Resilient Consensus-Based Distributed Filtering: Convergence Analysis Under Stealthy Attacks

In this article, we consider the security problem for the consensus-based distributed state estimation. To resist the malicious attacker who can falsify the data transmitted through the wireless channel, each node equips with an attack defender, which is based on the measurement of its built-in sensor. Under the stealthy attack, which can deceive the defender, we investigate the resilience and convergence of the distributed estimation in two different attack scenarios. For the attack with enough communication resources, we provide a sufficient condition of the optimal attack to quantify the maximum estimation performance degradation. We also analyze the resilience of the worst case distributed estimation caused by the attacker. For the attack with limited resources, the optimal Kalman gain for each node is derived to maximize its estimation performance under the attack. We also give a sufficient condition to guarantee the convergence of the distributed estimation in this case. Finally, numerical simulations are provided to illustrate the effect of the defender on guaranteeing the resilience of sensor networks against attacks.