Abstract: Using the modern time series analysis method, a unifying framework of steady-state Kalman filtering, smoothing and prediction for singular discrete linear stochastic systems, is presented. A new algorithm of steady-state Kalman estimator gain is given, where the solution of the Riccati equation is avoided. In order to ensure the asymptotic stability of the estimator, a formula of setting the initial estimate is given. A simulation example shows the effectiveness of the proposed results.