Globally Optimal Distributed Fusion Filter for Descriptor Systems with Time-Correlated Measurement Noises

This paper concerns the distributed fusion filtering problem for descriptor systems with time-correlated measurement noises. The original descriptor is transformed into two reduced-order subsystems (ROSs) based on singular value decomposition. For the first ROS, a new measurement is obtained using measurement difference technology. Each sensor produces a local filter based on the fusion predictor from the fusion center and its own new measurement and then sends it to the fusion center. In the fusion center, based on local filters, a distributed fusion filter with feedback (DFFWF) in the linear minimum variance (LMV) sense is proposed by applying an innovative approach. The DFFWF for the second ROS is also obtained based on the DFFWF for the first ROS. Then, the DFFWF for the original descriptor is obtained. The proposed DFFWF can achieve the same estimation accuracy as the centralized fusion filter (CFF) under the condition that all local filter gain matrices are of full column rank. Its optimality is strictly proved. Moreover, it has robustness and reliability due to the parallel processing of local filters. Two simulation examples demonstrate the effectiveness of the developed fusion algorithm.