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Continuous-Discrete Extended Kalman Filter on Matrix Lie Groups Using Concentrated Gaussian Distributions

hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
dc.contributor.authorBOURMAUD, Guillaume
hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
dc.contributor.authorMÉGRET, Rémi
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorARNAUDON, Marc
hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
dc.contributor.authorGIREMUS, Audrey
dc.date.accessioned2024-04-04T03:14:50Z
dc.date.available2024-04-04T03:14:50Z
dc.date.created2013
dc.date.issued2015
dc.identifier.issn0924-9907
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194098
dc.description.abstractEnIn this paper we generalize the Continuous-Discrete Extended Kalman Filter (CD-EKF) to the case where the state and the observations evolve on connected unimodular matrix Lie groups. We propose a new assumed density filter called Continuous-Discrete Extended Kalman Filter on Lie Groups (CD-LG-EKF). It is built upon a geometrically meaningful modeling of the concentrated Gaussian distribution on Lie Groups. Such a distribution is parametrized by a mean and a co-variance matrix defined on the Lie group and in its associated Lie algebra respectively. Our formalism yields tractable equations for both non-linear continuous time propagation and discrete update of the distribution parameters under the assumption that the posterior distribution of the state is a concentrated Gaussian. As a side effect, we contribute to the derivation of the first and second order differential of the matrix Lie group logarithm using left connection. We also show that the CD-LG-EKF reduces to the usual CD-EKF if the state and the observations evolve on Euclidean spaces. Our approach leads to a systematic methodology for the design of filters, which is illustrated by the application to a camera pose filtering problem with observations on Lie group. In this application, the CD-LG-EKF significantly outperforms two constrained non-linear filters (one based on a linearization technique and the other on the unscented transform) applied on the embedding space of the Lie group.
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enFiltering Kalman
dc.subject.enManifold
dc.subject.enLie group
dc.subject.enCamera pose
dc.title.enContinuous-Discrete Extended Kalman Filter on Matrix Lie Groups Using Concentrated Gaussian Distributions
dc.typeArticle de revue
dc.identifier.doi10.1007/s10851-014-0517-0
dc.subject.halSciences de l'ingénieur [physics]/Traitement du signal et de l'image
dc.description.sponsorshipEuropeDementia Ambient Care: Multi-Sensing Monitoring for Intelligent Remote Management and Decision Support
bordeaux.journalJournal of Mathematical Imaging and Vision
bordeaux.volume51
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01311170
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01311170v1
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