Nonparametric instrumental variables for identification of block-oriented systems

Grzegorz Mzyk

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 3, page 521-537
  • ISSN: 1641-876X

Abstract

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A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.

How to cite

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Grzegorz Mzyk. "Nonparametric instrumental variables for identification of block-oriented systems." International Journal of Applied Mathematics and Computer Science 23.3 (2013): 521-537. <http://eudml.org/doc/262481>.

@article{GrzegorzMzyk2013,
abstract = {A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.},
author = {Grzegorz Mzyk},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {system identification; instrumental variables; NARMAX system; Hammerstein system; Wiener system; Lur'e system; nonparametric methods},
language = {eng},
number = {3},
pages = {521-537},
title = {Nonparametric instrumental variables for identification of block-oriented systems},
url = {http://eudml.org/doc/262481},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Grzegorz Mzyk
TI - Nonparametric instrumental variables for identification of block-oriented systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 3
SP - 521
EP - 537
AB - A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.
LA - eng
KW - system identification; instrumental variables; NARMAX system; Hammerstein system; Wiener system; Lur'e system; nonparametric methods
UR - http://eudml.org/doc/262481
ER -

References

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