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Volume 3, Issue 4
Recursive Identification of Wiener-Hammerstein Systems with Nonparametric Nonlinearity

Xiao-Li Hu & Yue-Ping Jiang

East Asian J. Appl. Math., 3 (2013), pp. 311-332.

Published online: 2018-02

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  • Abstract

A recursive scheme is proposed for identifying a single input single output (SISO) Wiener-Hammerstein system, which consists of two linear dynamic subsystems and a sandwiched nonparametric static nonlinearity. The first linear block is assumed to be a finite impulse response (FIR) filter and the second an infinite impulse response (IIR) filter. By letting the input be a sequence of mutually independent Gaussian random variables, the recursive estimates for coefficients of the two linear blocks and the value of the static nonlinear function at any fixed given point are proven to converge to the true values, with probability one as the data size tends to infinity. The static nonlinearity is identified in a nonparametric way and no structural information is directly used. A numerical example is presented that illustrates the theoretical results.

  • Keywords

Wiener-Hammerstein system, nonparametric nonlinearity, recursive estimate, strong consistence.

  • AMS Subject Headings

60G35, 62F12, 93E12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-311, author = {}, title = {Recursive Identification of Wiener-Hammerstein Systems with Nonparametric Nonlinearity}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {4}, pages = {311--332}, abstract = {

A recursive scheme is proposed for identifying a single input single output (SISO) Wiener-Hammerstein system, which consists of two linear dynamic subsystems and a sandwiched nonparametric static nonlinearity. The first linear block is assumed to be a finite impulse response (FIR) filter and the second an infinite impulse response (IIR) filter. By letting the input be a sequence of mutually independent Gaussian random variables, the recursive estimates for coefficients of the two linear blocks and the value of the static nonlinear function at any fixed given point are proven to converge to the true values, with probability one as the data size tends to infinity. The static nonlinearity is identified in a nonparametric way and no structural information is directly used. A numerical example is presented that illustrates the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290913.111113a}, url = {http://global-sci.org/intro/article_detail/eajam/10860.html} }
TY - JOUR T1 - Recursive Identification of Wiener-Hammerstein Systems with Nonparametric Nonlinearity JO - East Asian Journal on Applied Mathematics VL - 4 SP - 311 EP - 332 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.290913.111113a UR - https://global-sci.org/intro/article_detail/eajam/10860.html KW - Wiener-Hammerstein system, nonparametric nonlinearity, recursive estimate, strong consistence. AB -

A recursive scheme is proposed for identifying a single input single output (SISO) Wiener-Hammerstein system, which consists of two linear dynamic subsystems and a sandwiched nonparametric static nonlinearity. The first linear block is assumed to be a finite impulse response (FIR) filter and the second an infinite impulse response (IIR) filter. By letting the input be a sequence of mutually independent Gaussian random variables, the recursive estimates for coefficients of the two linear blocks and the value of the static nonlinear function at any fixed given point are proven to converge to the true values, with probability one as the data size tends to infinity. The static nonlinearity is identified in a nonparametric way and no structural information is directly used. A numerical example is presented that illustrates the theoretical results.

Xiao-Li Hu & Yue-Ping Jiang. (1970). Recursive Identification of Wiener-Hammerstein Systems with Nonparametric Nonlinearity. East Asian Journal on Applied Mathematics. 3 (4). 311-332. doi:10.4208/eajam.290913.111113a
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