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

Abstract

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.