Discrete-time Least-squares Estimation in a Behavioral Framework
Osamu KANEKO, Takao FUJII
This paper addresses discrete-time least-squares estimation in a behavioral framework. Firstly, we formulate the problem we attack here in a behavioral setting. Next, we provide some new results on polynomial matrices, spectral factorizations and dissipation theory. By using these new results, we then give a necessary and sufficient condition for a latent variable to yield the optimal estimation of the measured signal with observations on the theoretical differences between the discrete-and the continuous-time case. Then, we discuss issues on the implementation of the optimal estimator and we give a real-time algorithm so as to obtain the optimal estimation on-line. In order to show the validity of the results, we also give a simple numerical example.