diff --git a/core/include/traccc/fitting/kalman_filter/gain_matrix_updater.hpp b/core/include/traccc/fitting/kalman_filter/gain_matrix_updater.hpp
index 183a0f50f..2d5618ef4 100644
--- a/core/include/traccc/fitting/kalman_filter/gain_matrix_updater.hpp
+++ b/core/include/traccc/fitting/kalman_filter/gain_matrix_updater.hpp
@@ -39,7 +39,7 @@ struct gain_matrix_updater {
     TRACCC_HOST_DEVICE inline bool operator()(
         const mask_group_t& /*mask_group*/, const index_t& /*index*/,
         track_state<algebra_t>& trk_state,
-        bound_track_parameters& bound_params) const {
+        const bound_track_parameters& bound_params) const {
 
         using shape_type = typename mask_group_t::value_type::shape;
 
@@ -57,7 +57,7 @@ struct gain_matrix_updater {
     template <size_type D, typename shape_t>
     TRACCC_HOST_DEVICE inline bool update(
         track_state<algebra_t>& trk_state,
-        bound_track_parameters& bound_params) const {
+        const bound_track_parameters& bound_params) const {
 
         static_assert(((D == 1u) || (D == 2u)),
                       "The measurement dimension should be 1 or 2");
@@ -123,10 +123,6 @@ struct gain_matrix_updater {
         const matrix_type<1, 1> chi2 = matrix_operator().transpose(residual) *
                                        matrix_operator().inverse(R) * residual;
 
-        // Set the stepper parameter
-        bound_params.set_vector(filtered_vec);
-        bound_params.set_covariance(filtered_cov);
-
         // Return false if track is parallel to z-axis or phi is not finite
         const scalar theta = bound_params.theta();
         if (theta <= 0.f || theta >= constant<traccc::scalar>::pi ||
@@ -134,14 +130,14 @@ struct gain_matrix_updater {
             return false;
         }
 
-        // Wrap the phi in the range of [-pi, pi]
-        wrap_phi(bound_params);
-
         // Set the track state parameters
         trk_state.filtered().set_vector(filtered_vec);
         trk_state.filtered().set_covariance(filtered_cov);
         trk_state.filtered_chi2() = matrix_operator().element(chi2, 0, 0);
 
+        // Wrap the phi in the range of [-pi, pi]
+        wrap_phi(trk_state.filtered());
+
         return true;
     }
 };
diff --git a/core/include/traccc/fitting/kalman_filter/kalman_actor.hpp b/core/include/traccc/fitting/kalman_filter/kalman_actor.hpp
index 23a886490..9db5b1fd3 100644
--- a/core/include/traccc/fitting/kalman_filter/kalman_actor.hpp
+++ b/core/include/traccc/fitting/kalman_filter/kalman_actor.hpp
@@ -78,7 +78,7 @@ struct kalman_actor : detray::actor {
     TRACCC_HOST_DEVICE void operator()(state& actor_state,
                                        propagator_state_t& propagation) const {
 
-        const auto& stepping = propagation._stepping;
+        auto& stepping = propagation._stepping;
         auto& navigation = propagation._navigation;
 
         // If the iterator reaches the end, terminate the propagation
@@ -114,6 +114,9 @@ struct kalman_actor : detray::actor {
                 return;
             }
 
+            // Update the propagation flow
+            stepping.bound_params() = trk_state.filtered();
+
             // Set full jacobian
             trk_state.jacobian() = stepping.full_jacobian();
 
diff --git a/core/src/finding/find_tracks.hpp b/core/src/finding/find_tracks.hpp
index 5a33d4b4d..f24cc28f6 100644
--- a/core/src/finding/find_tracks.hpp
+++ b/core/src/finding/find_tracks.hpp
@@ -239,10 +239,9 @@ track_candidate_container_types::host find_tracks(
                 track_state<algebra_type> trk_state(meas);
 
                 // Run the Kalman update on a copy of the track parameters
-                bound_track_parameters bound_param(in_param);
                 const bool res =
                     sf.template visit_mask<gain_matrix_updater<algebra_type>>(
-                        trk_state, bound_param);
+                        trk_state, in_param);
 
                 // The chi2 from Kalman update should be less than chi2_max
                 if (res && trk_state.filtered_chi2() < config.chi2_max) {
diff --git a/device/common/include/traccc/finding/device/impl/find_tracks.ipp b/device/common/include/traccc/finding/device/impl/find_tracks.ipp
index fe816bff8..b0024dca2 100644
--- a/device/common/include/traccc/finding/device/impl/find_tracks.ipp
+++ b/device/common/include/traccc/finding/device/impl/find_tracks.ipp
@@ -182,7 +182,7 @@ TRACCC_DEVICE inline void find_tracks(
                 owner_local_thread_id +
                 thread_id.getBlockDimX() * thread_id.getBlockIdX();
             assert(in_params_liveness.at(owner_global_thread_id) != 0u);
-            bound_track_parameters in_par =
+            const bound_track_parameters& in_par =
                 in_params.at(owner_global_thread_id);
             const unsigned int meas_idx =
                 shared_payload.shared_candidates[thread_id.getLocalThreadIdX()]