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.
The extended Kalman filter is an exponentially converging observer as soon as it is written in a canonical form of observability and in its high-gain form. It is shown that unlike extended Kalman filter, unscented Kalman filter can not be an exponentially converging observer. We propose a slight modification of the unscented Kalman filter to build an exponentially converging observer called unscented Kalman observer. Performances of this new observer are illustrated on an example of geolocation problem.
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