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Continuous-Discrete Extended Kalman Filter on Matrix Lie Groups Using Concentrated Gaussian Distributions
hal.structure.identifier | Laboratoire de l'intégration, du matériau au système [IMS] | |
dc.contributor.author | BOURMAUD, Guillaume | |
hal.structure.identifier | Laboratoire de l'intégration, du matériau au système [IMS] | |
dc.contributor.author | MÉGRET, Rémi | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | ARNAUDON, Marc | |
hal.structure.identifier | Laboratoire de l'intégration, du matériau au système [IMS] | |
dc.contributor.author | GIREMUS, Audrey | |
dc.date.accessioned | 2024-04-04T03:14:50Z | |
dc.date.available | 2024-04-04T03:14:50Z | |
dc.date.created | 2013 | |
dc.date.issued | 2015 | |
dc.identifier.issn | 0924-9907 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194098 | |
dc.description.abstractEn | In 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.iso | en | |
dc.publisher | Springer Verlag | |
dc.subject.en | Filtering Kalman | |
dc.subject.en | Manifold | |
dc.subject.en | Lie group | |
dc.subject.en | Camera pose | |
dc.title.en | Continuous-Discrete Extended Kalman Filter on Matrix Lie Groups Using Concentrated Gaussian Distributions | |
dc.type | Article de revue | |
dc.identifier.doi | 10.1007/s10851-014-0517-0 | |
dc.subject.hal | Sciences de l'ingénieur [physics]/Traitement du signal et de l'image | |
dc.description.sponsorshipEurope | Dementia Ambient Care: Multi-Sensing Monitoring for Intelligent Remote Management and Decision Support | |
bordeaux.journal | Journal of Mathematical Imaging and Vision | |
bordeaux.volume | 51 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 1 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-01311170 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-01311170v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Imaging%20and%20Vision&rft.date=2015&rft.volume=51&rft.issue=1&rft.eissn=0924-9907&rft.issn=0924-9907&rft.au=BOURMAUD,%20Guillaume&M%C3%89GRET,%20R%C3%A9mi&ARNAUDON,%20Marc&GIREMUS,%20Audrey&rft.genre=article |
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