Joint shape and centroid position tracking of a cluster of space debris by filtering on Lie groups

•The cluster of space debris is tracked as a whole instead of individually estimating the trajectories of the pieces of debris.•For that purpose, a random-matrix-based approach is proposed that is well-suited to non-ellipsoidal extended objects. It takes advantage of a Lie-group-based state space representation of both the cluster state and the measurements.•A computationally efficient iterated Kalman filter on Lie group is proposed to tackle the estimation problem.•Experiments on data generated according to the actual physical model describing the orbits of space objects validate the relevance of the proposed approach.•The obtained results are compared to those of a Gaussian process fitting method using the Hausdorff distance, which is independent of the considered parameterization of the cluster. Space surveillance aims at detecting and tracking pieces of debris that are orbiting around the Earth. When the latter are sufficiently close to each other to form a compact cluster, they can be considered as a single extended object. State-of-the-art random-matrix methods estimate the kinematics of the object shape and centroid by assuming that it is ellipsoidal and that the sensor observations are randomly distributed within its volume. However, in accordance with the laws of orbital motion, space debris scatters taking a specific curvature. To intrinsically capture the resulting cluster shape, we propose a novel Lie-group-based parameterization of both the cluster and the sensor measurements. Then, we derive an iterated extended Kalman filter on Lie group to sequentially estimate both the centroid trajectory and the evolution of the extent parameters. Finally, numerical experiments validate the interest of the proposed method compared to a generic Gaussian-process-based extended-object tracking algorithm.