Multichannel ARMA signal covariance intersection fusion Wiener filter for the two-sensor system with time-delayed measurements

Abstract

For the two-sensor, multi-channel autoregressive moving average (ARMA) signals with measurement delays, the system with measurement delays is converted into the system without measurement delays by the measurement transformation method. When the filtering error cross-covariances are known, by the Kalman filtering method, based on the white noise Wiener filters and measure- ment Wiener predictors, the optimal fusion Wiener signal filters weighted by matrices, diagonal matrices and scalars are presented. When the filtering error cross-covariances are unknown, by the covariance intersection (CI) fusion method, the CI fusion Wiener signal filter is presented. It is rigorously proven that the actual accuracy of the CI Wiener signal fuser is higher than that of each local Wiener signal filter, and is lower than that of the optimal Wiener signal fuser with the matrix weights. The geometric interpretation of the above accuracy relations are presented based on the covariance ellipses. A Monte-Carlo simulation example shows that the actual accuracy of the CI fuser is close to that of the fuser with the matrix weights, so that it has higher accuracy and good performance.