Secure State Estimation Against Sparse Sensor Attacks: A Distributed Adaptive Saturation Method

This paper investigates the problem of distributed secure state estimation for cyber-physical systems under sparse sensor attacks. Traditional centralized methods struggle with high computational complexity in large-scale systems, while existing distributed approaches either require strong robustness constraints for graphs or face challenges due to local unobservability. To address these challenges, we propose a distributed adaptive saturation method. This method designs an adaptive saturation function for each node to limit the impact of attacks on the estimation residual. Additionally, it integrates a consensus protocol to enable cooperative estimation of nodes, effectively mitigating the influence of malicious attacks. Theoretical analysis shows that the algorithm ensures consensus estimation under fixed attack channels, with estimation errors ultimately bounded. Furthermore, by refining the saturation mechanism for each node, the algorithm is extended to scenarios with time-varying attacks. Simulation experiments validate that the proposed method effectively handles sparse sensor attacks, reduces computational complexity, and significantly enhances system robustness.