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 the calculation of an optimal estimator gain matrix. The main contribution of the paper is the derivation of a simple method for computing the gain matrix. Our method involves solving one simple polynomial equation which is derived from the uniqueness of the autoregressive moving average (ARMA) innovation model. The approach covers prediction, filtering, and smoothing problems. Further, when the noise statistics of the model are not available, self-tuning estimation is performed by identifying one ARMA innovation model.