For the linear discrete time-varying stochastic systems with multisensor and with correlated noises, based on three optimal information fusion rules weighted by matrices, diagonal matrices, and scalars, respectively, the corresponding distributed optimal information fusion Kalman estimators is presented, which can handle the fused filtering, prediction, and smoothing problems in a unified framework. In order to compute the optimal weights, the formulas of computing the local estimation error covariances are presented. As a special case, the steady-state optimal information fusion Kalman estimators are presented for the time-invariant systems, where the local estimation error covariances are computed by solving the Lyapunov equations. Compared with the centralized Kalman estimators, they can reduce the computational burden. Compared with the single-sensor Kalman estimators, their accuracy is improved. They constitute a unified and general distributed Fusion Kalman filtering theory based on covariance information.