Distributed fusion filter for discrete-time stochastic systems with uncertain observation and correlated noises

This paper is concerned with the distributed fusion filtering problem for the linear discrete time-varying stochastic systems with uncertain observations and correlated noises at the same time and the adjacent time. Based on the projection theory, an optimal linear filter is developed in the linear minimum variance sense for systems measured by single sensor. Further, a distributed optimal weighted fusion filter is given based on the linear minimum variance fusion estimation algorithm for systems with multiple sensors. The computational formula for the filtering error cross-covariance matrix between any two subsystems is derived. A numerical example shows the effectiveness of the proposed filters.