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The Invariant Extended Kalman Filter as a Stable Observer

Abstract : We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic non-linear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. Then, we leverage the result to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging.
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Contributeur : Silvere Bonnabel <>
Soumis le : jeudi 25 janvier 2018 - 09:56:29
Dernière modification le : jeudi 24 septembre 2020 - 17:04:02
Archivage à long terme le : : jeudi 24 mai 2018 - 21:27:05


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Silvere Bonnabel, Axel Barrau. The Invariant Extended Kalman Filter as a Stable Observer. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62 (4), pp.1797-1812. ⟨10.1109/TAC.2016.2594085⟩. ⟨hal-01692380⟩



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