The optimality of Kalman filtering fusion with cross-correlated sensor noises

A rigorous performance analysis is dedicated to Kalman filtering fusion with sensor noises cross-correlated for distributed recursive state estimators of dynamic systems. When there is no feedback from the fusion center to local sensors, we present a distributed Kalman filtering fusion formula, and prove that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements, therefore, it achieves the best performance. When there is feedback, the corresponding fusion formula with feedback is, as the fusion without feedback, exactly equivalent to the corresponding centralized Kalman filtering fusion formula using all sensor measurements. Moreover, the so called P matrices in the feedback Kalman filtering at both local filters and the fusion center are still the covariance matrices of tracking errors. Although the feedback here cannot improve the performance at the fusion center, the feedback does reduce the covariance of each local tracking error. The above results can be extended to a hybrid track fusion with feedback received by partial local trackers.