Nonparametric instrumental variables for identification of block-oriented systems

Mzyk, G.

International Journal of Applied Mathematics and Computer Science, Tome 23 (2013) no. 3, pp. 521-537.

Résumé

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.

Détail

Keywords: system identification, instrumental variables, NARMAX system, Hammerstein system, Wiener system, Lur'e system, nonparametric method
Mots-clés : identyfikacja systemu, zmienna instrumentalna, system Hammersteina, system Wienera, metoda nieparametryczna

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