Distributed Recursive Filtering for Time-Varying System with Multiplicative Noise under Stochastic Protocol

This paper is concerned with the distributed recursive filtering problem for a class of linear discrete-time stochastic systems subject to the effect of time delay, multiplicative noise and stochastic protocol. In order to regulate communication between nodes, each node receives data from only one of its adjacent nodes at each communication moment by a stochastic protocol. The aim of the proposed filtering problem is to construct a Kalman-type filter so that the upper bound of the filtering error covariance is minimized by designing appropriate filter parameters. Moreover, a sufficient condition is proposed by utilizing mathematical induction, which is used to determine the boundedness of error covariance. Finally, the simulation results demonstrate the effectiveness of the proposed filtering scheme.