False-Data Injection Attacks Against Distributed Filters With Improved Complete-Stealthiness

In this article, the existence and the corresponding design of false-data injection attacks are studied such that the state estimation at every distributed filter is compromised. Different from the existing attack design approaches causing the bounded but persistent innovation fluctuation, we require that the attack impacts on every local innovation are gradually faded. Due to the consensus property of distributed filters, we further study the attacks that result in the consensually divergent distributed state estimation after a finite time. Thus, the designed attacks can bypass both the innovation-based and consensus-based detectors with arbitrarily long detection windows. By the equivalence transformation of systems and the reachability of system matrix eigenvectors, the necessary and sufficient conditions for the existence of such sensor attacks are presented. Not relying on the system transmission data in real time, an offline attack generation approach is provided. The simulation examples are given to verify the effectiveness of the theoretical results.