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Conference Papers Year : 2013

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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Dates and versions

hal-00903252 , version 1 (10-11-2013)

Identifiers

  • HAL Id : hal-00903252 , version 1

Cite

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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