Optimal Stealthy Attack Design for Distributed Consensus State Estimation: A Historical Innovation-Based Approach

This article investigates the design of stealthy false-data injection attacks against distributed Kalman consensus filtering (KCF) over wireless sensor networks. This attack aims to maximize the degradation of remote state estimation performance under a stealthiness constraint quantified by the Kullback-Leibler (K-L) divergence. Most existing literature concentrates on centralized estimation schemes, while the proposed framework targets transmitted innovation channels in distributed KCF and fully accommodates topology-induced structural constraints. A historical innovation-driven linear attack model is formulated to leverage temporal innovation data, enlarging the feasible stealthy attack region compared to what is afforded by traditional memoryless innovation-based adversarial schemes. The resulting worst case attack design is reformulated into a relaxed optimization problem at the covariance level. The least-favorable attacked innovation is verified to follow a Gaussian distribution, which enables the closed-form characterization of the unconstrained worst case covariance. To enforce the block-diagonal constraint induced by network topology, a projected gradient descent (PGD) algorithm is developed to synthesize topology-feasible attack gains for distributed practical implementation. Finally, numerical simulations validate the theoretical analysis and demonstrate the effectiveness of the proposed attack scheme.