Optimal Deception Attacks Against Remote State Estimation: An Information-Based Approach

This article studies the problem of deception attacks against remote state estimation from an information perspective. The Kullback-Leibler divergence between the compromised innovation and nominal one is utilized as the stealthiness measure. Without presupposing a linear attack model, the optimal attack policy that can cause maximum performance loss and deceive the false data detector is derived. For both attacks with strict and relaxed stealthiness, the optimal compromised innovation, which is shown to be generated by a linear time-varying system, can be determined with two steps. First, the minimum mean-square error (MMSE) estimate of the prediction error is obtained using attackers' available information. Then, the faked innovation is designed as a linear transformation of the MMSE estimate. Within a unified framework, this separation principle enables handling more general attack scenarios, where the attacker may obtain more (or less) measurement data than the remote estimator. The optimality of the information-based strategy is verified by theoretical analysis, numerical examples, as well as comparative studies with existing methods.