Distributed Secure State Estimation Under Stochastic Linear Attacks

With the widespread applications of Cyber-Physical Systems, the security problem of distributed state estimation has been exposed, and attracted considerable attentions. In this paper, we consider the issue of distributed secure state estimation under stochastic linear attacks. Inspired by the method applied in anomaly detection, we propose a K-L divergence detector to resist the hostile attacks to guarantee an accurate estimation. For the proposed estimator equipped with the detector, we derive the optimal estimator gain, and establish a sufficient condition to guarantee the convergence of estimation error covariance. Furthermore, we provide a critical threshold selection method for the K-L divergence detector by simplifying the form of K-L divergence under Gaussian distribution. Finally, the effectiveness of the detector is verified by some numerical examples, and the performance comparison with a typical detector is provided.