Distributed Weighting Fusion and Covariance Intersection Fusion Kalman Smoother for Systems with Colored Measurement Noises

Abstract

For two-sensor system with colored measurement noises, based on the classical Kalman filtering method, distributed weighting fusion method and the covariance intersection (CI) fusion method, a CI fusion steady-state Kalman smoother is presented, which is independent of the unknown cross-covariance. It is difficult or complex to compute the cross- covariance in most cases. The accuracy comparison of the CI fusion Kalman smoother with three classical distributed weighting fusion Kalman smoothers which are weighted respectively by matrices, diagonal matrices, and scalars is proven, i.e., its accuracy 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. The Monte-Carlo simulation results show its effectiveness and correctness.