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Recursive identification of Wiener systems

100%
Greblicki W.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 4
977-991
EN
A Wiener system, i.e. a cascade system consisting of a linear dynamic subsystem and a nonlinear memoryless subsystem is identified. The a priori information is nonparametric, i.e. neither the functional form of the nonlinear characteristic nor the order of the dynamic part are known. Both the input signal and the disturbance are Gaussian white random processes. Recursive algorithms to estimate the nonlinear characteristic are proposed and their convergence is shown. Results of numerical simulation are also given. A known algorithm recovering the impulse response of the dynamic part is presented in a recursive form.
2
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Nonparametric instrumental variables for identification of block-oriented systems

75%
Mzyk G.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 3
521-537
EN
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.
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