A stochastic singular system with correlated noises at the same time is transferred to the equivalent nonsingular system with correlated noises at the same and neighboring time. Applying time-domain innovation analysis method, the recursive full-order predictor, filter and smoother are presented for this nonsingular system. Further, the full-order filter and smoother are given for original stochastic singular linear systems with correlated noises. Recursive and nonrecursive computational formula
