  This paper studies the distributed state estimation problem for a class of
discrete-time stochastic systems with nonlinear uncertain dynamics over
time-varying topologies of sensor networks. An extended state vector consisting
of the original state and the nonlinear dynamics is constructed. By analyzing
the extended system, we provide a design method for the filtering gain and
fusion matrices, leading to the extended state distributed Kalman filter. It is
shown that the proposed filter can provide the upper bound of estimation
covariance in real time, which means the estimation accuracy can be evaluated
online.It is proven that the estimation covariance of the filter is bounded
under rather mild assumptions, i.e., collective observability of the system and
jointly strong connectedness of network topologies. Numerical simulation shows
the effectiveness of the proposed filter.
