The Frisch scheme in algebraic and dynamic identification problems

Roberto P. Guidorzi; Roberto Diversi; Umberto Soverini

Kybernetika (2008)

  • Volume: 44, Issue: 5, page 585-616
  • ISSN: 0023-5954

Abstract

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This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension of the Frisch scheme to the identification of dynamical systems is considered for both SISO and MIMO cases and the problem of its application to real processes is investigated. For this purpose suitable identification criteria and model parametrizations are described. Finally two classical identification problems are mapped into the Frisch scheme, the blind identification of FIR channels and the identification of AR + noise models. This allows some theoretical and practical extensions.

How to cite

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Guidorzi, Roberto P., Diversi, Roberto, and Soverini, Umberto. "The Frisch scheme in algebraic and dynamic identification problems." Kybernetika 44.5 (2008): 585-616. <http://eudml.org/doc/33952>.

@article{Guidorzi2008,
abstract = {This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension of the Frisch scheme to the identification of dynamical systems is considered for both SISO and MIMO cases and the problem of its application to real processes is investigated. For this purpose suitable identification criteria and model parametrizations are described. Finally two classical identification problems are mapped into the Frisch scheme, the blind identification of FIR channels and the identification of AR + noise models. This allows some theoretical and practical extensions.},
author = {Guidorzi, Roberto P., Diversi, Roberto, Soverini, Umberto},
journal = {Kybernetika},
keywords = {system identification; errors-in-variables models; Frisch scheme; linear systems; system identification; errors-in-variables models; Frisch scheme; linear systems},
language = {eng},
number = {5},
pages = {585-616},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The Frisch scheme in algebraic and dynamic identification problems},
url = {http://eudml.org/doc/33952},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Guidorzi, Roberto P.
AU - Diversi, Roberto
AU - Soverini, Umberto
TI - The Frisch scheme in algebraic and dynamic identification problems
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 5
SP - 585
EP - 616
AB - This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension of the Frisch scheme to the identification of dynamical systems is considered for both SISO and MIMO cases and the problem of its application to real processes is investigated. For this purpose suitable identification criteria and model parametrizations are described. Finally two classical identification problems are mapped into the Frisch scheme, the blind identification of FIR channels and the identification of AR + noise models. This allows some theoretical and practical extensions.
LA - eng
KW - system identification; errors-in-variables models; Frisch scheme; linear systems; system identification; errors-in-variables models; Frisch scheme; linear systems
UR - http://eudml.org/doc/33952
ER -

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