Covariance Intersection Fusion Kalman Filter for Two-Sensor ARMA Signal with Colored Measurement Noises

For two-sensor multi-channel autoregressive moving average(ARMA) signal with colored measurement noises, when the variance and cross-covariance of the local estimation errors are exactly known, based on classical Kalman filtering theory, a covariance intersection (CI) fusion filter without cross-covariance is presented by the augmented state space model. It has the advantage that the computation of cross-covariance is avoid, so it can significantly reduce the computational burden. Under the unbiased linear minimum variance (ULMV) criterion, the three optimal weighted fusion ARMA signal filters with matrix weights, scalar weights and diagonal weights are also presented. The accuracy comparison of the CI fuser with the other three weighted fusers is given. It is proved that its accuracy is higher than that of each local filter, and is lower than that of the optimal fuser weighted by matrix. The geometric interpretation of the accuracy relations is given by the covariance ellipses. A Monte-Carlo simulation results show the correctness of the proposed theoretical accuracy relations.