LAUSR

Abstract This paper introduces a new adaptive Kalman filter for nonlinear systems. The proposed method is an adaptive version of the square-root unscented Kalman filter (Sr-UKF). The presented adaptive square-root unscented Kalman filter (ASr-UKF) is developed to estimate/detect the states of a nonlinear system while noise statistics that affect system measurement and states are unknown. The filter attempts to adaptively estimate means and covariances of both process and measurement noises and also the states of the system simultaneously. This evaluation of the value of covariances helps the filter to modify itself in order to have more precise estimation. To test the efficiency of the investigated filter, it is applied to different approaches, including state estimation and fault detection. First, the proposed filter is used to predict states of two different nonlinear systems: a robot manipulator and a servo-hydraulic system. Second, the filter is employed to detect a leakage fault in a hydraulic system. All applications are tested under three assumptions: noises with known constant statistics, noises with unknown constant statistics and noises with unknown time-varying statistics. Simulation and experimental results prove the efficiency of the presented filter in comparison with the previous version.