Optimal recursive filtering, prediction, and smoothing for singular stochastic discrete-time systems

A new and 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 or a recursive identifier. The prediction problem for the singular systems is solved with the aid of an output predictor. Further, a simple solution is presented for the complex smoothing problem.