Abstract: Using the modern time-series analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, and in terms of the pole assignment principle in control theory, the pole-assignment descriptor steady-state Kalman estimators are presented for linear discrete-time descriptor stochastic systems. They have globally asymptotic stability, and can forget the effect of the initial state estimates at an exponentially decaying rate by assigning the poles of the estimators. They can handle the filtering, smoothing and prediction problems in a unified framework. They avoid the Riccati equation and the computation of the optimal initial state estimates so that reduce the computational burden. A simulation example shows their effectiveness.