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Refined instrumental variable estimation: maximum likelihood optimization of a unified Box-Jenkins model. (English) Zbl 1309.93178

Summary: For many years, various methods for the identification and estimation of parameters in linear, discrete-time transfer functions have been available and implemented in widely available Toolboxes for Matlab. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box-Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box-Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms.

MSC:

93E12 Identification in stochastic control theory
93E10 Estimation and detection in stochastic control theory
93C05 Linear systems in control theory
93B40 Computational methods in systems theory (MSC2010)

Software:

CAPTAIN; Matlab
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Full Text: DOI

References:

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