Recursive Fusion for Optimal Estimation with Cross-Correlated Noise

Many problems involve optimal estimation fusion, where there are multiple sensors observing a single target simultaneously. When the motion of a target is formulated by a linear dynamic system and the measurement noises are uncorrelated, the Kalman filter is optimal. In applications, however, the measurement noises may be correlated and also coupled with the system noise, which makes optimal estimation difficult. This paper is concerned with optimal estimation fusion for a class of linear dynamic systems when the measurement noises of different sensors are cross-correlated and also coupled with the system noise at the previous time step. By use of the orthogonal theorem, an optimal recursive fusion algorithm is presented, which is shown to be a generalization of the classical sequential Kalman filter when the noises are uncorrelated. The presented algorithm is compared with the optimal batch fusion algorithm, and the impact of the cross-correlation between the noises on the estimation accuracy is analyzed. From the simulation on a target tracking example, it is shown that the presented algorithm is effective.