A robust three-stage central difference Kalman filter for nonlinear discrete-time systems considering faults and unknown inputs

Abstract

In this study, a novel robust three-stage central difference Kalman filter (ThSCDKF) is proposed for nonlinear discrete-time systems involving unknown inputs (uncertainties) and fault terms in the state and measurement equations. It is assumed that the evolution models of the fault and unknown inputs are not available and there is no prior information about the statistical properties of these factors. The proposed method is developed by decoupling an Augmented CDKF (ACDKF) via U-V transformation. By modifying the measurement stage, a robust ThSCDKF is proposed to achieve a robust state estimation when we do not have prior knowledge about the statistical model of the fault or uncertainties. The stability of the proposed filters is proved by the Lyapunov theory. The proposed methods have been applied to the on-board calibration of a star sensor. Finally, the effectiveness of the proposed filters is demonstrated by conducting different simulations.