On the convergence of the unscented Kalman filter

Assia Daid (1) , Eric Busvelle (1) , Mohamed Aidene (2)

1 CDE - Contrôle et Diagnostic pour l’Environnement
2 L2CSP - Laboratoire de Conception et Conduite des systèmes de Production

A convergence analysis of the modified unscented Kalman filter (UKF), used as an observer for a class of nonlinear deterministic continuous time systems, is presented. Under certain conditions, the extended Kalman filter (EKF) is an exponential observer for non-linear systems, i.e., the dynamics of the estimation error is exponentially stable. It is shown that unlike the EKF, the UKF is not an exponentially converging observer. A modification of the UKF-the unscented Kalman observer-is proposed, which is a better candidate for an observer. This paper is a first step towards a proof of the global convergence of the high-gain version of the UKO.

Mots clés: Nonlinear observers; Unscented Kalman filter; Unscented Kalman Observer

Domaines: Automatique / Robotique

Assia Daid, Eric Busvelle, Mohamed Aidene. On the convergence of the unscented Kalman filter. European Journal of Control, In press, ⟨10.1016/j.ejcon.2020.05.003⟩. ⟨hal-02891724⟩