A Lyapunov-based distributed consensus filter for a class of nonlinear stochastic systems

This paper considers the distributed state estimation problem for nonlinear stochastic systems over sensor networks. It is assumed that the nonlinear functions are bounded in the pseudo Lipschitz condition. Based on the stochastic Lyapunov stability theory, a distributed consensus filter (DCF) is proposed for both continuous and discrete nonlinear stochastic systems for each node in a sensor network. It will be shown that the estimation errors of the proposed filters are exponentially ultimately bounded in the sense of mean square in terms of linear matrix inequality (LMI). Furthermore, a criterion is presented to optimize the filter gains based on minimizing the upper bound of mean-square error. Numerical examples are used to verify the theoretical results.