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Optimal and self-tuning state estimation for singular stochastic systems: a polynomial equation approach

This paper is concerned with the optimal steady-state estimation for singular stochastic discrete-time systems using a polynomial equation approach. The key to the optimal estimation is to calculate an optimal estimator gain matrix. The main contribution of the paper is to present a simple method for computing the gain matrix. Our method involves solving one simple polynomial equation which is derived based on the uniqueness of the ARMA innovation model. The approach covers the prediction, filtering and smoothing problems. Further, when the noise statistics of model are not available, self-tuning estimation is performed by identifying one ARMA innovation model.