The steady-state optimal state estimation problem for discrete-time stochastic singular linear systems is considered via the innovation analysis method in the time domain. The filter, predictor and smoother are derived by using the projection formula and are calculated based on the ARMA innovation model. The three cases of filter, predictor and smoother are shown to have a unified form. Also, the optimal white noise estimation method, including both input and measurement noises, is presented. Asymptotic stability of the estimators is proved. The results of this paper can be applied to normal systems as a special case.