Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [48 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01311170
Contributor : Guillaume Bourmaud <>
Submitted on : Tuesday, May 3, 2016 - 8:40:37 PM
Last modification on : Wednesday, November 21, 2018 - 5:52:06 PM
Document(s) archivé(s) le : Tuesday, November 15, 2016 - 7:49:16 PM

File

revisedv2(2).pdf
Files produced by the author(s)

Identifiers

Citation

Guillaume Bourmaud, Rémi Mégret, Marc Arnaudon, Audrey Giremus. Continuous-Discrete Extended Kalman Filter on Matrix Lie Groups Using Concentrated Gaussian Distributions. Journal of Mathematical Imaging and Vision, Springer Verlag, 2015, 51 (1), ⟨10.1007/s10851-014-0517-0⟩. ⟨hal-01311170⟩

Share

Metrics

Record views

393

Files downloads

917