Tracking a Cluster of Space Debris in Low Orbit by Filtering on Lie Groups

This paper addresses the problem of tracking a cluster of space debris sufficiently close to each other to be considered as a single ex-tended object. State-of-the-art random-matrix methods estimate the kinematics of the object centroid by assuming that its shape is elliptic and that the observations are randomly distributed within this ellipsoid. However, space debris, whose motion is driven by the gravitational force, spread out into a "banana"-like-shaped cluster. In this paper, we propose a novel Lie-group based parameterization to intrinsically capture the "banana"-like shape. More precisely, we first formulate the centroid tracking problem as filtering on Lie groups. Then, we derive an iterated extended Kalman filter on Lie groups to perform the estimation.