10z4NiThVyBpDbzBa/KBhuz7mkFIUVqV3g7gXkppLwBnALidENIrNN1yh79+ox+kUufzrc954dd3KNOcTs1TMevSArc3cY3VjnUHT2GPEkbPvC2YPfu4h+r1Rji4AfPtBrkoMhNSDj99W/VDwqRUf7E5qJtZIdQ4PLxlwiW0OrVIxZoDp/DX9/9Q83Xn5bgnJwtn0Vs9zMatf9FTikZZxNRjMUshSTPMZ+YLpR3cpkbFBi+GrA5n0DNWnob4kxtFZ/JEpQ2cUnqUUrpO+bsSwDYAxpVVQwAFv4jp+kH2nqzCO8v2Yci/Fmn2V6MCAxDgNUrk5oCO2Ug0m9zexHqXJ6aBs4IRgUw1bU6qejDs1y3C+atB61/qEnHZn6e8vtLtpRZKeLNB15ZpGKJkiwyX0MpSzCiLtp/A4u2yR9Av95+J8/q0RteWaep+kXTg6dFGfuEyN0WGTReuH0mYMBzdrQUSTKER4E7dvQ4V1hD9TqHQwnmz44kAFDFAXgfxRtT7gRNC8gD0B7DKoG0qIWQNIWTNyZMn3Y71G34RE64f5L3l+/HEd1vdbH2qBh6ACaVSsckxLwV3GzjVZLpjwor9H8iCisNJkZJgkutvKse5bOyejztdZ8MCxYdcPygkovVvDqWLlR7+JZOaaFbt1KfDlJ8lK1mr5bAoS0kiGg3Rmyi462w5B/g/J/q/sO0NpnnNurRAs71UWdA2NYIXChsTV5/RERYzCYmNmH9ZhzK7YjAa+NIHzsSUge0029YeONXgvvDXWNghK6BjfSXKO1RWg6W7SlBaVe91v2Bo8N0ghKQB+BLAXZTS0/p2SumblNIiSmlRixb+Ja0xQr+IyfCkYQSjgVfrBLh+amxzODUh80xDt6gJ3/1/WOyKm5nFRNTj2MvB29v6nk/X49aP1uFgaY2bBk6IK+yXP1844Ad8kkUKKENfMPDpBX6+Z7S60GgixO8p9F1nd8P+mRNDVqOShVC3zEjCvNuHq9tZsYfG0MD5fDQJJikkC5D8yzqQYiq+YG6zgQjw9s1S3IL4WI3ThsBfI4sD8BdfJhT2Qg9HZsoGCXBCiAWy8P6YUjo3NF0yhncj5CObPJkb2EAOZBGTPW45afIA0dtz7Q6qSZCl18ADWTxkbmYW7iFjswar3ekxtwqzv9ucTjdBv+dkNZpzqTVD6SOrh7fTJ1lMKA5BMi9v8IV5u3DTeJNeA4+gzOQjd7sb5D1pDBu46uKqjK3jp+uQN30+Pue8nQKFH2ehsDczbM7gTCj63zUUOWcasvDvrxtku2zvBWWCoSFeKATAOwC2UUpnha5LxlDwfuCuxEZGGsGGQ+WqMAzkIbppZCfce043XDVEznnQWWfvs+o0cKY4sAFoC2AQ2JwUJpP8kDEN3KpozMt2l6DX//1oeBybEnsKz+UrwIRTgPPmojqbI+x5r4s6GnuG6KNy2SwtXL7wzAyjx0iLbAwvFDXbokSQYJZwpFy25764eFfQ5wyfBq7k/gnQLMPWnnJSEzC2R8uQFHoIRoCzmUCKn67K4XihN0QDHw7gGgBnEULWK/8mhKhfbsjZCOUfgHDCy2g8/fWDNVzpLP9/tOQEE/4+tquanEYfsWd3OHUauLYogL/eI/K+TAMnOF1rx5LtJ1Cis5HNXVfsdpyN09aNrj1BI8DD55HBm1D2nKxGVZhzk+cp6VnH926t2W6StA8fe0i+/NuwsPTjhuH5htuNHs6G+DcHC18ViV/EbEjueI0AD6UGrkvt6y9qzhqJIDs1AeU1gQXRGcHkydgeLf0+5qO/DsEXtw71Gffw30sK3FLQhoqgRxildBn8izoNCbwGLnF+4EYDqqSqXnXjamhQydbHx2HtgVO45p3VsDkoHv/OlaubaQJM0/LX5swi9UySBItJwjcbjuAbxZWQZ9ZPO3HxAO2CDROcy3eXGLom8XklwqqBcy8rp5PiogFt8eHKA2H7PgD4YdpIt216EwozR+lL3oWKQGpcZiZHvm6qa+1HHltscT8QLdXucGqEKv/7htKbgmV1bIgJJcEsqTPXk5X1OFpRi37tsgLuC5u53DjC+AVtRK9c4xS+ev6iW3QNJbETienBD9zTlM7moX5doKQkmFVNyqbTsFk0Ips+++uF4io9RrxOH4tP1eKrP7VaODv20W+3GgYHRMqEwnv9jOzaHI9e0BuAKww9Uki6RUxmYgpXSt5ABHhWI+R1f3xSHwzKy0bv3AwkmCXVtOXvo/DNhiPoMuMH7OeKQWs18ND1taxadnP1lVlUD3uuKaWwSC4ngAkvLsWkl5cHlUKXyZHG9t0PlNgR4HB5hfCRmJRSdG2Zhr3/0lpv7A755oYCJmRtdifSEs1IMEmYc/MZ6Kx4fLgWMf0b3RuUREwmE/E5h3lv+X7NZz4vhaENnMuTHk43wpp6B4o6ZuP7O0di5l/6QZIItj8xHkv/cWbYvtMIXgM/VFaDWT/tVLeHA28zuq9uG4ZBeS5bfUG7zLD0wRt922Xi81uHIcli0tjl/Z2JssVOPjaBF+BuUacN0MhZMZPmAda0zM2SvURKqqyaNSR2voLHFuJoRWCL6vzibywRMwIcSkUeQKeBOykkJYT8ov6uOCKW0CgUmNWCAhSJZgmXFLXD0M456kPBpoD+vPntDif+8pqcwzrBJOFUgEmweLcwIxNKaoLLKhZOG/jq/WWgkKeRLBQ6yWJqUGrQYJCIK3UAn/I33BhlNOzfIVtzTxojFwoPP1vwVy6xMZzBmX+8LWI+8s0W5E2fH1T/WKItfxcBGaO6utyRLWYJdgd1e5GU+lkomSEEeJjReqEQzgbucudiARpts5KVdJ6huRlMkzlWUYfSaqum3Bbguun/WbgTy3d7T6B/jIvy6t8h200zukRnL/N2BRRyovnJSk6UqaM6aR6GQEwodTYHnvtpp1/HsPzboQigaCgmyWVCidTD9/uDY7HMw0zj1tFyAebZNw2JSF+8wduWvdnA+XzqRvefn+np15zYukcw7oU2J4XFFPg6FV+Fnrnh7jiuzdESaASqPsNorBA7ApxyofRwTd0opao7X05aIqYMbAdKKeyO0FVEYb7kx5XMe7m60Gle6/VVnZ5N8566qA8GdszGa1cN0LTrtRF9hOmY7rL20blFKiilkIhr4apjTormYQhEu/941UG8sGgX3l661+e+zDRz+aD2fp8/XDgpRbXVAUppxMqHtc5M8mjfPqdXK+yfORHDukSmmLE3+BmApydh8+EKFDy+EPPWHwbgEmSe7N5/eMixUx1E2loWzBYMs28agh/vGqWaSf/Yr1UmVuwpDeh8QgMPM9qKPK5ETg5KNdqFxURgd1LYnKFLqG8xy+dnuVL0C2R8QEeOjwWZa95ZDQA4o5NcyGFIpxxNu14w6Aszs9lARrIFTuXaHR4yL+4+WeW1LzzshXiqxrcQZAuFRXnN/D5/uGBrBD9uOR6y1KLxAi+LPJW5231CHiM/b5PNT0zZ5jVYO/f3vPWyt5TTSXGYy8++Zn/gszGbI/iMjcO6NEf31umwKM/iCt3M99kfdwR0vmAit6OB2BHgnAauj8TkBbhJkgW4I4Q1CdmLgGkZ3jxHfEVlMa+ATgZubv/762B0baUNHtJP6ZychuR0ymal8lpZ085U6gO+e71cQo55xazZX4Yxzy7xmtwqMYAKLixsPhCPjHBTXW9XBfidZ3Vp5N5EHy08LBSy9YtvNxzB5sMVhhHO9QbmiP/9fgDDZy5WP3+4cn/AfQrFM8oUmh82y1kSjRZE956swuu/7vF6HuYcEIliKKEkep5AH2gr8rgiMZ1Um7bTLEkoq7Zi3vojOFoeWFYxTzCB7UkD5/FUt5HRIj0RVwxub2j3G9m1hdsAGtFVOxVni0h2B4WTyrMSVkmGVfk5q0cr9Gidrvpqv7h4N/aX1mAlN61cs78MedPnq1oU+15/bOD1YXbVCwRW1NZBKV79RX5I7zm3e2N2KWrgnwtPhU2SOK+l819ahv2lcq71ai6y1qiI8+p9WlPK8CBMRnans8ELvc1Stb72r+pMki8u2oWz/vsrZv6wXXNNepjiIgR4mJDFlisSk4lJp1OrpfJTslBVEmFagqqBGwiub+6Qkxn5ilRz6mYMevReHHqzADv/qRorVu0rw96T1WqRXl6rN5tcWQ5Z3mzeNWz26oMAgN/3lOLpBdtx3+cbAABz1x322n/A9btGgwCffdMZAIA/D5Y3bkeikBRubcZTjIInm++tH61T/zZMVKY77Mn52/D8zzsD6p8tBK6+F/TLxblczVvmxlnQLhMnTtepbqWAd+WEtSUF6BHT2DT+E+gnlFJNJCYfyEP8sPU1BDZNYwuKRnkvspJl27Xd4X0xzUHdE/2/cHkh3rlONnvwftyAe65jNsU9qlT/KamqxytXDcBb1xZp7OcmSVJnAyxQggVOAK6cIcdO1+G1X7TTS1+Ln+ylktjIbnKAKxf3Zh+Lx00RPpR/1T7jxUd/gs9eXrxb89nppIZ1Mp//ObB8K1+sLcaRAKpYGWE2Sein+NtLRFbuzunVClYHdbvmOi9rJHVCAw8/Li8Ulw3cqat8kmJxDdqhugXCYGHuWCyfr5ENnL04/jx0CgWPLcSCzcaVS/Q2ewCYXNgWY3vKWoTervzD5mMaH1cjDb9ddgrO4bQQQI7ydDhl/1j2YBm5Vhkt9vh6pNlLRf+yaQxSE+UHzpf3T1PkqiEdMJIzwRkt8vpyt3v+553YpSx03jJaTsNbXmtTXUhvG9M5VN0NGjZrZY9GeqIZlXU2t2fFW3Hmyno7LEpyuVgitnqrIEmyTfy1X/ZgzYFTGgHOLyK+rFQibyjMXs3sg0amA2a6+eh32TTx4NyN+G2newEL/QtHj1F9QN6ufuK0f0nhTUqIMe+G6G/Obl9mIDVc3dT42orehtoYObijlVYZSfjfX4fgoQk9AMAtWRrgfc2Gf/kDQL+2WQCAjcXlqKi14c6xXfHA+B5ok+nKn/3nQZc3yrGKOgz99yLsK9FWnAo1zdO1nlvpSWZU1tlVrZopcrN+2qFRhn7eehx/7C/DPZ+ux67jVW7xHbFAzAhw7SImweHyWjy9QK6NuHSXy4WIF+A5AYboeoMtlgHGUXh6oXyqxoZr313tFiFmZELhMfLssHF5wvf6+TCYTbIGzmeh4yMzPeUbB3yHR4c730iw5GYmYccT5zV2N6KO3rmyiWH7Mbd6K+rY+t9fB7u1lepMaR2VtRSWkZON1fl3upKMfb7Wlbtn3vrDOFpRh9mrDsDhpHhx0S7VvBjKrIbn98vF+zcMwrbHxwMAUhLNqLG6BPhlSrzC95uOqW6yDifFTR+uwSWvr8TcPw9j2e6SgEP6o4HoegK9wFfkIdAGuKRzAtVXeaNgufaMjtx3uAtwT4UjTuq0HqfTe1ScUSg6y3LobRVdj1mSYHNSjetgvd2JlXtKkTd9vup2ZYSvnM9Mk482Af7eDYM1PvkCmd5K1rwZX212K+zAbODtDYoN8Glan7usQL3fbDGfzXaapSbgvRsGAdDWzORLpi3ddRKzftqJgscWAnB5fejLowWDxSRhTPeWqqdNktkEm4Pi0W/lzKF53OI+G7undetUEjGe/UY70fUEekFfkYdn8X1j1L8z/KyOESh8bgij3A2eFk8PKmYXhoOLHDWC18BvVHJPswchkKIJZonA4XRqjqmzOXDFW7/7PNZfE0q0+IHfc043ANpKPQIXrOTX0Yo63P/FRo0tnLmaWnT3MjPZgnIuqMuspD4GXIoEby8eqBTc4MfOp8rLwmKS3BQTNgMMR8KvJN3aDF+xhyl+5ToBXmdzxtwCJhBLAhwuAZ6nC4JpwaUwDZcGzgtwIx9u3n2RVwKX7irBjmOuPA0OJ/Wab4HXAlhQDxPggYQrMzdC3mzib/VuXwnmosmNEADuHNsV+2dOjLkw6Eihn5XwwVrMHJJsMeEsrpiBzeHUCHC706nebyNvLDb+eQF+qEyOMUi0SJqx8vqve1yBMwmhV7j4Zygz2YIkiwlvXjMQgFytCwCOG1Se1wv+WCBmesxX5Ln77K748m9DMbZHSzz9l76a/cLlGcG0mP4eKlbz2igf1PDCol0Y9/xv+H7TUXVwe5vm8wNdLZZs92xCYf7nesyShO3HKvHxqgPqef1NbuX3ImaUCHBBYNRz46C0uh4miSAr2aJZjKyzOXCi0mX+q7U6VZMJ81zivbHYy9NoUbT4VC0OcDEIM3/Yrr4EAs1E6A/8s7j43tEAXIFM93y2AQ4nxeVvus9EPQU7RTMx8wRSQPUjJIRgYMdmeOf6QbhsUAfNfl3DNI1mC5ee7Ne8Vj65sK1bCaXbPl6HxdvlfBPeNHBei2Sukiv2yIu0VYq2xLIuAvBZfeS7jUcByJqIvxq4r6or7EUQLSYUgW9YxkpAq4GXVlnRLDUBkkQwvo9crm5wfjM4KbDmQJnmGL37LB8Gz8Y0//Jn5szZqw7ins82aI6tUTXw0AtN5plU1DFbdWTgnxNPcRrJlvCYX8NJ7DyB1GftAwD+J64PlnbZyR7bmA0tLdFsGFpcfEq2h/u70Ma0lge/2gTApYH7Uy5ML1wzky2otzkwupuczfDsni012s8lA9thQl/5AfYlwKvq5Yc50rm/BcHzn0sK8PhkuWrSw/O2qDbokiqrmoBtZNcW+PaOEbhllOzvvfekS2vunZvh5iNdxnmpmDgTyuxVB7FsV4lXkxYzoaSEwe7co3U6mqUm4O9jXQWoM5Mt+Md42Z3S7qHwCu9pFivEzCuHr8jTGAztnIP7zu2Ga87I87gP895okZ5omKSHaT6+bLUvXdEfPVqn40slrJ1p/WxB0p8SVIm6ByMz2YKyaisqam0Ykt8Mb183CDuOVWLJjhNqDuv5G4/i+03HfJbNqqq3IS1Mi8WC8GAxSaqnyW87T2L57lKc06sVSqvrNe5zfdtl4ve98jjbdLgCfdtm4sMbByM7NcEtEGhAR1f1IUKIXB3JSfGQonB4cyg4WCYrMylhsIH3aZuJdQ+f47Y9WxHQxzxEf2bHoACPGQ2cchV5GgOTRHDHWV3VjH9GXKO4GnZpkaZJZTtV0WjqFK3DV9L4Cwpy0bVVunrc+f3aAHBp4Dmpvv1V9SvqmckW1Nkc2Hr0tOoX3L11uiq85WuU//elgVfW2Q194QXRTf8OWaodm2ngpVVW5KRpFQK2COhwUnRtlYZsRWHgg6R2P3UeBnTI1hzHMoEyvBX5ZouJkbQ7M8XJU2BRy4wkw+3RTOwIcAD+KuCrHvJcMSWc/HNiT6yeMRaZKRaNBs5MFS8qOSW2GQRUGNEsNQGdW6SqvrosKEcfeWaEfnEoM9mC0iorrHYnWmcavwCIgR3TiENlNWiVEXtBD02drJQErJg+FoAcxWx3OHGwrMZNIeDNb11bulzw+BmwURZBs0TUMmmA7Mkyvndrw76cUIqjhGMR0xPMBORpLah/+6yI9SVUxI4A99MGDsghxO0MAhPCDSEELdPltzjvVqgfpKv2GicWMiIz2aLm+66qtyPJIqnatbfiEdcPz3M7D3P/a+ZBg2czA28KeFW9HesPlWNQFBRzEAQOs/NuP1apVrHJSNbOpngB3jJdO1a8vbhNEtFEb9qdFD3apBvuy9LRRlKAM6Wq3sAbK795qtDAwwlfkScW4E0oFpOksXvfqiQF8oeslAR11Xx/STXSEi0ghODTqWdgkeIiZUTztES1sAEh2vB/fQ5lBuvyBS8v83jeilobnNQVVi2ILfiFyINlsilhpC7nPO9HrV/rWHjXaPx2v/Hs1iwRt2LC+oXPb+8YAQCoDqMXiieYUsXHRrCShr4qaUUrMWPIDEQDjwZ4DdxiklSzxJVDOuCaoXl+nycz2YLF20+g80Pfa0wb+lJshn1QHh6zRDRBCtke6jnyLpLlNVakJprVB/D7TUeRYJKQ30L2gInFsGOBlsNKwZNU3XoGv6ipTxuRmWLxuA50qsaGlXu1tSj1x/dSwvoZ3qpbhRqmVDE32C//NkydUVwWBfVdgyF2NHCKmJLgvKvgSS4ggi1I+kumEgEaTPIfJnwlQjQeBJ68WPhZQuHjP6HrjB/Ueoi3fbwON324hvMBFwI8Vnnywj4A5Go1gHtyNj5Ay58Fc0ZuprsJIoOLjJ590xA3D6xIzqqZCaWO5fIxSWiXnYJdT52HS4qEAA87JJYkOMeR8lp8futQvH/DIAzrHFjpKU8+q/7AvAZMEsFyrpxatgcBbhSktP1YpSZnNHPBisWwY4HMBQW5ms9GWfh+vGsUnriwD7q18j8wbvn0s9y2JZol/Hr/GHz01yEYpsRGXDygbYA9Dg0uDVwez+xlEms5wHliyIRC/fZCiRauH5aH91fsx/3juge9QNK9lbwIdOPwfLy7fF9Ax7KpcUqCCeN7t1aT8Kd7cAE0WrxMMEuazG3Ld8svAmFCiV0yubw+X98+3PBedm+dju6tjRcgPWFY57VbC6QlmtExxxV8NuvSQhwpr0UIM8r6BdPAWTxGPOSOJ75yP4eSoqIiumbNmqCOTW3TCQmwa7SFyy+/HE888QScTie6d3cvZHvTTTfhH//4ByorKzFgwAC39mnTpuGOO+7AsWPHMHLkSLf2hx56CDfccAP27NmD8ePHu7U/+eSTuOyyy7Bx40b85S9/cWt/7rnncP7552PlypW49tpr3drffPNNnHnmmfj555/xt7/9za39448/xqBBg/Dft2fjjWceRb3dCYkQdeDNmzcPvXr1wpw5c/B///d/bsc/+tpszPj5BCy7FgMbv1FrYuYpD9OKFSvQokULPP/883jllVdQVW/XJP1vc8NL+O7usfjg1efw4utvAZCnnVaHE22zUrB/r+wWOWPGDHz22Wea705LS8Off/4JALjrrrswf/58TXurVq2wbJm8WHrzzTfjl19+0bR36tQJP/74IwDgyiuvxB9//KFp79u3L+bOnQsAmDRpErZt26ZpP+OMM/C///0PAHD22WfjwIEDmvaxY8fi9ddfBwAMHToUJSUlmvYLLrgAs2bNAgD069cPtbW1mvZYH3vXPfAULO37YaC52OPYGzx4ML755hvce++9bu2ext6pGisSTBKkiQ/DnNkKMzofwTPPPON2vH7s6dmwYQNSUlLw1FNP4f3339e0EUKwc6dc6zKQsWe1O3Gkoham1Gy0vuoZLL53NP790N0RGXuPP/44rrjiCrfr9BdCyFpKaZF+e8xo4Kltu6F5soT+XPBAfn6++vfgwe4J6du3l+1aJpPJsD03V55KJiQkGLa3bi37sCYnJxu2t2ghh6WnpqYatufkyAuNGRkZhu1ZWVkAgOzsbMP2jIwMEEIwtFce/jRoT0lJUfthdHyPtjkATqBftzwkJQ1Ggd0BAqLaOC0WWRNr164dBg8ejBqrHQu3HlePJ0RCnc2JrJZtkNCmm7o9AcDgvq5peH5+vtv3Jye7Ug507tzZrT0723Ufu3XrhpoabdrdNm1cawU9evRw0+46dXJ58vTp0wfp6VptsUePHurf/fr1Q6tW2pJzXbu6wqz79++PigptSbbOnV0BTkVFRaiv1+Z1j/WxN7GoK/r374G1a6s9jj12HqN2X2Nv3JQBKEcq2tRSw3b92NMjKeaODh06uLXzYyGQsWd3OvHdxqMwJclmIbMkRWzssfsVahqkgRNCxgN4AYAJwNuU0pne9m+IBn7GvxZhVLfmeGZKQVDHN1XWHTyFri3T/E6zu2Z/Gaa8vhKXFbXHp2sOYUh+M9w6ujNueP8PnNGpGX5XfNj3/XtCTLl1CgQA8N7yfXhMKfSwYvpZyM3ynNsomvCkgQdtvSeEmAC8AuA8AL0AXEEI6RV8Fz3z3cYjOHa6zmv9PoExAzpkB5QjvSivGX65bwyuG5YHQK5mfsP7f8AsEfxzonx7p47qJIS3ICaZ0NelXevdJ2ORhlzBYAC7KaV7AYAQ8gmAyQC2hqJjPG/9thcA0LmFqLgSCVjBjGlju+IFxdVsdLcW6NM2EysfPAutYzBiTSAA5Cjtff+egCMVdZrF3FglaBMKIWQKgPGU0puUz9cAGEIpvUO331QAUwGgQ4cOA/WLSf5QZ3PgQGlNwKvigoZTUlWPR+ZtwT/P74k2mbEx3RQI4o2Qm1D8hVL6JqW0iFJaFKwhP8liEsK7kWielohXrhoghLdAEIU0RIAfBsCHL7VTtgkEAoEgAjREgP8BoCshJJ8QkgDgcgDfhKZbAoFAIPBF0IuYlFI7IeQOAD9CdiN8l1K6JWQ9EwgEAoFXGuRHQyn9HsD3IeqLQCAQCAIgdrO4CAQCQRNHCHCBQCCIUYQAFwgEghhFCHCBQCCIUSKaTpYQchJA4KGYMs0BlPjcKzaIl2uJl+sAxLVEK+JaZDpSSt0iISMqwBsCIWSNUShpLBIv1xIv1wGIa4lWxLV4R5hQBAKBIEYRAlwgEAhilFgS4G82dgdCSLxcS7xcByCuJVoR1+KFmLGBCwQCgUBLLGngAoFAIOAQAlwgEAhilKgX4ISQ8YSQHYSQ3YSQ6Y3dn4ZACNlPCNlECFlPCAmuunMjQQh5lxByghCymdvWjBDyEyFkl/J/trdzRAseruVRQshh5d6sJ4RMaMw++gshpD0hZAkhZCshZAshZJqyPabujZfriLn7QghJIoSsJoRsUK7lMWV7PiFklSLLPlXScDfsu6LZBq4UTt4J4BwAxZBzkF9BKQ153c1IQAjZD6CIUhpzgQmEkFEAqgB8SCnto2x7BkAZpXSm8nLNppT+ozH76Q8eruVRAFWU0v80Zt8ChRDSBkAbSuk6Qkg6gLUALgRwPWLo3ni5jksRY/eFyBW/UymlVYQQC4BlAKYBuAfAXErpJ4SQ1wFsoJS+1pDvinYNXC2cTCm1AmCFkwURhlL6G4Ay3ebJAD5Q/v4A8gMX9Xi4lpiEUnqUUrpO+bsSwDYAbRFj98bLdcQcVKZK+WhR/lEAZwH4QtkeknsS7QK8LYBD3OdixOhNVaAAFhJC1irFnmOdVpTSo8rfxwC0aszOhIA7CCEbFRNLVJscjCCE5AHoD2AVYvje6K4DiMH7QggxEULWAzgB4CcAewCUU0rtyi4hkWXRLsDjjRGU0gEAzgNwuzKVjwuobIuLXnucb14D0BlAIYCjAP7bqL0JEEJIGoAvAdxFKT3Nt8XSvTG4jpi8L5RSB6W0EHKt4MEAeoTje6JdgMdV4WRK6WHl/xMAvoJ8Y2OZ44rtktkwTzRyf4KGUnpceeicAN5CDN0bxc76JYCPKaVzlc0xd2+MriOW7wsAUErLASwBMBRAFiGEVUELiSyLdgEeN4WTCSGpyuIMCCGpAM4FsNn7UVHPNwCuU/6+DsC8RuxLg2DCTuEixMi9URbM3gGwjVI6i2uKqXvj6Tpi8b4QQloQQrKUv5MhO2FsgyzIpyi7heSeRLUXCgAobkPPw1U4+anG7VFwEEI6Qda6AbkW6exYuhZCyBwAYyCnxDwO4BEAXwP4DEAHyGmCL6WURv3ioIdrGQN5mk4B7AdwC2dDjloIISMALAWwCYBT2fwQZPtxzNwbL9dxBWLsvhBC+kFepDRBVpI/o5Q+rsiATwA0A/AngKsppfUN+q5oF+ACgUAgMCbaTSgCgUAg8IAQ4AKBQBCjCAEuEAgEMYoQ4AKBQBCjCAEuEAgEMYoQ4IKYhBCSw2WoO8ZlrKsihLwapu+8ixByrZf28wkhj4fjuwUCI4QboSDmiUQmQSWCbh2AAVw+C/0+RNlnOKW0Jlx9EQgYQgMXxBWEkDGEkO+Uvx8lhHxACFlKCDlACLmYEPIMkXOyL1BCt0EIGUgI+VVJMvajLvqPcRaAdUx4E0LuVHJXbySEfAKoOUd+AXB+RC5W0OQRAlwQ73SGLHwnAfgIwBJKaV8AtQAmKkL8JQBTKKUDAbwLwChCdjjkHNWM6QD6U0r7AbiV274GwMiQX4VAYIDZ9y4CQUzzA6XURgjZBDm0eYGyfROAPADdAfQB8JNsAYEJctY7PW0g57NgbATwMSHka8gpBRgnAOSGrvsCgWeEABfEO/UAQCl1EkJs1LXo44Q8/gmALZTSoT7OUwsgifs8EcAoABcAmEEI6auYV5KUfQWCsCNMKIKmzg4ALQghQwE5pSkhpLfBftsAdFH2kQC0p5QuAfAPAJkA0pT9uiEGMuYJ4gMhwAVNGqVU3xQATxNCNgBYD2CYwa4/QNa4AdnM8pFilvkTwItK3mcAOBPA/HD2WSBgCDdCgcBPCCFfAXiAUrrLQ3sryGmCx0a2Z4KmihDgAoGfEEK6Q641+ZuH9kEAbJTS9RHtmKDJIgS4QCAQxCjCBi4QCAQxihDgAoFAEKMIAS4QCAQxihDgAoFAEKMIAS4QCAQxyv8DsBRqqPTYNm8AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())\n", + "\n", + "\n", + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Built-in Lie group states \n", + "While we implemented our own `SE2State` from scratch here for pedagogical purposes, navlie comes with many built-in Lie group states that you can use out of the box. Some of the built-in Lie group states include:\n", + "\n", + "- `nav.lib.SO2State`: representing 2D rotations using, beloning to the group $SO(2)$\n", + "- `nav.lib.SO3State`: representing 3D rotations using, beloning to the group $SO(3)$\n", + "- `nav.lib.SE2State`: representing 2D poses using, beloning to the group $SE(2)$\n", + "- `nav.lib.SE3State`: representing 3D poses using, beloning to the group $SE(3)$\n", + "- `nav.lib.SE23State`: representing \"extended\" poses that also contain velocity information, belonging to the group $SE_2(3)$\n", + "- `nav.lib.SL3State`: representing 3D homographies, belonging to the group $SL(3)$\n", + "\n", + "Each of these classes stores the value as a square numpy array in the `x.value` property. Moreover, closed-form formulas for the exponential and logarithmic maps have been implemented for each of these states, which is faster than using `scipy.linalg.expm` and `scipy.linalg.logm`. These underlying operations have even been implemented in C++ for maximum speed. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/source/tutorial/traditional.ipynb b/source/tutorial/traditional.ipynb new file mode 100644 index 00000000..f18bd608 --- /dev/null +++ b/source/tutorial/traditional.ipynb @@ -0,0 +1,393 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Toy Problem - Traditional Approach\n", + "\n", + "In this tutorial, we'll simulate a simple 2D localization problem as per the figure below. We'll assume that we have a robot following a simple body-frame-velocity model, which has access to noisy measurements of its forward velocity $v$ and angular velocity $\\omega$. In addition, this robot will have a time-of-flight sensor that gives it range measurements to a few known landmarks in the environment. \n", + "\n", + "![Toy Problem](../toy_problem.png)\n", + "\n", + "\n", + "## Define the State\n", + "The first step is to define the state of the robot. We'll start with a more traditional approach and define the state of the robot to be a vector of the form $\\mathbf{x} = [\\theta, x, y ]^T$, where $x$ and $y$ are the robot's position in the world and $\\theta$ is its orientation. We'll also define the control inputs to be $\\mathbf{u} = [\\omega, v]^T$, the robot's forward and angular velocity. The process (motion) model of the robot is then given by:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\dot{\\theta} &= \\omega,\\\\\n", + " \\dot{x} &= v \\cos(\\theta), \\\\\n", + " \\dot{y} &= v \\sin(\\theta). \n", + "\\end{aligned}\n", + "$$\n", + "\n", + "However, this is in continuous time, and we need to discretize it to use it in a filter. For now, we'll use the simple Euler discretization method, which gives us the following discrete-time process model:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " \\theta_{k+1} &= \\theta_k + \\omega_k \\Delta t, \\\\\n", + " x_{k+1} &= x_k + v_k \\cos(\\theta_k) \\Delta t, \\\\\n", + " y_{k+1} &= y_k + v_k \\sin(\\theta_k) \\Delta t.\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Lets now code up our state and process model using navlie's framework. Since our state is just a regular 3x1 vector, we can use a standard type from the built-in library: [navlie.lib.VectorState](../_autosummary/navlie.lib.states.VectorState.rst)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "np.random.seed(0)\n", + "import navlie as nav\n", + "from navlie.lib import VectorState\n", + "\n", + "x = VectorState([0, 0, 0], stamp=0.0)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `VectorState` is a subclass of the abstract [State](../_autosummary/navlie.types.State.rst) class in navlie, which is one of the core primitive types. The value of the state is stored as a numpy array, and can be accessed directly through `x.value`. \n", + "\n", + "\n", + "## Define the Process Model\n", + "For the process model, we'll choose to define our own from scratch here. Process models in navlie *must* inherit from the abstract [navlie.ProcessModel](../_autosummary/navlie.types.ProcessModel.rst) class and implement the `evaluate` and either the `input_covariance` or `covariance` methods." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "from navlie.lib import VectorInput\n", + "\n", + "Q = np.eye(2) * 0.1**2 # Input noise covariance with 0.1 m/s of standard deviation\n", + "\n", + "class WheeledRobot(nav.ProcessModel):\n", + " def __init__(self, input_covariance):\n", + " self.Q = input_covariance\n", + "\n", + " def evaluate(self, x: VectorState, u: VectorInput, dt: float) -> VectorState:\n", + " x_next = x.copy()\n", + " x_next.value[0] += u.value[0] * dt\n", + " x_next.value[1] += u.value[1] * dt * np.cos(x.value[0])\n", + " x_next.value[2] += u.value[1] * dt * np.sin(x.value[0])\n", + " return x_next\n", + "\n", + " def input_covariance(self, x: VectorState, u: VectorInput, dt: float) -> np.ndarray:\n", + " return self.Q\n", + " \n", + "process_model = WheeledRobot(Q) # instantiate it" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The methods in navlie process models must always accept the arguments shown above: a `State` object, an `Input` object, and a float `dt`. The `evaluate` method must always return a valid (i.e. subclass of a) `State` object, and the `input_covariance` method must always return a square numpy array. There are more optional methods that can be implemented for performance reasons, but we will cover those later.\n", + "\n", + "## Define the Measurement Model(s)\n", + "Moving on to the measurement model, if $\\mathbf{r}_a = [x,y]^T$ denotes the position vector of the robot resolved in the world frame, and $\\mathbf{\\ell}^{(i)}_{a} \\in \\mathbb{R}^2$ is the 2 x 1 position vector of landmark $i$, then the measurement model for each landmark is simply \n", + "\n", + "$$ \n", + "y_i = ||\\mathbf{r}_a - \\mathbf{\\ell}^{(i)}_{a}||\n", + "$$\n", + "\n", + "In navlie, measurement models must be implemented in a similar way to process models: inherit from the [navlie.MeasurementModel](../_autosummary/navlie.types.MeasurementModel.rst) abstract class, and then implement the `evaluate` and `covariance` methods. Here's an example for this problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "class RangeToLandmark(nav.MeasurementModel):\n", + " def __init__(self, landmark_position: np.ndarray):\n", + " self.landmark_position = landmark_position\n", + "\n", + " def evaluate(self, x: VectorState) -> np.ndarray:\n", + " return np.linalg.norm(x.value[1:] - self.landmark_position)\n", + " \n", + " def covariance(self, x: VectorState) -> np.ndarray:\n", + " return 0.1**2\n", + " \n", + "landmarks = np.array([[1, 1], [1, 2], [2, 2], [2, 1]])\n", + "meas_models = [RangeToLandmark(landmark) for landmark in landmarks]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## (Simulation only) Generate fake data\n", + "\n", + "The next step is to generate some fake data for our simulation (although navlie is also compatible with real data). To do this, we will use the [DataGenerator](../_autosummary/navlie.datagen.DataGenerator.rst) class which is used as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VectorState(stamp=0.0, dof=3, state_id=None)\n", + " [0. 0. 0.]\n", + "VectorInput(stamp=0.0, state_id=None)\n", + " [0.4867558 0.40227221]\n", + "Measurement(stamp=0.0, state_id=None) of RangeToLandmark\n", + " 1.5906187969698615\n" + ] + } + ], + "source": [ + "dg = nav.DataGenerator(\n", + " process_model=process_model, # process model to use\n", + " input_func=lambda t, x: np.array([0.3, 0.5]), # a callable that specifies the input values over time\n", + " input_covariance= Q, # numpy array or callable that specifies the input covariance over time\n", + " input_freq=50, # the frequency (Hz) at which the input is sampled (and the process model integrated)\n", + " meas_model_list=meas_models, # a list of measurement models to use\n", + " meas_freq_list=[10, 10, 10, 10] # corresponding measurement frequencies (Hz)\n", + ")\n", + "\n", + "state_data, input_data, meas_data = dg.generate(x, start=0, stop=30, noise=True)\n", + "\n", + "print(state_data[0])\n", + "print(input_data[0])\n", + "print(meas_data[0])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output of the `DataGenerator.generate` method is three lists: a list of ground-truth `State` objects, a list of `Input` objects, and a list of [Measurement](../_autosummary/navlie.types.Measurement.rst) objects, with the input/measurement lists possibly being corrupted by random noise if the `noise=True` flag is set. Each item in these lists correspond to different points in time. We can plot the trajectory as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Plot the state trajectory\n", + "pos = np.array([state.value[1:] for state in state_data])\n", + "plt.plot(pos[:, 0], pos[:, 1])\n", + "plt.scatter(landmarks[:, 0], landmarks[:, 1])\n", + "# add labels\n", + "for i, landmark in enumerate(landmarks):\n", + " plt.annotate(f\"Landmark {i}\", landmark)\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "plt.title(\"Simulated Trajectory\")\n", + "plt.axis(\"equal\")\n", + "\n", + "\n", + "# Plot the input data\n", + "plt.figure()\n", + "u_array = np.array([u.value for u in input_data])\n", + "u_stamps = np.array([u.stamp for u in input_data])\n", + "plt.plot(u_stamps, u_array[:, 0], label=\"omega\")\n", + "plt.plot(u_stamps, u_array[:, 1], label=\"v\")\n", + "plt.xlabel(\"Time (s)\")\n", + "plt.ylabel(\"Input\")\n", + "plt.title(\"Input Data\")\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run a filter!\n", + "\n", + "Finally, lets run an extended Kalman filter on this data to get a state estimate that uses only the noisy measurements. In the below filter, we instantiate the [ExtendedKalmanFilter](../_autosummary/navlie.filters.ExtendedKalmanFilter.rst) to use on our data, and looping over the input measurements while also calling the correction step whenever a measurement occurs." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# First, define the filter\n", + "kalman_filter = nav.ExtendedKalmanFilter(process_model)\n", + "\n", + "# You can try other filters too!\n", + "# kalman_filter = nav.UnscentedKalmanFilter(process_model)\n", + "# kalman_filter = nav.IteratedKalmanFIlter(process_model)\n", + "\n", + "P0 = np.diag([0.1**2, 1**2, 1**2]) # Initial covariance\n", + "x = nav.StateWithCovariance(x, P0) # Estimate and covariance in one container\n", + "\n", + "meas_idx = 0\n", + "y = meas_data[meas_idx]\n", + "estimates = []\n", + "for k in range(len(input_data) - 1):\n", + " u = input_data[k]\n", + "\n", + " # Fuse any measurements that have occurred.\n", + " while y.stamp < input_data[k + 1].stamp and meas_idx < len(meas_data):\n", + " x = kalman_filter.correct(x, y, u)\n", + "\n", + " # Load the next measurement\n", + " meas_idx += 1\n", + " if meas_idx < len(meas_data):\n", + " y = meas_data[meas_idx]\n", + "\n", + " # Predict until the next input is available\n", + " dt = input_data[k + 1].stamp - x.state.stamp\n", + " x = kalman_filter.predict(x, u, dt)\n", + "\n", + " estimates.append(x.copy())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filters in navlie are all designed to be *stateless*: this means that the actual state estimate is stored externally to the filter objects, in this case in a container called [StateWithCovariance](../_autosummary/navlie.types.StateWithCovariance.rst). Although this adds a slight burden on the user, it has the advantage of being more transparent, and also providing the ability to combine different filters in the same loop! For example, you could use an EKF for the prediction, but a UKF for the correction, or even to use different filters for different measurement models!\n", + "\n", + "\n", + "Once estimates have been obtained, we will often be interested in evaluating the performance. The [GaussianResultList](../_autosummary/navlie.utils.GaussianResultList.rst) object is a useful container for evaluating the quality of the state estimates when ground truth data is available. It calculates useful metrics such as raw error, Mahalanobis distance, and normalized estimation error squared (NEES). " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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bvHCWdBJ8fL+2INAK+UgTdT/wTp06obi4GCLVbPyRkpKi+ssLBIkIL5v17t7PXVaAs57+KaomlKgLcIvFgm7duvm07uLNx3D3RxvxxswijOwhqrgJBILwwmvgRKeBpyeZQUh0TYlRN6H4wy0L1qPe5sCM11dHuysCgaAZQLmCO3oNXJIIJBJdE0pcCfDczOSmVxIIBIIQ4U0DBwAC0rwnMf0hNYoRTwKBoPnBC+eCTllu7URo4L6THMWsXwKBoPnBy+YhXbPUzyO6ZwOQPVOavR+4r0QzbaNAoKeq3obV+8qi3Q1BGOE1cPYx1WLCwE4t1eW7TlTj0td+Ra3VHunuCQEuEATKze+tw2Xzf0NdY+QfXEFksNpcs5jM28RBqRrUQwiwqbgKaw6U47covMx9Kan2JiGkhBCyhVv2FCFkByFkEyHkM0JIVlh7qSBifQSxxLZjcmmtmgYhwBOVWu7l7KTA5uIqNNpdQp0P7omGfPJFpX0bwGTdsu8A5FNKBwHYBeD+EPfLkB65co3HKOZPFwhUquptAIBTDbYo90QQLmqtDvUzpcD/LVgHADheJVel5x1TouGN0qQAp5SuBFCuW7aMUspeTb8BiEg4XopF7m5+x5ZNrCkQRI5TQgNPWHi7tlFYvUYDj1y3XP0IwTauA7DEUyMhZBYhZC0hZG2w4fLsBAlTiiCWaGh0NL2SIC7h5zcq6hpRXCFX21Jt4Ny6sWpC8QghZC4AO4AFntahlM6nlBZRSotyc3OD2Z16gmhUHXcEAi1WziYqSCx4E8q7vx5UP0tGEjwKcingXCiEkJkAzgUwjkYsGYC8G6GBC2KJBpvQwBOVpjyMoj2JGZAAJ4RMBnAvgDGU0rrQdskzqgYuBLgghhAaeOJSYzV+OTN7OK+AV9RFfjLbFzfChQB+BdCHEFJMCLkewEsAMgF8RwjZQAh5Lcz9BBCdWV6BoCmEBp641DXaQQhg1rm+GU1iPvDZ5oj2DfBBA6eUXmGw+I0w9KVJXDZwgSB2EBp44lJrdSA9yaz4frskj0kR3EZVeiJJXIU2urxQhAgXxA5CA09c6hrtSEsyuQlqkyk2glHiS4ALuS2IIUzKsFpo4IlLbaMDGclmdwFuYELpnpseya7J+4/4HoOACi8UQQzBHl2hgScutVY70pJNbvUw2cubX+xw0ohbB+JKgEP4gQtiCDapLjTwxKXWakdakhl6g4lkYAM/WFaH9347iEgSVwKcPTBCAxdEG0opnMp9KDTwxKWu0YH0JJNbNZ5kJa2HXjP/euOxiPUNiIGixv4g5LYgVnByN6PQwBOP1fvK4KAUtY12dE1Oc7OB3zK2BwC4aeZWR2TvhfgS4MKNUBAj8DEJQoAnHpfN/w0A0K5FiuyFwrVZTASZKRYA7nUybRG+F+LKhCLcCAWxgoNTwYUJJXGx2h1INpsgcYE8ZsklNk26AJ/GCGvg8SXAmQ08yv0QCIQG3jyoqLPBbCIaDZwX2kcr6yPfKY74EuBuHwSCyEMpxcEyVwogoYEnNmaJaCYreauJXgOPNHElwKGzgVNKYYvwkEUgWLSuGFNe+Fn9LjTwxMZs0opJXpgn6dr2lNREpE9qXyK6tyBxuRHK/59YvB295i6BXQhxQQT541CF5rtVaOAJjVkiqOEq8/Ba9x0TekejSypxJcD1c5cL1xwGANSLB0gQQfSeBzuOVwslIgocLq/TTCaHC7MkaUZZ14zIUz+f3beN2/qR6BMjvgQ4tJOYSWa5+zaHMIoLIoeR2fPnPScj35FmzMGyWoz+5wq8+MPusO/LzCWuev6yQswe11P9rjehAIioWTe+BLiuoINFObGNwgYpiCC8DfT07q0BCNfWSHNE8f74dV9Z2PfF5wJP00VlWgyyEtqFBm6MOnmpfHJp4EKACyIHL8C7tpYz0DXYxD0YSZzK6dYXWggHvM07PVkb+8iEeXZ6krrMEUGLQHwJcDcNXO6+8AIQRBLeBH7B4A4AgHpRmT6iOBQhEAk3PgtnJklNMrm1fzjrdCy5YzTum9wXAGBzxpAJhRDyJiGkhBCyhVvWmhDyHSFkt/K/VXi7KUN1yaySVAEuHh5B5Fi82ZWwqGduBgAxkR5pHIqQjIQAN+lMKHqGd89Gm8wUtEyVw+vtMaaBvw1gsm7ZHAA/UEp7AfhB+R529KeFmVCEDVwQSU6csqqfU5QHWgTzRBYmJE0RqGmWbHaJyTSL5/RRbLIzpiYxKaUrAZTrFl8A4B3l8zsALgxttzz2RfNfmFAE0SbVIgR4NGAThT/sKAn7vtq2SFE/G5lQGGxCMx4mMdtSStk48jiAtp5WJITMIoSsJYSsLS0tDXB3Mm4auElo4ILoYjFJMElEmFAigNXuQGVdI4DICsn2LVPQpXUaAO8CnCW5imRMQNDpZCmllBDi8WxSSucDmA8ARUVFQZ11fTpZi1lo4ILo0alVKgBZC69vFPdgOCmttuK0x78HAByYN1W1gUeCti1T8P6Nw/HTrlJkJHsxoUjxo4GfIIS0BwDlf/jHMeBzoMj/hQYuiBYSAb6ZPRoAkGIxoUFMpIeVj9Ye1nwP50Sh3qc/M9mMTq3ScOXwrl5/x3KmxNokphFfArhG+XwNgC9C0x3vuNLJMj9wVhVcPDyCyJGeZMJ1Z3RTvQ5SkyQ0CDfCsPHebwfx1Lc7NcvCGa6uj8nSp07whDqJGWNuhAsB/AqgDyGkmBByPYB5ACYQQnYDGK98Dzt6P3C9Bl5WY8W+0shmAxM0P5xU6wueYjYJG3gY+WDNIbdl4TRTOAOMqrVIkdfAm7SBU0qv8NA0LsR98ciWI1V4/ed9qqat2sA5L5QvNx7F7IV/AJBtZAJBuKCgmmjM1CST8EKJMLwGTin1WUv2Bf7dcN0Z3Xz+HdPA42oSMxLc/sEf2Ftaq/p9sxckc6qvbbTjk/XF0eqeoJnhpNBUs02xCA08nOhls8NJNRo4pe7rBAMz0d4zqQ/+fFbPJtZ2YVFNKLFvA48o/756KAD3yUom0GutdrTJTI54vwTNFKrNhyILcDGRHimq6m149Ott6vdQi0umIEp+vhWYG2EkPWRIJLOoFRUV0bVr1/r9u5JTDeh+xrmwV50AIJtOhnZtBUd2dxzudTFmjszDgifuxOGjsmv66d2zAQBjxozBww8/DAA499xzUVOjtY9PmTIF9913HwBg3LhxcDi0WtTFF1+M2267DY2NjZg4caJbv6666irccMMNqKysxIUXXujWPmvWLMyYMQNHjx7FjBkz3Npvv/12TJs2DXv27MENN9zg1n7//fdj0qRJ2Lx5M2677Ta39kcffRSjR4/GmjVrcO+997q1P/300ygqKsKPP/6Ihx56yK39lVdeQf/+/bF48WL885//dGt/66230K1bN3z88cd46aWX3No//PBDtG3bFu+99x7eeOMNt/avvvoKmZmZmD9/Pt5//3239u+//x5msxnPP/88Pv/8c01bUlISli1bBgB44okn1M+Mli1b4osv5Lnzv/71r/jll1807e3bt8fChQsBAHfffTfWrVunae/Ro4fa51tuuQXbtm3TtOfn56vHPHPmTBw4cEBtW72/HMOHnYYfF8m/7z5sAo4eP46BHVuqyY7EvRe6e++m+x9HLVdQoV3LFDjG3g5TeivUbFmOAdXr3DTwYO49k9mCvUV3YM6Uvij/34c+33u1Vjs2H6nC6fk98ePizwC47r0ZM2Zg1qxZbv3wFULIOkppkX55XGjgmSkWr+01VrthjmaBIHy4bjg26bXjeHW0OtOsMMrBHQ78lSnMDh9JpTguNHBKKfo9uFRN2dk6PQnr/zYBj369DW/8sh8XFHZARrIZC1bLs9ViElMQTrrd/w1uPasn7p7YBwBw83vrsHTrcbRtkYzVD4yPcu8Sj/Nf+gWbiqvU71cO76I+6wCw67Epqjk1FFQ32DDwoWX469R+uGF0d59/t7e0BuOe+QkvXF6ICwo7hqw/QJxr4IQQDOzYUv2uz0pocziRbPYc4hoOSqobRBL/Zoo8aeZSz5ItzPYZrR4lNnpFmBfegGvSMVQEOgfJ3AgjGRkeFwIc0JpR9IUdbA6K1KTIHcqTi7dj2OM/4MuNRyO2T0FswF7a/PCahdSzPB2CENPEZOJHvx/GobK60O0vwEnMlmmyjNoVQVNa3AhwPievPqDH7nCqJ5tlhwsn/165D4Dsny5oXjDtjHB6IXM1i2QODIGLv32xFVe/uTpk23MavKR9oWWqBTkZyahttDe9coiIGwHOEsUYndT9J2sDPun+wptNstKSvKwpSESMNPC0pLgIp4hbfHmkD4ZQA2eyJJDgILNERFV6IyTJpWHr84IfKKtDnZKLItznjt8+GzoLmg+qBi68nqLO1ad7Ty4VKOwRD0QZNEkkonMh8SPAlScm2WLibOAu2MRBoHkMfIXXwJnjvqD5wOZd9NpZ2xYikCwUUErh1GlhdR5MEpYwuRMGo4FLUvhlkGZ/EdtTkFiVUOVks6RKbv48sSjNcJ87/t6K5IUSxAbUgwZ+aVFnEBJZH+BEZN6SHej+wGKNGaK81ma4Li+/Q2k69XSNfcEsSXGRDzzisEQx6clmNy8UwOUBEGqXIj389sWj2vzwFGadYjGBUqBR+BIGxVurDgDQ1pVs3zLFcF2Jk9qhTGYVaCi9/Bu4jSDCSdzMvjx0/gB0bpUGq92JRUpyd17Z+X67XFMi3OeO36fQtpofnibLk7nqUJGOSUgkzBJBI2QBnqJ4lHlKEc0XNA7laDgYhwiTmMQ0pk1mCu4/px/MEjG0gTPCbwM3/ixoHqj2UZ1vRLIibLYUC9fSYGDuwjYup3ath2IZvIYcymfR0zX2BYkQOIQN3DP8qMboPFEaXs1Ya0IREry5wa64fnTNNPAZ/1mNI5X1ke1UAsHchRf8drDJdaUw+QwHYwM3SSSiJpS4E+CAXPFCPknGJyqcL0Cn0MCbNVQxzeptrslcLo6yGmsku5RQmBTPrme+24VjVd5fhKYw+XIGYwM3SUID9wohBI0OJ25duN6jAA2nGYXX7kXgXfODjbr0yl8KFwEsimwHjpk7sQdOysE5nVsbx1uEKymhy43Q/9/GlQ2cEHInIWQrIWQLIWQhIcR4ujiEsHO6ePNxLwI8fPvXauBCgjc3XKH0WngNvLohcqHUiQafMuPEqQb8sP2ExxqTofQ84WEatCkAE42JRFaAB+yFQgjpCGA2gP6U0npCyEcALgfwdoj6Zkgyp+l4skGHdSKTGn4UNBPUUHrJ3Y2QUScq1AcMcxcGgDs+3ADAsyYciID1hco62e+8Rar3OgRGSPGkgUN+AaQSQswA0gCEPT1f77YZ6mdPcjq88ltbTFXQvPBFAxf1MQPHyK7NP2Z/O7e/13VDAZvDyE73P9eRiZD4iMSklB4B8DSAQwCOAaiilC7Tr0cImUUIWUsIWVtaWhp4TxUykl2DBgqgA+fk37ddJoDwauBiErN54ymUnvf9FgI8cJrSqvlm/SjI6aR477eDuGfRxqD6UFUva+BZqQEI8HjRwAkhrQBcAKAbgA4A0gkhV+nXo5TOp5QWUUqLcnNzA++pwuAurbhtax+k6UM7AYjcJKaQ380Pz5GYrkepQZhQAqZpAU64z9q2RocTf/t8CxatKw6qDzVK/c3MFP8tzPtP1mL9ocqIjc6DMaGMB7CfUlpKKbUB+BTAyNB0yzMtUy0Y368NBnRo4WYDZxc3UpOYIhdK88OTh0KysIEHxINfbEHenG/U77wN3AheaOuFfagq4dQok9Dpyf4LcNb/SFXlCUaAHwJwOiEkjchq8DgA20PTLe8QQsDcwPkHiV3PiAXyCPnd7HBp4NrlKZwN3CbyofjMu79qA3ZMTWT45EfcegEeKvfNGqsdyWYpoDqb147MAyBXqI8EwdjAVwP4GMB6AJuVbc0PUb+8QuT9g0InwJUL2pQN6o1f9uPZ73YFtnPhhdKsYfeWmw2c08BtTiHA/WXJ5mOglGr8wI3gTSj6SUyr3TXyeft/+wPuS7XVHpD5BHBp7bXWyIzCgvJCoZT+nVLal1KaTym9mlIakRA0SZnppZSCgOCHu8fgk/8boeYHtnnwG7XaHXjh+9149OttePGH3QHtW/iBN29ONSguZroHnPdC8eS3LPDM/y1Yj30na/2axNSbsXgNfPlO3x0mXl6xB3tKXHUsaxrsGmcJf2CCn90n4SbuIjEBOWk6pVA18B65GRjatTUnwI01oFdW7MVz3weoeSsIE0rzhnko6H2ELSYJ6/46HhnJZmFCCZA6qwNr9pd7XUeTQlbnzMmn8rX46CPeYHPgqW934sKXV6nLaqx2ZASogXfNTgcA7PWQQTHUxKUAJ6oGrvXHTeJSehpRXht81XAxidm8KTklDzJbGgR5ZGckI8Vi8jgCFHjHl1zqGu8fLxq4v1GaNZzNOhgNvFuOLMBZGoBwE5cCXCKE08BdFypJ0cA9TWaEQuBq3AjFc9rsYNGBngpaW0wEdqGBBwT/3HbMMs5/InmW35rfG71gjTCSCdVWOzKS/Y/CBOSI3JyMJBw/FZmMlHFT0IGHAJwN3AWzQ3oawoZGgHOfg96aIJ7YetSV69uTgDCbSERLaiUSvAauT8n7/o3DsfXIKY2NXK9lN9qdGNatNdbsL0erNN8EsJHDQ43VhozkDIO1fSPFYoLVFvtuhFFDIrIpgwKa1zCzgXsaioXCOUBU5GmevPW//fhq4zH1e3qScdUdi0kSZdX8gPf2sHlxAxzZIwc3ntldU8hYr4FbHU5VQ/f1Japfrb7RgcPl9QHbwAGguKIen/5xBDuPVze9cpDEpQYuESJPJnqwgetNKIs3H0OvNhmh0cDFJGaz5OGvtqmfv75tlEcbq0WShAnFD3i3Qf7F16dtJnaecBeASbwAN7CBM43a13B2vRK2bNtxAED7lsYmHH9YuasUfZT0HuEiLjVwQgicTlmY8g9SljJs2n+yVl22+0Q1blmwHhOeWxmSROsaN8IEM6JsPFyJ3n9dgpJTDdHuSsySl52G/I4tPbabTUS4EfpAfaMDDTaH5vnlTZ9/GtnV8Hd8cI03AR6oBs5SAV+ipOUIhu+2nwh6G00RlwJcIkogj04D79VGtlvxAuhfy/eon4OV3zVWOxycHSbRTJ2v/bQXjXYnJj2/MtpdiVkOlHn3LjALE4pP9HtwKUY8+YNmVPzHoUoAwMge2bh4SCeM7pXj9juNANe7EdqdYO9Oh4/2Uv2o/K+fbwGgDcwKlKZcIkNBnApwOZSe6kLpCSFIMklo9KABBWNCabA5kP/3b/HI165sAYlmQmHBBxV1kQlCiEeemDbQa3uS0MA98sL3u3H1G6vV7xV1Nji4c/X2qgMAgNO7ZyPFYsKcKX3dtuFNAz9aWa/Wo/RdA+cqbHG/SQ4gjF5Plo8TqcEQlzZwQhQvFFC3t7DFRDRDMd5sEozGzLa5cpcrwivRTCgsSEWghT3Yd4zvhRnDu3hd1yxJsItQekOMguiM0g4wTxMWFMOT5KWO2jPf7UL/9i0ANG0Dr2904GB5LVpx7qB//3Kr+jkUAryoa6umVwqSuNTACSGgcNfAAcBiljQCvGeuyx3Ik+dAoCSaBl4pNG9DmJbmSwEBs4mIQB4/aDBwt2MTm0bBNMkaDdz9erBr1ZQGfv+nmzD5+Z819/x7v7kSawVTri2/o/wSsYSraCdHXApw1QZu0GYxSWiwObDzeDVKTjWgNVdVIxj/XKOfJpoboajlaAy79voCAkYkmSQRSt8EfNIpnvZKcRbe1/uJaQPxxjVF6vfOrdPUz/zlmDSgLXIykrFDcd1ryhNo0xHZp/9IZegjJhfdJGfVDlPBIA1xaUKRiKzl/Ly7FN1ytA73DTYHPlpbjI/Wyknd/zq1n9oWTI5eI2GdYPI7opVE4gl/qpQLL5Sm2XXcOE/IsSrZ+aCizpXyQm+y4muP8ubTFIsJJ2tcufSaysmeqWj3J2uCT6+hJzXJhD5tMyPyPMWlBl5Vb0NVvQ0NNie2HzuladNrkbzWbfWx1BWlFLt1PqhGFyPR5F2YasTGPf6ZUCSRTtYDnVrJvtUrd3vPFLh8h/f2rDQLcjOTNS/UFLPWPFrTRD5u9uiGK2+3XNw4LJvW7if8uwg9G4srfV6XH0r5WqvwPz/vx4TnVmITtx9DE0qCTWKyoINAirkmMuzlrS+jZoRFEhq4J1qkyF4ZTY2En7+s0Gv7mgfGY9WcszXuC3xJO0B2Saxr9Cyc2eiZD9AKJSYpMibWuBTg9X6UrOI18J93n9S0eTrBK3aWANBO6jUnE4o+VWpzxx8buEXYwD3CFChPNnBGU9GLSWYJFpOk0cCN/LZrvMzpeHMpfve6YV737wsSISEJHGxyP2HfQxjwdvIvGtJR892bNuTJBMJsafyMt9G6C1YfdF8Yx7BTJdLkanGqGnjT6yaZpYjVQ4wnrHYHDpbJEdKhM1twNnDuWb1osCwDvN3F3m7xAR1aBNsxWYDHug2cEJJFCPmYELKDELKdEDIiVB3zhrfadx10OQxKqj2HhR+rMk75WKZMbPAPopFQO1nTqHH+j3fYsQgBrkW1gfsgwbPTk1BR1yjyoehoaHSqSpC3cmPMTu4LvAbOB/iwsmZG9/Gn64ux/dgpr/d4dkayz33whEkiEXmOgtXAXwCwlFLaF0ABIlTU2Jufrd73ck+J58oYn64/goe+3Iqix77XmGXYC4KF1QKePTTKQlAkIlZg5iYxB6fFoXqhNC3Ac1ukgNLQFA9JJKwO1/Oln2D87s4zcWmRnHtk6qD2AW3fzD33TAboH9myGivu+mgjbv7vuoD24Q8mJV9TuAlYgBNCWgI4E8AbAEApbaSUVoaoX17hc024B/JoF3jzbf5tXxneXnUAJ2usOMpr48omDpXXqbZvTy/TRHpQhQZuDDsdvnihMPe0Wj/maZoDvNKlN6G0TLOoE5zJfgS/9OCC9Phrw2SAfnTMRtQHy+rcFLLZ43r5vF9fIAQRsYEH4wfeDUApgLcIIQUA1gG4nVJay69ECJkFYBYAdOniPQzZV9jJX3TzCHTQVe6wSNobwEiAF3TOwsbDlRqf0lQPyWusdidSLCaPQi2Rws/ZDScEuBaHHzZwdk/5M9HeHOBzfes1cIskqfbqJD9C2Hu2ycCrVw7B0aoGzbVhMkB/G/P39W7dyDzUnlcmiWDV3jKs2FGCs/q2Cem2eYIxoZgBDAHwKqV0MIBaAHP0K1FK51NKiyilRbm5uUHszgXLd1DUtZVb6SWLSfuU1Vq19e2emj4I/7hYTkjEux7x15rPj9CgzJx7EmqVdYmogUe5IzEGu/a+eKGkKukafHVZbS7wo2Y3AW6WVGHrb/j5lIHtcf2obpr5CZcJRXsje9NLQj3hyPpz7du/h3S7eoIR4MUAiimlLL3Yx5AFeth5/8bh+OyWkYY2SYvuDW51ODWadpfWaTArb2g+DwPvJshvlq2jvxk+vlmer02kvBf7lDzqiZYiIFiYLdMXP3A2kmtIEAHudFLsMiis4C+844HehGIxEQSbNoSXBWZFidObMLzd1sz187KizsF1RMGXeyUk+wn0h5TS4wAOE0L6KIvGAQiPV7yOrLQkDO5inOlLb0KxOZwaTdtiltSMZst3lKjL+YtbXtOoruPSwLX7YTUREyWYZ93BCvWzCKnXomrgPjyTTIA3FcodL7y2ci8mPrcSm4urml7ZC7wzgd4LxSJJ6ugmULuxxgauCHC9IqJXwv4ysTeuH9UNgGwq3fHoZDxxkfd0wb4SqajmYL1QbgOwgBCyCUAhgCeC7lGQ6CcxKdXatzOTzeobmodd3EVrD6PaaleHfA12YxMKe+MngqwrrqjDxa+uUr8nwjGFEn/cCFOT5EcqUUwoG5QiC8EmffrH0h3qZ70JRZKImhc8UM1VYwP34IWiv61vPbuXqog1KnNdvlxjX4hUYeugkllRSjcAKGpqvUhiZEPjTSg9cjMMXf/Y+f5he4lmuc1u7FrH7rNEMDeUVls138UkphZXMqumH252rzUkiAbuus+D2w7zABmW1xprDrhXqqlTXniBpnzm5yfMHmzgRvf1QKU8XqhrV4qq9AFiltwPia+MIUnEbaIT8JxxjplI9BefaQqJIOvSkrTv8UQ4plDC5jksPmhn7FwmigbOMv4Fe0swd9v0ZGMB3Vsph9izTWCCVGNCkZgboexkkDfnGyxae9jwvj6rbxus+MtYnFfQIaD9eqKpdAGhIuEEeJLZ/SHrq3u7GmnpdgfFs9/tcnMLZJq5mwkFxsvjEb3NuznawEuqG/DdNuMitCwpUppBgQE9zFyXKAKcEarbnH/2rhjWBUOVqjV/GpGHr28bhRE9sgPaLq+3MVdEJ6VYe0Ce27nn400eR8vdctwr/wSLp7KOoSYu84F7w0g41+gmTYxs4Ct3leLFH3a7LXcYuNaN69smoTRwXmBfMawzPl1/JIq9iQ7XvvU7th49he2PTFZdARlLNh8HAGR40B55WP6cRJnEVE0oIZqs573EZp3ZXRWekkSQr5gzAoG3nWcqQUGUav3K+Wf4w1mnB7wvX4hUKoWEE+BGJhR9bm+9pwrgSiavh721mab9zCUFmDqovWo3TgQNnK/hmGoxJ8RLyV+OVsqRuFX1NjcB/p9f9gNw5djwBjPRJUoulFApKhYTwcVDOmnyC/kTtNMUvABnOpyTUo2yxl5Cr145BMO7B6bp+wpzS0w2Szhe1YCKukb0ax98kiw9CWdCMbJv6wMwjAIy3vzffsPtsbc2E+S5mclIsZhCNrkTC/AaeIpFSoiXkr8w23VlvefALBbu3RQmKTKZ6CKCqoEHh81BkZWWpMnwmRJCAc68R1qmWjgPMYpNnPsjc1+MhIs2mzdJsZgw+p/LMeWFn8Oyn4QT4EbuO3+b2t/v7bCLzISZQxfMoWomCeAHzgsbkxSZPMaxBnvx64NM+HPDajY2hVyZPjHOIZN1wXhb/axU4Fl/sEIzuvFlROMrTCdr3zJFndB0UmDeEpf74g/b5TmOYAoW+wrTwFMsUliD/RJOgA/La+22LDfT//SQVwyT87YwAV7dIE9usll0l4APpJexBRNSL1xeCIkQUJoY7pH+cKBM9nPWP2zsQbx3ch+fH/yE0sBDAJtIXHOgXJ3kNUlEo40HC1OoUiwmzuyjvQav/LgXABABBVx9gad4yLEUKhJOgBuZRwLxzb+wUEkKT2Un/+vfWQsAaKdoYRI3TIt32M3WMSsVyRb3NAOJDv+g6wuAsICuJD9ivc0S0cwrxDOh0FaZ0pNkllQBnmyWQqoJuwS4pD7vTupeao1fN5yw/Eu8U4W3OgaBknAC3AhfkhDxjO6Vw90EVFMlu22mLMADtYH/+6e9eFXRBGIFZjIxSQTpii3YWx71RIMvnacvSMyy6Pkz4SYlkAbOnpxg6ny2U4qszL96qGpCCaX5hCfVYtLYwMf0zkWftrIbcXfF4yUSNvD3rpfLsvGBSeHIUNksBLgveZx5tDeB9oKzl4Ea4OCnBH9yyQ5NWLE3nv1uF/44VNH0ikHCwpjNkqQK7tkf/BH2/cYKtVzxW72gUoN4/NXAEyTJmVPnhRUI7CXYPSdDFeB52WnBd46DpbxITTJplC+r3amOKlmytkho4F2z03F23zbYyE2i1tlCVUrORbMQ4L5q4CwTmZNCcxMYPYysPdDbuinB/9/fDuLFH3Zj2iurvK4XCpgJRZJcs/kRSqYWE/BD2+U7Thi2+SPAE8kGzm7TYAS4aobiTCihtjxWKKOolqlJ6vNOqZyMLsWstUNH6t7Wvyi8lZILeB8h32IMsOPRyXjoPJfniZH8/tu57p4pzL7ds02GZiLEqMq4agMP8EF98IutXtv5cm7hYufxalBK1YfTLEn481k9AQAXD+kU9v3HCrxv8sI1hzVtTPgYuad6wpxAnjwsJPw/Pxu72fqC6yVIVAEe6rkjNsrunpOuPu+7T1Sj1upw8+uPhBcKAHy/XasM1DUKDdwnUiwmzeyvUYaxa0Z0RYsUMy4sdOVAOC2vNf57/XDcPbE3J6BhKMCD9UL5eF1xYD8MEesOlmPS8ytx68I/1HzPJolLk5sgAsgXvE0u2QKYxDRJJGHcCFlKgN0lNQGPKhq5eQQmTEN9ei4t6oQnpg3EtWfkqQL6oa+2YfORKmRnaKvtRCrVqx6hgfsBP3yRCMELlxfi8Wn56jKzScKmhybh0tNcCdxNEsGoXjmwmCSNH3ij3f1uYzdJoPdhi9ToBsEer5IjSb/ZdAzPfy+nEEhNMquaZiIVqmiKRt0L+m0uqIsJsBQ/suSZJQk/bD+hRnduLq7CvwzSNMQD/MQbc6X1F5ZWIMVi4kwoob2/zCYJM4Z3gdkkuZkuzDqJTSLiSOhOQxgSXCWsAOevkUkiuKCwI64c3tVtNW0ILnFb7qQuLexfVwx2bT7IdLLRVnDTDARSepI8eWtKIDc4X9hx7JTm+0NfueqSMAGW5oc/ryQRNNicmK7kWD/vpV/wzHe7sGJHSRO/jD14d1LeW8cfSqob0CrNAotJUmvYdmoV2klMnm7Z6cjJcMV+zB7XC2N6u8o5RkoDv2dSH/Xz/43tgbP6hL42ZsIKcL0G7st6GgGunBneBq5JSxtkjggjs0wkSTbwj2Xh5InkRdEU5bWN+JuX+YitR2UvAn3KXW+wa3tUl1/nsW8iUrAqpPCl4SoDLOB9qLwO7RVXws6t0/DGNUX4+/n+R0f7Sss0C36fO0793qlVGm4a0921QoQEOG/GPaNHTlj2kbACnHfg9/bG5dvMHjRwZsPjE2XxXiqB9S+8EVpNYWTPZL7OSSbJzayQqNQ0uCaWCjpnqZ+Z5v3EYtnlk1Xa8QVPdvM2mb6F4scSfFrcQAt47y2pQd/2rpTO4/q1Dfu50E9Uap/dyEhw/uU3qleMCnBCiIkQ8gch5OtQdChU8GXUvM06E52phcELaGbD45PRMzuav5MxnVvLmkjbFik+2RQDrVDSFHoNm/fLNZuajwbOe4t0Uob3ALDtWJVmPX80cOZymGKR8L89J9Xl4XqIwwkvhPS58n3FandqnsdIMaBDC5ypmE74d2mkBHiP3NDnGdcTCg38dgDbQ7CdkOLrDeNJuPPRXCzQg48eCzRPMtPKNhyuxEVefLzH9pFvvG5hugn0Jpy5XMIvs0lqNjZwB3ect43rqX7W55Bvna71ZPAGE+CpSSZNjnlrGEKpww2vgQfqRdFod4Y0dayvfDN7NN69To6I5IV2pPzAJ+e3x5e3noEtD08K2z6COquEkE4ApgL4T2i6Ezp89RrgLyxvDuFt3OzGTU8yEOB+Kqr8+ru9hKszv9Zw5E8A3E0ovJ+zRSLNxguFd/fr3SYTX982CgBgtTk0E9T+mLzYuUw2mzQCMFzXMlw02p2aScwGmwMv/rAb32497td2rA4nks3RNRkamT8jwaBOWWpelHAQ7GvxeQD3AvB4ZxJCZhFC1hJC1paWlga5O9/xVQPnLyYv03gTyr5SWdDyJhRPGc+awlebORva6wXp3M8247M/gvcht+kEOG+vtZglt4IEx6rqg95nLMJMRU9NHwSJy5DX6HCqwr1dC//stUwDP1Rep8lHHak6iaGipFo7CWu1O/Hsd7tw03vrfN4GpTRqGjiPtoZL4oQZB3xWCSHnAiihlHq9mpTS+ZTSIkppUW5urrdVQ4qvApwPkaYGGriTuiqy8G9Svt0ffF2fach6rW3B6kO488ONAIATpxow/tmfUFxR518n4F7yiS91ZdZp4Kv3lWHEk8vx5cajfu8n1mHnmQV7MEFjtTlV4f6nke7up964c3xvw+XxpoHry8I1BFDns5GrTBNNoqWBh5tgzuoZAM4nhBwA8AGAswkh/w1Jr0KAkZ+zEckeaubpCzrIyzg7GtzbfcHX9dl63rxBPvr9MPaU1GDhmkN+9QFwn8TkX2QWk6SxkW8+ImuR6w+GP7FWpGFatkl5wNlQ32p34rd9ZQD8i8IEPE9WxpsNXJ+Rkg9E8TUsnL20oi3A+UsYqVD6SBDwWaWU3k8p7UQpzQNwOYDllNKrQtazIPHVBs4P7fI7umrWMQ373o83AQCGddMWigjUBu5r7hSmGXrzF2dmlpdX7MU6P4WrPm0qbwM3m1yh4JRSPL5YnqOO1Ox9pKi12nGxEmzD5hyYoLHaHbj27d8BuEfyBUq8aeC3LFiv+W7l7OE/bPctKMkaQDrecKCNC4liR0JMwvqB+2pC4SdX+M/6fMV6R3z2Fv/sD/8quPsiv3/aVYrf9pUD0D70erdD/mVwz6KNKDllXJjZCL0GzmuZZsmlgVvtTvUlFc83/qK1h90iIXm7PnMhTU82I8ksYccxVyFss58auBE5GclxZwPXw/e/Rapv9UFjRQPnJ+0TSREJyVmllP5IKT03FNsKFb6m//SkGbRMtWD2uF7qd34Ck+dQuX/2Z19MKNe8uUb9zGvgTy7R5hHnfZj3nazFuf/6xed+6DV7/nwlcSYU3ksjFIIsUCilmL9yr5pfxF/u+XiTqlEzDle4tsWqlyeZJfRqk6G5roFUmH/tqiGa7x2zUuJCA1+8+Rj6/m2Joc+33iPFFxpjRANvy9UzTSD5nbgaOAA8dF5/fDN7lNd1vGkGQ7pkqZ/9CeTwhr+TnjYHVTVtvQ1aL1dKqq0+Cxt9tjzNJCYXyONw8JqLz90OOcUV9Xhi8Q7Mem9tyLZ57Vsugc6PSDKSzSirtarf6wMoLzc5v736edHNI5BklvDLnpNY5qcLXiShlOKWBevRYHNitWL/5+E1cF8FuGpCMUXXjbBFimvE0NLH0UM8kNACfOYZ3TCgQ0uv6zDTQSEXRs3gZ649aeD+EkjyK2av1t94Rttaf6jSp226eaFobOCS6mbIB/REM0UqG7kEmlCpKfhq9BnJZpyscYWN1wfgfQEAOYpnS1HXVth/sg42B8Ws99Zh3cHy4DobJvhJVqM4AF4Df3Kxb1WlXlwuBzJF24TC409QVqwTO2c1SkgSwed/PgPvKBFbPHxofag0cAelOGdgOwDa3BuMFTtddtpJA9oCcD1MAzvKL6PMFKUvBhqxr94BemGs8QOXiCrgedthLJgAAkk9U1HbdA4P/kWVnmxGOfebQNznAOCr20bh3euGgRCCkzUujX7lrpNefhU9eI8n/qX1j4sHokduuuY8HD/VAIeTIm/ON/jvbwcBAJfP/xXXvuUy/wFyumIg+iYUAPjr1H5ISzJFJaw/XET/rMYAhZ2zDIdVZk4rNcpJctvZPUGIf1V5nE6KNpkpGN0rxzCc4AtuUpQl/GGCk+0mV0mVaTQZ46uwsTuo5gWldyNkJgVe0EczgyJ7iR0JwAa+1oOHzml5rQAAt4ztgfH92qrLQ2Uqat8yVc3F8fD5A9TlgeYUCTf8C7qGmzDv0jod7VqmaPzCT8trpSoL85S5md/2lWPFTuNgvVhwobxhdHdse2SycCNsLvACrl1L92i8zBSzHGrvR6kkSmXBa/ZQN7GNEvX3l4m91QxuTHAyM4LN6YTV7tC4dTEafLTX2pxOjXucWedGyPbJe9n4q4HvLa1B3pxv8O6vB/z6nRGBav//XLoDN75rbDdPsZhQ2DkL907uq5mgNXGms95tM3Db2T2Nfu4X+R1dprxTMSrA+Rd0NZelsWt2GpLNJpzihHpWWpJ6r/kiD1kSN0FoEQLcC7yA65bjnlQqU5kYqbH6LsCdlEIiip3ZQKOtqrOhbYtk3Hp2L3WoV1otD79V33A7xbSXV+FNrnKMv9gdVKt1S1oNnNndn/p2p7rcXw38//4rB+m+9uNen9a3OZwe5wgC0f5rrXa84mXfdY0Ow4Av/ro/fH6+ep2DYVCnlji/QC7fF6vl1viXJBslzJnSFx2yUlFabcW+0lq13e5wqqM9fclCtpyNTG8e0wN927WAIPSQSNY+LCoqomvXBuBF8MEHwE8/hb5DTVBe24jFm2Ub3lWnu4dTHyirxS+7T+LcQR00xR48YbU5sGhdMfq1b4HaRjuq6mw4r6CDZp3/7TmJkmorpg3uiMo6G77edBRn9MxBt5x0rN5fht0natwiJXlG9shG99yMJvvy+4Fy7D9Zqz60/PF9vuEIahrsmJzfDku3uLwmumanYXQv93QIFXWN+GbTMYzulQubw4mebeT9f7PpGCrqGtG7XSaG5bV2+x0PpRQLVh9Cv/YtkJ2RhF0najChXxt1uFtS3YBlW0+49dUbtVa7m58+/9tvNh1DerJZzfzIYOcZAK4Y1sWwpmqgfLnxKFqlWQzPY7SpqrfhKyVdQtfsNBwsq0NRXiv0bddCtXMz2rdMwdCurfH1Jnn9y07rjA9/lwtCs+fB7qT4YM0hDO7SCgM6CAGOW28FBgxoej0DCCHrKKVFbsvjQoDPmQO89VboO9QEdidFheL1kJvhPnPd6HCiqt6OrDQLLD485NVWOxpsTnVG3u6kaK0T/NUNdtiU5Q4qv0Qyk81IsUjq772RmWJGig8TRjVWO6x2J2dXdx1faY3xpF+yWUKLFPfJXP36rdMtMBGCijob7E6KFIuEzCYysjkBlNU0yvMCRDY1se0AQKODqlphdkaST0NH/vox+OMsr7PBLBG3Y6ptdKCu0YH0ZJNfpdR8oaLOBpPBPmMB/nxZTHI+nIxkedJPf40tJoL0ZLOhV1CrNAvMEoGTAmW1jeo2mj0LFwJnnx3QT+NbgEeJPSU1GP/sT0hPMmHrI5Pd2tcdrMDFr67CW9ee5lO9u5dX7MFT3+7E0jtGY/5P+7DmQDl+uU97QW99fz22HT2F5X8Zi6o6GwoeWYa/ndsf14/qhnsWbcSiJqrZP3Zhvk8a6u0f/IGNhytR2DkLn284igPzpqpteXO+MfzN2D65ePtad28d/frPXlqAi4Z0wrhnfsReZdj9+9zxyM1Mdvst40hlPc6YtxwWE0HbFikorqjHG9cUYZwyufjt1uOaLHhbHp7UZJrO9Ycq3HKu73/yHFWrP+3x7zGubxvMu3iQZp2Pfj+Mez/ZhCemDcSM4V287sNfprzwMzpmpeI/17g9i1Fnw+FKXPjy/zTLnrxoIK4Y1sXtGp+W1wp/mdgHl83/zXBbB+ZNxbGqeox4crm6DUHgeBLgwgbuBTZ0zs4wFjzMnY8vy+UN5tnRMzfDY9UbSl2TQilKGa+PFaHt8OFl62sgzxcbjqKq3obnLivEvifO8ek3vtqhjym1IPlJ2rs+2uD1N38ckj1FJEJUu/T177he9kcqtN4n+rQCDTYHlijmLkatwdwE82apqrehvLYRLQ1MX5cUdcJrVw3BZad19trnQJA109i0gc9b4l6XxVMeGJuD4v0mkqidqpfPf4sQzCEIjBEC3AvsQfNkA2U3t68P5KkGG1IsEswmCSZJMpzMcjhd7n3MN3u7UjXdk7viIxe47Gq+FGJgeZ4r6mwghEDy0cZrs/t2nGwSiz++n3efxNoDngNY2ERtp1ap6N1W9r7hy7zpC+rqU53OW7ID/7dgvZpB8GSN1c1uC7gy6pVWW+FwUvQzmFwjhGByfvuQ2r4ZkkRichLT7nCq+XduPcvldcN7J2nWdzrxxQbv6YWZySuRIh9jDSHAvcAEpic3KeaHbeQOaMS2o6fQQ5lgtJiIYdkyB6XqdvX+qp4e/D+NyMOXt54BwD3LoBHFijY7eUA7n/oNyNGEaw6Uo8rA5qlPt8oEuP68fKPTkAF58vLJxdux4XAlANk9jR03P/Kx6vzb63TlvdgxMaFx1X9W41tl0pOHuV6yvkU6wMQsEb/iBiJFA+eBwkcls2hk/SSkLzVTmbtki9TYs/cnCkKAe4FppjnpxiYUk6qB+7a9ukY7chShZJYkDyYUqgnQmTqwverV4S1xFksZ4IuWzPbrqzfHzJF52HdStmXf/9km9z7r6oKyiVa7U3aZZA8/G1LzFFfU498r96nanN1JVTMQbw5qsDk0mlxTBaF3HHdlE5wzpa/6mQWfsJdnOLRsb5iI8Ys72rCcN/dN7quZq2AT7gtuGK5Z35f0AkIDDz9CgHuhR24GHj5/AF6+cohhu1r0wUcJbndSNeeI2UTQaHe6+ZDzJhRADjapb3Sg1mrXlOfSw37z3Pe7mu6HIhg9DY9f1R1verLcBwCaEHOG3oL03m8HseVIFZxOihnDu+Cb2aPRt10mKurcf6vPLtjQ6FDNQLw5qN7mQIpFwvd3jQEAlHKh6U1x7Rl5eOHyQgDAmKd+hM3hVDVwU4Sj8kwSQQzKb3V+JS3JpBmVsInirDSX947FRHzKScMCf4QNPHwIAd4E14zM8+g9wYSmL5OLgDZ83SwRNDqcyP/7t5rgFQeFxiadYpHQYHOgpNpYYBmF+DcFy3lh8SDA+ahBALhpTA9V4zLKCWM0B7B48zHYnVQdgtfbHFi+owSv/aQNrKnTaXK1jXZU1cuCnjfBlFRbkWoxoW0L+Vqc8JD7/MSpBkx/Vet5kmw2aXK9n6yxuirxeDgH4cIkxaYGzo9I+PuCN+Ox1AMtUy041WBzM509Pi1f/byvtAYPf7UNAJe7RxByhAAPAlddTF81cKcq0PjQbV7TpJSClympFrmyeX2j8ZCVD9q5Y7ycv7wpTxRmQvGUM53XwFIskkaD0gcsOZ3U0ISUajFpRhMHy2Tzz3JdJRf9cRVX1OP3A7JHyvFTDWqRij8OVUKSCNKVF4h+EpNdgwe/2GqY+4QXmg6nK0VvqKrt+IrJQwqFaOPgzgefSqALN5HMzHSt05NAqXu5v06tXOue/Ywr8C6aeeQTHXFmg0AV4H6USWNmC15wHCyr1azD28BTk2QBfthD4WL+AWPD3VoPwp7BhJlZ8iDAuQeOBWDcPKYHANkWzYdc60cfFxTKkaU2J1VeWFoB2TLNgpM1Vsxe+AeqG2weX0yAbEMd9sQP2Hm8GlX1NpzRI0cdnSxYfUhz3pt6ifIC3+GkXC3MyApws0R8HrFFEvZSN0lEc806ZrlymNw5oTdmjszDdWd0M9xGLGSrbG4EU5W+MyFkBSFkGyFkKyHk9lB2LB7wdxLTxptQODV7wnMr1c8OJ9WZUEygFGoQy0WDO2q2yUf0sTJwRv7P+n4Ank0ovJZ9/5R+AJScGC1TsHjzcdy20FUrUa9Ndm2dhlSLCQ02h+Z4uyu5ZCwmgldW7MWXG49i0dpiNxOKEef+62cAUM0ngOwGOOyJ79VMeNm6ieYrhnXB7HG9cKHyQuna2vWiszspp3FGVoeRJGP//2ijng8T8Tg30jLVgofOH4C2LdwTu00f2gln9s7BpUWdNMvPHdTebV1B6Ajm7rUDuJtS2h/A6QD+TAjpH5puxQdMzvo6JHY4qZo0yuJBcFCqnVjThyDrtbcUrp1p4E0l1/rbF1sAeB7aEkKw/8lzcGDeVFzKBbOww+Td8/THbpIkpCaZMH/lPjicVJ24/OjmEQBkD5W9pXKeEZvD2aQ3ibyescvfyZpGvPbTXjTanW6TmllpFtw1oTeev3wwAGB492zcN7mv2udoauA7jlejwebAlxuPBlSuLRy4zofU5Dkxyvvz9CUFSDab8M/pBZpKVv/QRbkKQkswVemPUUrXK5+rAWwH0NH7rxILSfLdBv7Ql1tx/FSDOmnm6SFxUApetqcqk5Qsr/Q4Lm81oBXwTIAv2ey9bFcll+/CE0Y5kyvrXV4kLPCmWheFapK0fZo+VNbIcjKSUdS1FbYercJPu+Sc0fU2Bz5Xkk11aZ2Gq073Hm7tSVu++NVVKK+1aqq+tDIQMiyjpN1B4VDNSJEV4Mwk0fdvSzF74R9451f3YKNowNvAmxqVtErzXtGGrwqlLw4uCC0hGT8SQvIADAaw2qBtFiFkLSFkbWmpcbL3eMWfScy3Vx0A4BIYnoSn3gbOhLLV5kCLFLNbaappnEmFaai+uBICvgVj8PCJtJg3yf2fav3CmQYOyOaeoV1dWQjrbQ6cOOXSlIsr6nGq3o6WqRasvPcsDOqYZbhflsnwQuVY9YmgNh+pwpYjpzSlsvQmFcB17nccP4VdSrbBSGvgN4zurvm+8/ipiO7fCEopnl4mpw02SZ5NKIymMm/ykcGC8BK0ACeEZAD4BMAdlFK3u5FSOp9SWkQpLcrNjb0UmsFgUiMxff8N025MOi2HTchRqvUD79VW9jLZeaIaZpOkTjCmJ5lwYN5U9FLCzuXfura3w4tgYK6H7bPcbZm+0lWZPN1yVLsfkySnGgWAZIv2GPXVdD5eV4zjpxpw0RDlJeRBbrRINSMzxawK6O8UX3A92VymwU6t3AsIsPN610cbVdt5pAV4u5Yp6NXG5Tmkz5YYDcpqG/HdNtksZtZNYhrBeyWd1ScXl+tyxjBvlUuGau3hgtATlAAnhFggC+8FlNJPQ9Ol+EEN5PHDq2D/SVnz02s5rOSUQxeJySI3K5U0pBmK9mkzsLuP7JGtfp698A/D/dsdTvRr3wJDu7bS+Eb7C7O9600VyWYT8rLT1c88zHRT0DkLfbgXD3spje/XFl1ap+HCwg6a9lMNdo1QadsiBX8aIUeRzj2nn7q8M+fGZpSAzEhYR9qEAmht+eEKq99cXIW8Od9gzf6mCyjz95skkSZfavwk+5XDu7plcxzSJQtPX1KAB89rVlNiUSEYLxQC4A0A2ymlz4auS/GD6oWiewjrGx0eK8swm7HehFKv5g/RPlB8GLKJEPW7kcuWJBFV89x1ogYblfwiAFBWY8XSLcfRc+4SrD1YgRRLcIMvh5PiSGU9dp2owcyReeryCws7qrZmvTfMa1cNxeheOfj8lpEaIcY059bpSVh571l4/vLBKFKCRgA526N+wvXuiX3w9CUF+NPIruiRK++PL3tnFDxiJKw9ZZoMJ/yxh8ul8Jc9cuHkH3a454PRw09EmyXicYLdCItBLhlCCKYP7RSSSkYC7wTzFJ8B4GoAZxNCNih/vuUlTRBMqg3ctayq3oZ+Dy7Fyyv2GP7mJsWfWm9C4ctQ8bLKYpLU9KomiagTSH3bZcKI/u1dSYeYmQCQU7Pe/F9XPm1fshbqyeFMFHYnxSyl1qRZInjkggF47/phaJlmQV6OrAnrPVQm57fDe9cPByFEFWIpFgnXj9LahQHgb+f2xxXD5KF5tdXm7k+easH0oZ2QbDapQpgVgQZgmCtcr1kO6ZKlsZtHCt7Pnp2jDYcrcajMc64bf2GH6sv7gb9OFpOkatje8rf/Pnc87pnUByO6Z3tcRxB+gvFC+YVSSiilgyilhcrf4lB2LtZhijKvRZ1U3Nk+Wa8t5ZWTkYQrhnXBhP6yF4m+gg8T4Fa7A0k60wObyTebCHIzk/HC5YV49zr3wgqANmc3368NnDYO+O76yLP0jjPxvpLUyOFwokyp0nKksh5/GpGnlgkb2SMHl5/WGTPPyPO4LTYCOb+gg+GQPcViwuWnyV4pJ6sbvQ7rWUvn1qnorcwZGNa61I16ouWOrTGhUDkq9MKX/4f/W7DOy6/8g6gCvOmD5O8T5kH05swifHXrKI+/yc1Mxp/P6hnxbI4CLeLsBwEhBBLRPiTMtLH/ZC3KON9km4MiyWRsGgG0bnn64T+vgQPABYUd1er1euZOddkdvQnpN2ee5vnAPJCTkYz8TvIEld1JMapXDgDgjvG9NeulWEyYd/EgDOqU5XFbLDOht2E2O+56mwPHq4xznwBAjqIptk5LwsIbT8dHN40wdIPUh9/rJ98iBe9J5HBS/KyYO7YeDZ1HCoHvQWYO7k3G5jbO7ttWY5ISxCbCSTNInBT41/I9+NfyPVhww3CNRvLwV9vw4hVyIInN4dTkHmmV7rL7ltc2Yu3BCvy4qxRltY0GAlz+7kvmvJ6ch4M+2RBPoCk+mSljb2kNlmw+hjaZyejjwZzjjW1KkQpvLxm+Wo63IggPnz8APXMzMLx7NkwS8WjXbse99DY+ONGwGk8kWMflanE6gf/8vC9k27Y5nDhZY+U08KZ/w+eJCXZuRBBZxNUKIV9vOqZWMwe0/rJ2B9VMxPVtl4lHL8zHt3ecCUAWaK/+KPtW6wsAp+s08KZ4SJn9/1WpTgO4vFmChblBLlxzGLWNnrMkNsWsM2W7tzctj7dpeyMnIxl3Tujd5Pnp1TYT/5tzNjY9FD3hDbiCsgDZfMFepvkdg6/cfs+ijRjx5HI89o1cHq0pn25A+xJNEcWH4wohwENI//aZeEcJ2AFcEWt1jXY0OpwauywhBFef3hW5mclIMknYwwl+fcpWFhjjy8MIADO5ZEOsjJnV3nTOEV8Ildvd/VP64v0bh+P6UcaJkcJFx6zUqOenfuHywfjpnrEY3SsHDidVvXWCjapvtDvxua7M2cpdTQfP8aMbo7kDQewiBHiQ3D+lr0bzO1ljVaMj1x4sR96cb9QgCT6Agyc92YRjVa4gF32aznQ/TCh6mHsi73Y4bXDgGQ98rZ/ZFIQQjOyR4zGlrZ5XPBTViFe6ZqfDJBEcKKvFip2ykA02L8rnG464LeMrE3mCaeAXFnYQrn9xhhDgQXLTmB5YO3c8AFmTaXQ4kZVmQVqSCf/bI5swbv9gAwCghQe7c7LZhFNcTpE6nf90WrKsFfkq7ABXcn0nlSdZrZwAj6cEQ49emI85U/rinIGJl9XORLSVbYItduxtzsMbTICfr2RuFMQPQoCHAKaVOpwUjXYnkkySobD1ZF88rqsuc16B9kE6qbjrGRUq8MTQrnIgTJ3VjkVri9XlvdtmxJXr19Wnd1VzkSca/GjmjJ7Z2H+yFovWHg54e/woK8kkqTb1rzcd9Zp3nc9EKIgvxBULAcwu7KQUNocTSWZjAe6LfVGf3wQAij0Uc/AGM7vUNjrUgsRmiWDZncZ5RPxhzpS+ePBceaK0gKtgLvAPZhLr2SYDB07K1/iejzfhj0O+v6h5ahtdI7eu2Wm4eIici+TW9//AXz/f4vF30aoPKgge4UYYApgNvNHuhJPKpo6TBkV39bm9feXFywfj3H/94tdv2MuirtGODkrSqkuKQuP3zDTicwvaIzNZ2EwDhd03SSYJJxpco7Bpr6zCgXlT/d4e7+feNTtdM1m79ajngth8PUxBfCE08BDAbnw2YZhkllTXv79OdSVbCtT3mhUZ1lc78QaL3nzh+91q4MitZ/cMaP+eaJOZonrICPyHmVCSLZJq8gqGp77dqX5u2yJZE0+gnxjn+VgxsbVIFfpcvCEEeAhgQ8/6RlbtXcJHN4/Az/eehRtGd0eKRUKrNIsavKOHhad7Y/+T5+Cf0wt87hMT2mW1jbjvk80AgJQ4sn03B5hXaLJZwkszhqh5zwNBnyohPdmsmTTXF97g+VQpqhGqWAFB5BCv3BDANClW1ivFIqk5kQFg3V8naDIM6hnZM6fJfRiFhvu7vgjSiC1YBPvRygZkJJs1+czLaxvVRFs2hxNv/rIf5xV0QIcs9zznALDliGwi6ZqdhoNldUhLMmlS8pZWW+UJdi8vcSHA4w+hkoUIs0Tw1UY5iILPCAjI2lA0TA16t7JAbfCC8MAKPbPUuX8+y2Xieo8rtfbqj3vx5JIdGDlvueb3DifFNiV/CpukfO6yQgDAuYM6uI34DpXXGvajW046zh3UXtjA4xAhwEME7xI2uIv/9sw3rinC17d5zv4WCA+c01f9/N2dZ4YsCEcQGu6c0BtbHp6EZy8tBCDPdayZOw6Atv7os9+5SuQdLnd5JP175V6c8+LPWK7k/E5LMmFIl1Y4MG+qmhPny1vPwBPTBgIAjnlICFZZ19hkmTRBbCIEeIhgroTdleIC/jKuX1t1sjJU8AVlg6m+Iwgf+rzlLP/LW/87ALvDiV0ntJGUvDDfekTWvj/6XZ6E/K/BXMqgTlkYrWSNLK6ox9Itx9XUxYCcf76q3tZkoWJBbCJs4CGGDYtjAd4LIZ6CdwQyy3eUoLJeWzOTz2TIzHJltfLcS45BIWcAaNNCXn7/p/Jk9k1juuP+KbJ31KkGG5wUyBICPC6JGwF+7Ngx2GzamzklJQVt2rQBABw5cgQOhzbaLDU1FayQ8uHDh92S26enpyM7W64ocujQIbd9ZmZmolWrVqCU4vBh9wi5Fi1aICsrCw6HA6dOHgMAZCNF3VbLli3RsmVL2O12HD161O33rVq1QmZmJhobG3H8+HG39tatWyMjIwNWqxUnTriXxsrJyUFaWhrq6+tRWuqetKi14qPttDWg9FgxGqu0D2nbtm2RnJyMmpoalJe7105s164dkpKScOrUKVRWVrq1d+jQAWazGVVVVaiqcvcz7tSpEyRJQmVlJU6dcs913blzZxBCUF5ejpqaGrf2Ll3kgg5lZWWordXabyVJQqdOsltlaWkp6uu1BZNNJhM6dpRzvpSUlKChQWs+sFgsaN9eDs8/fvw4GhsbNe1JSUlo164dgMjfe/+9vAeueHsj5i3dgey0JNhPlQAA0iwm7DtQguVrt6JTm2x8vK4Y1OnAnn0HYK+x4uSJYqBW1uD5e+/E0aM4p5sFX26UvU3WbLLj/qpqTCzMwxNfbYb9VAnsVTk4dMg1Sgv23svNzUVqairq6upw8uRJt/bmdu8xWRFyKKUB/wGYDGAngD0A5jS1/tChQ2mg9O/fnwLQ/E2aNElt79y5s1v79OnT1fasrCy39muvvVZtN5vNbu2zZ8+mlFJaX1/v1gaAPvDAA5RSSktKSgzbn3zySUoppXv37jVsf+mllyillG7YsMGw/Z133qGUUvrLL78Ytn/66aeUUkqXLFli2P7Z14tp1/u+pjkXzDFs//XXXymllL7xxhuG7Vu2bKGUUvr8888bth88eJBSSuljjz1m2F5eXk4ppfS+++4zbG9sbKSUUnrLLbe4tSUnJ6vX5uqrr3Zrz8nJUdsvvPBCt/Zu3bqp7ePHj3drHzRokNo+fPhwt/aRI0dG9d5rM+JC2vW+r2mXuz81PHctRlxKu973Ne1024KA7r3WE26mXe/7mra/9sWw3HvLli2jlFL60UcfiXsPoPfddx8NBgBrqYFMDVgDJ4SYALwMYAKAYgC/E0K+pJRuC3Sb3nj00Ufd3sTsLQcATz31lNubMi8vT/38r3/9y03L6tWrl/p5/vz5blpS//5yuLjZbMYbb7zh1qeCggIAQEZGBp5/+TWs2FGK8f3aIE2xaxYVFQGQtRWj348YMQKArA0YtY8cORIA0LNnT8P2wYPlYhH5+fmG7acVDgJ+3oCkdj0x//XX3XJddO8u5+QeNWqU4e87dJBzsowfP96wvXVr2W956tSpqjbLk5Ym18a8+OKL0bt3b7d2k0nW+K688koMHTrUsA0Arr/+eowdO1bTnpLiyhV+66234rzzztO0Z2a6XOjuvvtuXHHFFZr2Vq1cE81z58510yKZdg1E595bV5WGb04AkEy48p4ncHbftnA4naoZxNJGvnbEkoLsKbMBAE9eNFC9xkb3ns3hxIe/H8am4kokd5BNKKbMXGRPmY27JvTR5GYP9t5jz05RUZFhe3O79wYOHOjWh1BA9DeOzz8kZASAhyilk5Tv9wMApfRJT78pKiqia9euDWh/gsDYcqQKu0uqMW2w71GcguhTVWdDwSPLAAAf3zwCRUqQT1mNFUMf+95t/bQkE7Y9MrnJ7W4ursI9H2/E9KGd1KIPi2ePRv8OwReTEIQPQsg6SmmR2/IgBPh0AJMppTco368GMJxSeqtuvVkAZgFAly5dhh48eNBtWwKBwJ2dx6uxZMsx3D6ulyYwq6zGitIaKxxOCgKC7IwkNNqd6Nw6za/tl9VYUVHXiJ5t/C+JJ4gsngR42CcxKaXzAcwHZA083PsTCBKFPu0yDeuNZmcke6z76Q+h2o4gegTjW3YEAJ/erpOyTCAQCAQRIBgB/juAXoSQboSQJACXA/gyNN0SCAQCQVMEbEKhlNoJIbcC+BaACcCblNKtIeuZQCAQCLwSlA2cUroYwOIQ9UUgEAgEfiDiqwUCgSBOEQJcIBAI4hQhwAUCgSBOEQJcIBAI4pSAIzED2hkhpQACDcXMAeCe1iw+EccSeyTKcQDiWGKVYI6lK6U0V78wogI8GAgha41CSeMRcSyxR6IcByCOJVYJx7EIE4pAIBDEKUKACwQCQZwSTwJ8frQ7EELEscQeiXIcgDiWWCXkxxI3NnCBQCAQaIknDVwgEAgEHEKACwQCQZwS8wKcEDKZELKTELKHEDIn2v0JBkLIAULIZkLIBkJIXNWWI4S8SQgpIYRs4Za1JoR8RwjZrfxv5W0bsYKHY3mIEHJEuTYbCCHnRLOPvkII6UwIWUEI2UYI2UoIuV1ZHlfXxstxxN11IYSkEELWEEI2KsfysLK8GyFktSLLPlTScAe3r1i2gSuFk3eBK5wM4IpwFU4ON4SQAwCKKKVxF5hACDkTQA2Adyml+cqyfwIop5TOU16urSil90Wzn77g4VgeAlBDKX06mn3zF0JIewDtKaXrCSGZANYBuBDATMTRtfFyHJcizq4LkevfpVNKawghFgC/ALgdwF0APqWUfkAIeQ3ARkrpq8HsK9Y18GEA9lBK91FKGwF8AOCCKPepWUIpXQmgXLf4AgDvKJ/fgfzAxTwejiUuoZQeo5SuVz5XA9gOoCPi7Np4OY64g8rUKF8tyh8FcDaAj5XlIbkmsS7AOwI4zH0vRpxeVAUKYBkhZJ1S7DneaUspPaZ8Pg6gbTQ7EwJuJYRsUkwsMW1yMIIQkgdgMIDViONrozsOIA6vCyHERAjZAKAEwHcA9gKopJTalVVCIstiXYAnGqMopUMATAHwZ2UonxBQ2RYXu/a4pnkVQA8AhQCOAXgmqr3xE0JIBoBPANxBKT3Ft8XTtTE4jri8LpRSB6W0EHKt4GEA+oZjP7EuwBOqcDKl9IjyvwTAZ5AvbDxzQrFdMhtmSZT7EzCU0hPKQ+cE8Dri6NoodtZPACyglH6qLI67a2N0HPF8XQCAUloJYAWAEQCyCCGsClpIZFmsC/CEKZxMCElXJmdACEkHMBHAFu+/inm+BHCN8vkaAF9EsS9BwYSdwjTEybVRJszeALCdUvos1xRX18bTccTjdSGE5BJCspTPqZCdMLZDFuTTldVCck1i2gsFABS3oefhKpz8eHR7FBiEkO6QtW5ArkX6fjwdCyFkIYCxkFNingDwdwCfA/gIQBfIaYIvpZTG/OSgh2MZC3mYTgEcAHATZ0OOWQghowD8DGAzAKey+AHI9uO4uTZejuMKxNl1IYQMgjxJaYKsJH9EKX1EkQEfAGgN4A8AV1FKrUHtK9YFuEAgEAiMiXUTikAgEAg8IAS4QCAQxClCgAsEAkGcIgS4QCAQxClCgAsEAkGcIgS4IC4hhGRzGeqOcxnragghr4Rpn3cQQv7kpf1cQsgj4di3QGCEcCMUxD2RyCSoRNCtBzCEy2ehX4co65xBKa0LV18EAobQwAUJBSFkLCHka+XzQ4SQdwghPxNCDhJCLiKE/JPIOdmXKqHbIIQMJYT8pCQZ+1YX/cc4G8B6JrwJIbOV3NWbCCEfAGrOkR8BnBuRgxU0e4QAFyQ6PSAL3/MB/BfACkrpQAD1AKYqQvxfAKZTSocCeBOAUYTsGZBzVDPmABhMKR0E4GZu+VoAo0N+FAKBAeamVxEI4pollFIbIWQz5NDmpcryzQDyAPQBkA/gO9kCAhPkrHd62kPOZ8HYBGABIeRzyCkFGCUAOoSu+wKBZ4QAFyQ6VgCglDoJITbqmvRxQr7/CYCtlNIRTWynHkAK930qgDMBnAdgLiFkoGJeSVHWFQjCjjChCJo7OwHkEkJGAHJKU0LIAIP1tgPoqawjAehMKV0B4D4ALQFkKOv1RhxkzBMkBkKAC5o1Sqm+6QD+QQjZCGADgJEGqy6BrHEDspnlv4pZ5g8ALyp5nwHgLADfhLPPAgFDuBEKBD5CCPkMwL2U0t0e2ttCThM8LrI9EzRXhAAXCHyEENIHcq3JlR7aTwNgo5RuiGjHBM0WIcAFAoEgThE2cIFAIIhThAAXCASCOEUIcIFAIIhThAAXCASCOEUIcIFAIIhT/h/hppCPQnJnigAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = nav.GaussianResultList.from_estimates(estimates, state_data)\n", + "# results.nees \n", + "# results.three_sigma\n", + "# results.error\n", + "# results.md # mahalanobis distance\n", + "# # and more...\n", + "\n", + "# Some plotting functions that work directly with GaussianResultList\n", + "fig, axs = nav.plot_error(results)\n", + "axs[0].set_title(\"Estimation Errors\")\n", + "axs[0].set_ylabel(\"theta (rad)\")\n", + "axs[1].set_ylabel(\"x (m)\")\n", + "axs[2].set_ylabel(\"y (m)\")\n", + "axs[2].set_xlabel(\"Time (s)\")\n", + "\n", + "fig, ax = nav.plot_nees(results)\n", + "ax.set_title(\"NEES\")\n", + "ax.set_xlabel(\"Time (s)\")\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a final note, `GaussianResultList` will invoke the `State.minus` method of the state objects to calculate the error. As we will see next, this allows us to implement a custom measure of error, when it might not make sense to directly subtract two of our state objects." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +}