The Stochastic Stability Analysis for Outlier Robustness of Kalman-Type Filtering Framework Based on Correntropy-Induced Cost

Abstract

This note introduces the modified extended Kalman filter (MEKF), reformulating the EKF update step within a nonlinear regression framework. We propose a novel outlier-robust scheme, MCIC-MEKF, utilizing the minimum correntropy-induced cost (MCIC) criterion. We provide a theoretical analysis of its outlier robustness through stochastic stability, proving exponentially bounded mean square posterior estimation error under natural conditions. In addition, we present a technical approximation for the adaptive Kalman gain, enhancing efficiency without compromising performance. Simulation results confirm MCIC-MEKF's robustness against various non-Gaussian noises with large outliers, outperforming several filtering benchmarks.