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Based on the optimal fusion algorithm weighted by matrices in the linear minimum variance (LMV) sense, a distributed optimal information fusion for the steady-state Kalman multi-step predictor is given for discrete linear stochastic control systems with multiple sensors and correlated noises, where the same sample period is assumed. When the noise statistics information is unknown, the distributed information fusion estimators for the noise statistics parameters are presented based on the correlation functions and the weighting average approach. Further, a self-tuning information fusion multi-step predictor is obtained. It has a two-stage fusion structure. The first-stage fusion is to obtain the fused noise statistics information. The second-stage fusion is to obtain the fused multi-step predictor. A simulation example shows the effectiveness.