Abstract: Using the modern time series analysis method, based on ARMA innovation model and white noise estimators, and by recursive version of non-recursive state estimators, the ARMA steady state optimal recursive state estimators are presented for descriptor systems which have a Wiener filter form. They can handle the descriptor systems with singular state transition matrices and/or with correlated noises, can handle the filtering, smoothing and prediction problems in a unified form ,and can handle the state estimation problems of descriptor and non-descriptor systems in a unified framework. A simulation example shows their effectiveness.