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Generalized kernel regression estimatefor the identification of Hammerstein systems

Grzegorz Mzyk — 2007

International Journal of Applied Mathematics and Computer Science

A modified version of the classical kernel nonparametric identification algorithm for nonlinearity recovering in a Hammerstein system under the existence of random noise is proposed. The assumptions imposed on the unknown characteristic are weak. The generalized kernel method proposed in the paper provides more accurate results in comparison with the classical kernel nonparametric estimate, regardless of the number of measurements. The convergence in probability of the proposed estimate to the unknown...

Nonparametric instrumental variables for identification of block-oriented systems

Grzegorz Mzyk — 2013

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 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...

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