Consensus-based recursive distributed filtering with stochastic nonlinearities over sensor networks

In this paper, the distributed filtering problem is addressed for a class of discrete time-varying systems in sensor networks. The stochastic nonlinearities, which are described by first and second-order statistics, enter into both the target plant and the sensor measurements. The goal of the proposed problem is to develop a distributed filter for each sensor node by making use of the topological information of the sensor networks. The consensus process subjected to a given directed graph is proposed to accelerate the information fusion, and then sub-optimal filer gain matrices are obtained by employing the least square method to minimize certain upper bound of the estimation error covariance. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed consensus-based filters.