Multisensor Information Fusion Kalman Smoother for Time-Varying Systems

Based on the optimal information fusion rules weighted by matrices, diagonal matrices and scalars in the linear minimum variance sense, three distributed optimal fusion Kalman smoothers are presented for the linear discrete time-varying stochastic control systems with multisensor and colored measurement noises. Compared with the centralized fuser, they are locally optimal, but are globally suboptimal. The accuracy of the fuser with matrix weights is higher than that of the fuser with scalar weights, and the accuracy of the fuser with diagonal matrix weights is between both of them. The accuracy of all the three fusers is higher than that of each local Kalman smoother. Further, the corresponding three steady-state fusion Kalman smoothers are also given for the linear discrete time-invariant stochastic control systems, which can reduce the on-line computational burden. In order to compute optimal weights, the formula of computing the cross-covariances among local smoothing errors is presented. A Monte Carlo simulation example for the tracking systems shows the performance of the proposed fusers.