Convergence of an adaptive filter algorithm

1 May 1978

journal article
research article
Published by Taylor & Francis in International Journal of Control

Vol. 27 (5) , 673-693
https://doi.org/10.1080/00207177808922403

Abstract

A state-space representation of a dynamical, stochastic system is given. A corresponding model, parametrized in a particular way, is considered and an algorithm for the estimation of its parameters is analysed. The class of estimation algorithms thus considered contains general output error methods and model reference methods applied to stochastic systems. It also contains adaptive filtering schemes and, e.g. the extended least squares method. It is shown that if a certain transfer function associated with the true system is positive real, then the estimation algorithm converges with probability 1 to a value that gives a correct input-output model.

Keywords

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