Distributed optimal fusion prior filter for systems with multiple packet dropouts

This paper is concerned with the optimal prior filtering problem for linear discrete-time stochastic systems with multiple packet dropouts and correlated noises. Firstly, based on a recent packet dropout model, a new unbiased optimal prior filter is developed in the linear minimum variance sense for a single sensor system. The prior filter is reduced to the standard Kalman one-step predictor when there are no packet dropouts. A distributed optimal fusion prior filter is proposed based on the fusion algorithm weighted by scalars for systems with multiple sensors of different packet dropout rates. The computation formula for the prior filtering error cross-covariance matrix between any two subsystems is given. Finally, the steady-state fusion filter is investigated. A numerical example shows the effectiveness of the proposed prior filters.