The accuracy comparison of multisensor covariance intersection fuser and three weighting fusers

For multisensor systems with exactly known local filtering error variances and cross-covariances, a covariance intersection (CI) fusion steady-state Kalman filter without cross-covariances is presented. It is rigorously proved that it has consistency, and its accuracy is higher than that of each local Kalman filter and is lower than that of the optimal Kalman fuser with matrix weights. Under the unbiased linear minimum variance (ULMV) criterion, it is proved that the accuracy of the fuser with matrix weights is higher than that of the fuser with scalar weights, and the accuracy of the fuser with diagonal matrix weights is in between both of them, and the accuracies of all three weighting fusers and the CI fuser are lower than that of centralized Kalman fuser, and are higher than that of each local Kalman filter. The geometric interpretations of the above accuracy relations are given based on the covariance ellipsoids. A Monte-Carlo simulation example for tracking system verifies correctiveness of the proposed theoretical accuracy relations, and shows that the actual accuracy of the CI Kalman fuser is close to that of the optimal Kalman fuser, so that it has higher accuracy and good performance. When the actual local filtering error variances and cross-covariances are unknown, if the local filtering estimates are consistent, then the corresponding robust CI fuser is also consistent, and its robust accuracy is higher than that of each local filter.