Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
Discrete-time Least-squares Estimation in a Behavioral Framework
Osamu KANEKOTakao FUJII
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2007 Volume 20 Issue 6 Pages 227-237

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Abstract

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.

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