Robust state estimation based on statistical similarity measure with sliding window for non-Gaussian systems under multiple cyber attacks

• Published in: Journal of the Franklin Institute Vol. 362; no. 15; p. 107971
• Main Authors: Wang, Guoqing, Zhu, Zhaolei, Yang, Chunyu, Rong, Wanting, Ma, Lei
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.2025
• Subjects: Cyber attacks; Robust Kalman filter; Sliding window; Statistical similarity measure; Student’s t kernel function; Variational Bayesian; Variational Bayesian; Cyber attacks; Robust Kalman filter; Statistical similarity measure; Sliding window; Student’s t kernel function
• ISSN: 0016-0032
• DOI: 10.1016/j.jfranklin.2025.107971

This work proposes a robust and resilient state estimation framework for non-Gaussian systems under multiple cyber attacks, where the inputs and measurements are both threatened by random deception attacks with unknown probabilities. Motivated by the fact that existing robust estimation algorithms struggle to accurately estimate the system state only using the current measurement value under non-Gaussian noises, especially when coupled with cyber attacks, we design a novel robust estimation algorithm, namely RSSWKF, based on the statistical similarity measure, which is derived through fixed-point iteration and utilizing the advantage of the student’s t kernel in handling non-Gaussian noises. Moreover, the multiple measurements within the sliding window are leveraged to adjust the polluted covariance matrices through Variational Bayesian methods adaptively to further enhance the estimation accuracy. Compared with related algorithms through the target tracking example, the higher tracking accuracy and adaptive capability of our RSSWKF are verified.