Covariance Intersection Fusion Kalman Smoother for Systems with Colored Measurement Noises

Abstract

For the two-sensor system with unknown cross-covariances, and with colored measurement noises, by the classical Kalman filtering method and the covariance intersection (CI) fusion method, a covariance intersection fusion steadystate Kalman smoother is presented, which avoids the computation of cross-covariances. The accuracy relations of the CI Kalman smoother, the local and optimal fused Kalman smoother are proved, i.e., the accuracy of CI fuser is higher than that of each local Kalman smoother, and lower than that of optimal fuser weighted by matrices with known cross-covariance. The formula of the actual smoothing error variance of the CI fuser is given and the geometric interpretation of the above accuracy relations is presented based on the covariance ellipses. A Monte-Carlo simulation results show its effectiveness and correctness.