Recursive Secure Filtering over Gilbert-Elliott Channels in Sensor Networks: The Distributed Case

Abstract

IEEE This paper is concerned with the recursive secure filtering problem for a class of discrete-time nonlinear stochastic systems subject to unreliable communication due to the security vulnerability of sensor networks. The unreliable communication, caused probably by denial-of-service cyber attacks, is described by the well-known Gilbert-Elliott model. The addressed nonlinearities are applicable for some of the most investigated stochastic nonlinear models, including the well-known state-dependent multiplicative noises as special cases. The aim of this paper is to design a novel distributed filter that uses the information not only from the individual node itself but also from its neighboring nodes according to the given topology. In order to improve the security of designed filter, a <formula><tex>$\chi^2$</tex></formula> detector is utilized to detect abnormal innovations. By means of the failure and recovery rates of the Gilbert-Elliott channels, sufficient conditions are established to ensure the existence of an upper bound on the estimation error covariance, and then the desired filter parameters are designed by minimizing the trace of such an upper bound. The asymptotic boundedness of the estimation error covariance is subsequently investigated. Finally, a simulation example on the target tracking problem is employed to verify the effectiveness and the security of the proposed filtering scheme.