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Based on the multi-sensor optimal information fusion criterion weighted by scalars in the linear minimum variance sense, the distributed optimal fusion Kalman multi-step predictor is given for discrete multi-channel ARMA (autoregressive moving average) signals. The precision of the fusion predictor is higher than that of any local predictor. It only requires the computation of scalar weights, the computational burden can be reduced comparing with one weighted by matrices. An example of double-channel signal system with three sensors shows the effectiveness.