A Lie-group based modelling for centroid and shape estimation of a cluster of space debris
Samy Labsir, Audrey Giremus, Brice Yver, Thomas Benoudiba‐Campanini · 2020
In the context of spatial surveillance, we are interested in estimating the outline and centroid position of a cluster of debris from a set of noisy sensor observations. The motion of the pieces of debris is completely driven by Kepler's law, therefore they scatter taking a specific curvature. This spreading resembles that of samples drawn on the Lie group SE(3). For this reason, we propose a reformulation of the cluster observation model on Lie groups to intrinsically capture its shape. Then, we derive an optimization algorithm on Lie group to solve the estimation problem. The presented approach is validated on simulated data and compared to a state-of-the-art method based on a Gaussian process modelling.