Optimal deception attacks on remote state estimators equipped with interval anomaly detectors

Abstract

This paper studies the problem of optimal deception attacks on remote state estimation, where an interval χ2 detector is deployed to reveal anomalies. The information-based attack policy that can bypass the anomaly detector and cause the maximum estimation quality degradation is derived. For both attacks with strict and relaxed stealthiness, the optimal compromised measurements can be designed with three steps: obtain the minimum mean-square error estimation of the prediction error, de-correlate the estimate with historical compromised innovations, and design the compromised innovation as an optimal linear transformation. All available information for attackers is fully utilized for performance maximization while the stealthiness constraint is satisfied precisely to deceive the anomaly detector. The attack effect depends on both the amount of online information and the duration of detection interval. Contrary to well-studied innovation-based attacks using static linear combinations, the information-based deception policy is shown to be generated by a linear time-varying system, whose coefficients can be completely determined offline. The optimality of the proposed attack is verified with numerical examples and comparative studies.