Robust quaternion Kalman filter for state saturation systems with stochastic nonlinear disturbances

Abstract

To tackle the quaternion robust state estimation problem, the robust quaternion Kalman filter (RQKF) has been developed for quaternion signals by the quaternion maximum correntropy criterion (QMCC) under non-Gaussian noises. However, in the presence of saturation phenomena and nonlinear disturbances impacting quaternion systems, the performance of RQKF may deteriorate. Hence, this paper focuses on the quaternion Kalman filtering issue for state saturation systems with stochastic nonlinear disturbances under non-Gaussian noises. First, a feasible upper bound on the filtering error covariance is first obtained by some quaternion matrix techniques, and then a QMCC-based RQKF for state saturation systems (MCQKF-SS) is developed. The posterior estimate of the MCQKF-SS algorithm, developed as an iterative online method with a recursive structure, is updated by a quaternion iterative equation (QIE). Subsequently, a sufficient condition is proposed to ensure the uniqueness of the QIE’s fixed point, thereby guaranteeing the convergence of MCQKF-SS. Moreover, an adaptive kernel width strategy addresses the kernel width selection problem, leading to the development of a variable kernel width version of MCQKF-SS (VKMCQKF-SS). Finally, simulation results of two numerical examples verify the effectiveness and robustness of proposed quaternion algorithms in the considered environment.