Estimation de paramètres évoluant sur des groupes de Lie : application à la cartographie et à la localisation d'une caméra monoculaire

Abstract : In this thesis, we derive novel parameter estimation algorithmsdedicated to parameters evolving on Lie groups. These algorithms are casted in aBayesian formalism, which allows us to establish a notion of uncertainty for theestimated parameters. To do so, a generalization of the multivariate normaldistribution to Lie groups, called concentrated normal distribution on Lie groups, isemployed.In a first part, we generalize the Continuous-Discrete Extended Kalman Filter (CDEKF),as well as the Discrete Extended Kalman Filter (D-EKF), to the case where thestate and the observations evolve on Lie groups. We obtain two novel algorithmscalled Continuous-Discrete Extended Kalman Filter on Lie Groups (CD-LG-EKF) andDiscrete Extended Kalman Filter on Lie Groups (D-LG-EKF).In a second part, we focus on bridging the gap between the formulation of intrinsicnon linear least squares criteria and Kalman filtering/smoothing on Lie groups. Wepropose a generalization of the Euclidean Iterated Extended Kalman Filter (IEKF) toLie groups, called LG-IEKF. We also derive a generalization of the Rauch-Tung-Striebel smoother (RTS), also known as Extended Kalman Smoother, to Lie groups,called LG-RTS.Finally, the concepts and algorithms presented in the thesis are employed in a seriesof applications. Firstly, we propose a novel simultaneous localization and mappingapproach. Secondly we develop an indoor camera localization framework. For thislatter purpose, we derived a novel Rao-Blackwellized particle smoother on Liegroups, which builds upon the LG-IEKF and the LG-RTS.
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Guillaume Bourmaud. Estimation de paramètres évoluant sur des groupes de Lie : application à la cartographie et à la localisation d'une caméra monoculaire. Instrumentations et Détecteurs [physics.ins-det]. Université de Bordeaux, 2015. Français. ⟨NNT : 2015BORD0242⟩. ⟨tel-01271029⟩

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