Recursive distributed filtering for two-dimensional shift-varying systems over sensor networks under stochastic communication protocols

Abstract This paper is concerned with the distributed filtering problem for a class of two-dimensional shift-varying systems over sensor networks subject to stochastic communication protocol (SCP) over a finite horizon. The communication between the sensor nodes and the filters is implemented through shared channels of limited capacity. To avoid data collisions, the SCP is applied to determine the transmission order of the signals/packets for each sensor. The considered scheduling behavior is characterized by mutually uncorrelated random variables with known probability distributions. Recursive distributed filters are proposed to estimate the system state through available information from both individual and neighboring nodes in the sensor network according to a given topology. Attention is focused on the design of distributed filters in order to ensure the locally minimal upper bound on the error variance of the state estimation. Sufficient conditions are first established, via intensive stochastic analysis and mathematical induction, on the existence of an upper bound of the estimation error variance. Then, by means of a matrix simplification technique, the desired filter gains are designed to optimize the obtained upper bound at each shift step. Finally, a practical example is given to verify the effectiveness of the proposed filter strategy.