By means of a linear transformation of the observation equation, the system with coloured observation noise istransformed into the system with white observation noise. Based on the autoregressive moving average (ARMA) innovation mod-el, the asymptotically stable Wiener state estimators are derived via the steady-state optimal Kalman estimators. They can han-dle the filtering, smoothing and prediction problems in a unified framework. A simulation example shows their effectiveness.