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This paper studies the distributed state estimation problem for a class ofdiscrete-time stochastic systems with nonlinear uncertain dynamics overtime-varying topologies of sensor networks. An extended state vector consistingof the original state and the nonlinear dynamics is constructed. By analyzingthe extended system, we provide a design method for the filtering gain andfusion matrices, leading to the extended state distributed Kalman filter. It isshown that the proposed filter can provide the upper bound of estimationcovariance in real time, which means the estimation accuracy can be evaluatedonline.It is proven that the estimation covariance of the filter is boundedunder rather mild assumptions, i.e., collective observability of the system andjointly strong connectedness of network topologies. Numerical simulation showsthe effectiveness of the proposed filter.

Distributed Kalman Filter for A Class of Nonlinear Uncertain Systems: An Extended State Method