On vulnerability of Kalman filtering with holistic estimation performance loss

This article addresses the problem of optimal deception attacks against remote state estimation, where the measurement data is transmitted through an unreliable wireless channel. A malicious adversary can intercept and tamper with raw data to maximize estimation quality degradation and deceive ${\chi }^2$ detectors. In contrast to prior studies that concentrate on greedy attack performance, we consider a more general scenario where attackers aim to maximize the sum of estimation errors within a fixed interval. It is demonstrated that the optimal attack policy, based on information-theoretic principles, is a linear combination of minimum mean-square error estimates of historical prediction errors. The combination coefficients are then obtained by solving a convex optimization problem. Furthermore, the proposed attack approach is extended to deceive multiple-step ${\chi }^2$ detectors of varying widths with strict/relaxed stealthiness by slightly adjusting some linear equality constraints. The effectiveness of the proposed approach is validated through numerical examples and comparative studies with existing methods.