The Invariant Extended Kalman Filter as a Stable Observer

We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear 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 gr...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 62; no. 4; pp. 1797 - 1812
Main Authors Barrau, Axel, Bonnabel, Silvere
Format Journal Article
LanguageEnglish
Published IEEE 01.04.2017
Institute of Electrical and Electronics Engineers
Subjects
Asymptotic observers
Automatic
Convergence
Differential equations
Engineering Sciences
Estimation error
Kalman filters
Mathematical model
nonlinear filters
Observers
Trajectory
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Summary:We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear 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. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this "log-linear" property of the error evolution, 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2594085