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Méthodes statistiques fondées sur les groupes de Lie pour le suivi d'un amas de débris spatiaux.

Abstract : In the context of space surveillance, we are interested in a cluster of debris evolving in orbit around the Earth and observed by a radar sensor.It is then observed that the debris spreads out taking a bananoid shape due to their movement constrained by Kepler's laws.This distribution is representative of concentrated Gaussian samples on the Lie group SE (3) and can be completely characterized by anunknown covariance matrix.We propose in this thesis an original reformulation of the cluster observation model on Lie groups. The latter is then modeled as an extended targetcharacterized by its shape and its centroid. In this way, we reconsiderits estimation as a manifold inference problem.The geometry of the cluster is thus intrinsically taken into account. Two algorithms on Lie groups are then proposed in order to estimate respectively statically and dynamically the parameters of the cluster.In the first part of the manuscript, the issue of space surveillance is underlined and the main methods for tracking debris are recalled.In a second part, the foundations of Lie groups arepresented. The third part focuses on the contributions of the thesis andproposes a model and two algorithms for estimating the shape and centroid of a cluster which are then tested on different simulation scenarios.The last part is devoted to a theoretical contribution inwhich is proposed a bound for Bayesian estimation error on Lie groups.
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Submitted on : Friday, January 8, 2021 - 2:29:07 PM
Last modification on : Saturday, January 9, 2021 - 3:26:31 AM


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  • HAL Id : tel-03103892, version 1


Samy Labsir. Méthodes statistiques fondées sur les groupes de Lie pour le suivi d'un amas de débris spatiaux.. Traitement du signal et de l'image [eess.SP]. Université de Bordeaux, 2020. Français. ⟨NNT : 2020BORD0294⟩. ⟨tel-03103892⟩



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