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

• 成果类型: Article
• 署名作者: Tao, Yangtianze; Kang, Jiayi; Yau, Stephen Shing-Toung
• 署名单位: Tsinghua University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3485469
• 发表日期: 2025
• 页码: 2098-2104
• 关键词: costs; noise; Kalman filters; Robustness; estimation error; vectors; uncertainty; Adaptation models; Stochastic processes; Stability criteria; Extended Kalman filter (EKF); maximum correntropy criterion (MCC); outliers; stochastic stability

摘要

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.