Distributed Filtering and Detection for a Class of Multi‐Rate Systems With Stochastic Nonlinearities Under False Data Injection Attacks

ABSTRACT In this article, a distributed secure filtering problem is studied for a class of discrete time‐varying multi‐rate systems with stochastic nonlinearities subject to false data injection (FDI) attacks over wireless sensor networks (WSNs). The state iteration method is employed to convert the multi‐rate system to a single‐rate one due to asynchronous state updates and sensor sampling cycles. In order to counter the malicious attacks, a detector featuring an adaptive decision rule is developed for each sensor and a compensation strategy is established based on a memory mechanism. The main objective of this article is to develop a distributed filter for addressing the multi‐rate sampling scheme, hostile attacks and stochastic nonlinearities. An upper bound of the filtering error covariance is deduced via mathematical induction and the filter gains are formulated by minimizing this upper bound. Subsequently, a sufficient condition is provided to guarantee the uniform boundedness of the filtering error. Finally, illustrative simulations including comparative experiments are implemented to demonstrate the effectiveness of the proposed distributed filtering algorithm with a memory‐based compensation strategy.