ABSTRACT This paper proposes a novel robust cubature Kalman filter to address the challenge of measurement outliers in nonlinear systems. First, a multiple statistical similarity measure (MSSM) is introduced to evaluate the interdimensional similarity between random vectors. To overcome the sensitivity of filter performance to the choice of a single similarity function and its parameter, a weighted MSSM (WMSSM) is constructed to form a more robust cost function, whose lower bound maximization leads to the WMSSM‐based cubature Kalman filter (WMSSM‐CKF). Furthermore, an adaptive parameter strategy that leverages the numerical characteristics of measurement residuals within a sliding window is developed, and corresponding weighting factors for the similarity functions are designed. On this basis, a WMSSM‐based adaptive cubature Kalman filtering algorithm (WMSSM‐ACKF) is developed, which effectively mitigates the performance degradation caused by the inappropriate selection of the similarity function or its parameters. Furthermore, the stability, convergence, and computational complexity of the WMSSM‐ACKF are theoretically analyzed. Finally, the numerical simulation results demonstrate that the WMSSM‐ACKF achieves higher estimation accuracy than the other compared algorithms when dealing with multiple measurement outliers.
Yang et al. (Fri,) studied this question.