Distributed Secure State Estimation Against Sparse Sensor Attacks: An Adaptive Gain Modulation Approach

This paper studies the distributed secure state estimation problem in cyber-physical systems under sparse sensor attacks, by employing an adaptive dynamic gain modulation strategy. Unlike most existing attack detection and isolation-based strategies, a dual-layer collaborative state estimation framework based on attack suppression is established. The framework integrates decentralized and distributed observers, thereby decoupling attack suppression from residual feedback. By analyzing the dynamic behaviors of state deviations between the two observer layers, a universal dynamic suppression gain is derived to guarantee the robustness against sparse attacks. Furthermore, a distributed adaptive dynamic gain modulation strategy is introduced to avoid centralized processing, which enhances the applicability of the attack suppression mechanism while preserving the estimation accuracy. Finally, a numerical simulation is presented to demonstrate the effectiveness of the proposed framework.