Distributed Fusion Filter for Multi-rate Sampling Stochastic Singular Systems with Multiplicative Noises

The distributed fusion filtering problem is studied for multi-rate sampling stochastic singular linear systems with multiple sensors and stochastic multiplicative noises. The system is described at the highest sampling rate and different sensors may have different lower sampling rates. The white noise in measurement matrix is introduced to describe the stochastic disturbance. Firstly, based on decomposition in canonical form, the original singular system is transformed into fast and slow two subsystems. For the two reduced-order subsystems, the local filters (LFs) are given based on the “dummy” random variables. The cross-covariance matrices between any two local filtering errors are derived. Further, the distributed fusion filter weighted by matrices (FFWM) is obtained for the original singular system based on the well-known fusion algorithm in the linear minimum variance sense. Simulation example verifies the correctness and feasibility of the proposed algorithm.