Covariance Intersection Fusion Kalman Filter for Two-Sensor ARMA Signal with Time-Delayed Measurements and Colored Measurement Noises

Abstract

For the two-sensor multi-channel autoregressive moving average(ARMA) signal with colored measurement noises and time-delayed measurements, a covariance intersection (CI) fusion Kalman filter without cross-covariance is presented based on the classical Kalman filtering and a deconvolution method. Under the unbiased linear minimum variance (ULMV) criterion, three optimal fusion Kalman filters weighted by matrices, diagonal matrices and scalars are also presented respectively. Their accuracy relations are proved. It is shown that the accuracy of CI fuser is higher than that of each local filter and is lower than that of the fused filter weighted by matrices. These fusers can be considered as a new signal observer or a new intelligent sensor, which computed via the information fusion algorithms based on the local Kalman filters obtained form the local sensors. The geometric interpretation of the accuracy relations is given based on covariance ellipses. A Monte-Carlo simulation example verifies the correctness of the proposed theoretical accuracy relations.