Robust M-estimation-based maximum correntropy Kalman filter

In this paper, a framework that combines an M-estimation and information-theoretic-learning (ITL)-based Kalman filter under impulsive noises is presented. The ITL-based methods make the most of the features of the data itself and can improve robustness by choosing an appropriate kernel bandwidth. However, small kernel bandwidths may lead to divergence. Nonetheless, robust-regression methods can improve the robustness from the statistical perspective and are independent of kernel bandwidth. This motivates us to fuse M-estimation-based weighting methods and the ITL-based Kalman filter. The proposed framework inhibits the divergence trend of ITL-based Kalman filters at low kernel bandwidth and improves the performance at large kernel bandwidth. Additionally, we use the unscented Kalman filtering method to extend the proposed algorithm to the nonlinear case. Monte Carlo simulations demonstrate the robustness and effectiveness of the proposed algorithm.