Appropriate model for projected hemisphere use case?

[Antoine101]

Hi everyone,

I am using Stone Soup for a project where I locate UAVs on an hemispherical grid and I want to track them.

My hemisphere is flattened for visualization purpose as shown below. Each aerial vehicle is associated with (theta, phi) coordinate couples. Imagine you are the sensor at the center of the hemisphere and you are facing towards the top of the hemisphere, looking at the sky. Each marker on this hemisphere is a projection of a vehicle in the sky on this hemisphere.

If the vehicles come straight in line with the hemisphere center (the sensor), it will give a motionless marker on the radar plot. But if it passes sideways in front of the sensor it will cross the radar plot at a steady speed, or maybe accelerating. That's for the range of motions.

I receive the sensor measurements at each timesteps which are couples of angles already of these markers.

I wondered what is the appropriate measurement model for my use case. In tutorial 2, a CartesianToBearingRange class is used to simulate bearing range measurements from x, y cartesian coordinates from a ground truth that's generated itself from a CombinedLinearGaussianTransitionModel.

I'm not 100% confident with the library yet but the CartesianToBearingRange class is just to generate some measurements based on a linear gaussian model right?

In my case, where I already have access to angle measurements, is a measurement model like shown ok and appropriate for the types of motions of my targets and my setup?

measurement_model = LinearGaussian(
                            ndim_state=4,
                            mapping=(0, 2),
                            noise_covar=np.array([[0.5, 0],
                                                  [0, 0.5]]))

As an additional question, why not using a CombinedLinearGuassianModel in this case?
I use a simple LinearGaussian measurement model as it's the one used in tutorial 10