Information fusion Kalman filters with time-delayed measurements

For the linear discrete time-invariant stochastic control systems with time-delayed measurements, they can be transformed into the systems without time-delayed measurements by introducing new measurement processes. Three distributed optimal information fusion Kalman filters weighted by matrices, diagonal matrices and scalars are presented in the linear minimum variance sense. They overcome the drawback that the augmented state method requires a large computational burden. They are locally optimal and are globally suboptimal. The accuracy of the fusers is higher than that of each local Kalman estimator. In order to compute the optimal weights, the formula of computing the cross-covariances among local smoothing errors is given. A Monte Carlo simulation example for the tracking system with time-delayed measurements and 3 sensors shows their effectiveness.