<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Nonparametric instrumental variables for identification of block-oriented systems

Institute of Computer Engineering, Control and Robotics Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

International Journal of Applied Mathematics and Computer Science

A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are...

Nonparametric instrumental variables for identification of block-oriented systems

Published Online: Sep 30, 2013

Page range: 521 - 537

DOI: https://doi.org/10.2478/amcs-2013-0040

This content is open access.