The Variational Bayesian-Variable Structure Filter For Uncertain System With Model Imprecision And Unknown Measurement Noise

Variable structure filter (VSF) is a robust filter for linear uncertain system. In order to remove the chattering caused by high-frequency gain switching of VSF, the smoothing boundary layer (SBL) has been introduced. And similar to Kalman filter, the optimal state estimation of VSF can be got at the optimal smoothing boundary layer (OSBL). However, in practical applications, the statistical characteristics of the measurement noise are unknown. It is difficult to obtain the exact solution of the OSBL which is related to the measurement noise covariance. On the other hand, it is considered that the variational Bayesian adaptive Kalman filter (VB-AKF) is an adaptive filter with noise estimator for linear system with unknown measurement noise covariance. Therefore this paper proposes a variational Bayesian-variable structure filter (VB-VSF), which can make full use of VB-AKF's adaptive measurement noise estimation performance and the robustness of VSF. And the OSBL calculated from initial values is readjusted by the proposed VB-VSF algorithm. In this way, the calculated real OSBL can approach the theoretically OSBL. And the theoretically optimal state estimation can be obtained. In the end, the accuracy and the robustness of the proposed VB-VSF are verified through by simulation examples.