Resilient Distributed State Estimation for LTI Systems Under Time-Varying Deception Attacks

This article studies the resilient distributed state estimation over the sensor networks under measurement attacks, which make the measurements of variant subsets of sensors aberrant at different time instants. For this problem, while most of the existing works focus on the static target states that do not change over time, we investigate the estimation for the dynamic ones, which evolve according to general linear time-invariant (LTI) systems. To achieve the resilient distributed state estimation for the general LTI systems under the measurement attacks, we propose a dynamic-target regulative gain estimation (DTRGE) algorithm, in which an attack detector, a regulative gain matrix, and an adaptive gain are designed. The detector helps agents monitor the measurement anomalies, and once the attacks are detected, the adaptive gain can counteract the deviation of the estimates induced by them. The regulative gain matrix restrains the negative effects on the convergence of the estimates caused by the system matrix of the target LTI system, especially the unstable one. We demonstrate that all the sensors can recover the target state by running the DTRGE algorithm, if the topology and the observability of the sensor network satisfy certain conditions. Moreover, we further apply the DTRGE algorithm to the sensor networks with switching topologies, and demonstrate that the estimation task can also be completed by these sensors. Finally, simulation and experiment results are given to illustrate the performance of the DTRGE algorithm.