On the Relation Between Smooth Variable Structure and Adaptive Kalman Filter

Abstract

This article is addressed to the topic of robust state estimation of uncertain nonlinear systems. In particular, the smooth variable structure filter (SVSF) and its relation to the Kalman filter is studied. An adaptive Kalman filter is obtained from the SVSF approach by replacing the gain of the original filter. Boundedness of the estimation error of the adaptive filter is proven. The SVSF approach and the adaptive Kalman filter achieve improved robustness against model uncertainties if filter parameters are suitably optimized. Therefore, a parameter optimization process is developed and the estimation performance is studied.