Abstract: Based on the innovation analysis approach, a non-augmented optimal filter with a white noise estimator is presented for a multiple time-delay system with colored measurement noise. It is equivalent to the first-step predictor for a multiple time-delay system with correlated white noise. When the system contains multiple sensors, the estimation error cross-covariance matrix between any two sensor subsystems is derived for the multiple time-delay system. A distributed weighted fusion optimal filter is given based on the optimal weighted fusion estimation algorithm in the linear minimum variance sense. The distributed fusion filter has a higher accuracy than the local filter based on each sensor. It has better reliability than the centralized optimal filter by augmentation, and avoids the high-dimensional computation and the large space memory. An example shows its effectiveness.