Stealthy integrity attacks and optimal selective protection for distributed state estimation

This paper studies the security of distributed state estimation under integrity attacks. Considering cost and energy constraints, only a subset of the sensors within the network is protected. To reveal the vulnerability of such partial protection schemes, we investigate integrity attacks in distributed networks that can bypass anomaly detectors and lead to unbounded estimation errors. First, the feasibility analyses of such attacks under both strict and non-strict stealthiness are derived using matrix decomposition theory, along with the corresponding necessary conditions and sufficient conditions. Second, an explicit form of integrity attack is presented, and an offline algorithm for generating attack sequences is provided. These reflect how an adversary can undermine the estimation performance by targeting only unprotected sensors. It is demonstrated that the deviations of the detected quantities induced by the attack sequences decay exponentially, suggesting that the stealthiness of the proposed attack is enhanced compared to previous methods, particularly with an increased detection interval. Third, a sufficient condition for securing sensor networks is established. Utilizing the constraints determined by this condition, the optimization of the selective protection strategy is formulated, which identifies both the minimum number of sensors to protect and which specific sensors they are. Finally, a numerical simulation is conducted to validate the proposed results.