Optimal recursive state estimation for singular stochastic discrete-time systems

A simple approach to optimal recursive filtering, prediction and smoothing for singular stochastic discrete-time systems is presented by using a time-domain innovation analysis method. The estimators are calculated based on an ARMA innovation model which can be obtained using spectral factorization. It is shown that the prediction problem for the singular systems can be easily solved with the aid of an output predictor. Further, a simple solution is presented for the complex smoothing problem. The asymptotic stability of the estimators is established. The major difference between the state estimation of singular and non-singular systems is clarified.