The invariant extended Kalman filter as a stable observer

2014/10/06 by Axel Barrau, Barrau, Axel, Silvère Bonnabel +1 · 22 citations
Computer Science · Engineering · #Adaptive Control of Nonlinear Systems #FOS: Electrical engineering #Inertial Sensor and Navigation #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1410.1465

openalex publication_date 2014/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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