Reduced-order Wiener state estimators for descriptor system with multi-observation lags and MA colored observation noise

Using the projection theory and modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, the reduced-order Wiener state estimators for descriptor system with MA colored observation noise and multi-observation lags are presented. They can handle the prediction, filtering and smoothing in a unified framework. They avoid the solutions of the Riccati equations and Diophantine equations. The estimators have the ARMA recursive form and have asymptotic stability. A simulation example shows their effectiveness.