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Discrete extended Kalman filter on lie groups

Abstract : In this paper, we generalize the Discrete Extended Kalman Filter (D-EKF) to the case where the state and the observa- tions evolve on Lie group manifolds. We propose a new filter called Discrete Extended Kalman Filter on Lie Groups (D- LG-EKF). It assumes that the posterior distribution of the state is a concentrated Gaussian distribution on Lie group. Our formalism yields closed-form equations for both non- linear discrete propagation and update of the distribution pa- rameters based on the likelihood. We also show that the D- LG-EKF reduces to the traditional D-EKF if the state evolves on an Euclidean space. Our approach leads to a systematic methodology for the design of filters, which is illustrated by the application to a camera pose estimation problem. Results show that the D-LG-EKF outperforms both a constrained D- EKF and a D-EKF applied on the Lie algebra of the Lie group.
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https://hal.archives-ouvertes.fr/hal-00903252
Contributor : Guillaume Bourmaud <>
Submitted on : Sunday, November 10, 2013 - 7:04:03 PM
Last modification on : Wednesday, January 31, 2018 - 1:46:02 PM
Document(s) archivé(s) le : Tuesday, February 11, 2014 - 4:36:26 AM

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  • HAL Id : hal-00903252, version 1

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Guillaume Bourmaud, Rémi Mégret, Audrey Giremus, Yannick Berthoumieu. Discrete extended Kalman filter on lie groups. European Signal Processing Conference, Sep 2013, Marrakech, Morocco. ⟨hal-00903252⟩

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