Multi-Sensor Distributed Fusion Filter for Discrete Stochastic Multi-Delayed Systems with Correlated Noise

This paper is concerned with the distributed fusion estimation problem for discrete-time linear stochastic multi-delayed systems with multiple sensors and correlated noise. Firstly, a new optimal filter in the least mean square sense is presented for discrete stochastic multi-delayed systems with a single sensor, where the white noise filter is used to obtain the optimal state estimate. Then, a distributed optimal scalar-weighted fusion filter is given for discrete-time linear stochastic multi-delayed systems with multiple sensors. A recursive formula for the estimation error cross-covariance matrix between any two local optimal estimates is derived. Compared with the centralized filter, it has a little accuracy loss but better reliability. At last, a simulation example shows the effectiveness of the proposed algorithms.