Distributed Matrix-Weighted Fusion Consensus Filtering With Two-Stage Filtering for Sensor Networks

This article is concerned with a distributed consensus filtering problem in a sensor network (SN). In the SN, each sensor node plays a local fusion center. By diffusion and fusion of information among sensor nodes, estimates of all nodes in the SN tend to consensus. At each sensor node, a distributed consensus filtering algorithm with a two-stage filtering structure is devised. At each time, the first stage filtering is that each sensor node produces its local filter estimate based on its own measurement and previous fused estimate, and then transmits it to its neighbor nodes; and the second stage filtering is that each sensor node produces a fused estimate by using a matrix-weighted optimal fusion algorithm in the linear unbiased minimum variance (LUMV) criterion to iteratively fuse estimates of sensor itself and neighbor nodes, where cross-covariance matrices (CCMs) between sensor nodes at different fusion times are derived. Its estimation accuracy is gradually improved with the increase of fusion times and approximates a centralized fusion filter (CFF). To avoid calculation of CCMs between sensor nodes, a suboptimal distributed consensus filtering algorithm is also presented by minimizing an upper bound of the fusion filtering error covariance at each fusion in the second stage. It has reduced computational cost at the expense of accuracy loss. The performance of the proposed distributed consensus filters is analyzed. A tracking system is used to verify the effectiveness of the algorithms.