Robust interacting multiple model cubature Kalman filter for nonlinear filtering with unknown non-Gaussian noise

Abstract

Estimating noise covariance matrices and suppressing outliers simultaneously is a huge challenge because they are coupled. In order to solve the nonlinear filtering problem with unknown non-Gaussian noise, the maximum correntropy criterion (MCC) is used to suppress the outliers, while the variational Bayesian (VB) technique is used to estimate the one-step prediction error covariance matrix (PECM) and the measurement noise covariance matrix (MNCM), and the nonlinear problem is solved by the third-order spherical radial cubature rule. In this paper, nominal measurement is constructed to eliminate the influence of outliers on the recursive estimation of MNCM. Through these operations, the variational Bayesian and maximum correntropy based cubature Kalman filter (VBMCCKF) and the maximum correntropy cubature Kalman filter (MCCKF) are derived. The interacting multiple model (IMM) fusion framework is used to promote the collaborative work of VBMCCKF and MCCKF, thus a novel filter is proposed in this paper. The simulation verifies the validity and universal applicability of the proposed filter. The estimation error of the proposed filter in spacecraft autonomous celestial navigation is about 30% less than that of the existing filter with the best performance.