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dc.rights.licenseopenen_US
dc.contributor.authorLABSIR, Samy
hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
dc.contributor.authorGIREMUS, Audrey
IDREF: 163238766
dc.contributor.authorYVER, B.
dc.contributor.authorBENOUDIBA-CAMPANINI, Thomas
dc.date.accessioned2023-12-19T10:05:39Z
dc.date.available2023-12-19T10:05:39Z
dc.date.issued2023-08-26
dc.identifier.issn0165-1684en_US
dc.identifier.urioai:crossref.org:10.1016/j.sigpro.2023.109232
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/186718
dc.description.abstractIn the past decade, estimation on manifolds has been paid an increased attention for making it possible to intrinsically account for constraints on the unknown parameters. Applications are widespread from computer vision to target tracking. To evaluate the performance of the algorithms, it is of interest to derive bounds on the estimation error. This issue has been mostly investigated for parametric estimation on Riemannian manifolds. This paper addresses the problem of computing a Bayesian lower bound on the norm of the estimation error when both the unknown variables and the observations belong to specific manifolds called Lie groups (LGs). For that purpose, a metric is considered that preserves the geometric properties of the latter. We firstly derive an inequality on the correlation matrix of this intrinsic error under the mild assumption of unimodular matrix LGs. Then, we obtain a closed-form expression of the bound for the special orthogonal group SO(3) and the special Euclidean group SE(3). Finally, we detail its derivation in the case when both the prior distribution and the likelihood are concentrated Gaussian distributions. The proposed Bayesian bound is implemented and tested on two estimation problems involving both unknown parameters and observations on SE(3): the inference of the pose of a camera and that of the centroid of a cluster of space debris.
dc.language.isoENen_US
dc.sourcecrossref
dc.subjectEstimation on Lie groups
dc.subjectCramér-Rao bounds
dc.subjectGaussian distribution on Lie groups
dc.title.enAn intrinsic Bayesian bound for estimators on the Lie groups SO(3) and SE(3)
dc.typeArticle de revueen_US
dc.identifier.doi10.1016/j.sigpro.2023.109232en_US
dc.subject.halSciences de l'ingénieur [physics]en_US
bordeaux.journalSignal Processingen_US
bordeaux.page109232en_US
bordeaux.volume214en_US
bordeaux.hal.laboratoriesIMS : Laboratoire de l'Intégration du Matériau au Système - UMR 5218en_US
bordeaux.institutionUniversité de Bordeauxen_US
bordeaux.institutionBordeaux INPen_US
bordeaux.institutionCNRSen_US
bordeaux.teamSIGNAL AND IMAGE PROCESSING-MOTIVEen_US
bordeaux.peerReviewedouien_US
bordeaux.inpressnonen_US
bordeaux.import.sourcedissemin
hal.identifierhal-04352851
hal.version1
hal.date.transferred2023-12-19T10:05:41Z
hal.popularnonen_US
hal.audienceInternationaleen_US
hal.exporttrue
workflow.import.sourcedissemin
dc.rights.ccPas de Licence CCen_US
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Signal%20Processing&rft.date=2023-08-26&rft.volume=214&rft.spage=109232&rft.epage=109232&rft.eissn=0165-1684&rft.issn=0165-1684&rft.au=LABSIR,%20Samy&GIREMUS,%20Audrey&YVER,%20B.&BENOUDIBA-CAMPANINI,%20Thomas&rft.genre=article


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