Nonparametric identification of Wiener systems

Greblicki, Wlodzimierz

doi:10.1109/18.149500

Cited by 178 publications

(90 citation statements)

References 26 publications

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“…Many authors have studied Wiener system identification under the assumption that the non-linearity is unknown but one-to-one (Brillinger 1970, Pajunen 1985, Hasiewicz 1987, Greblicki 1992, 1997, Westwick and Kearney 1992, Wigren 1994, Westwick and Verhaegen 1996, Bai 1998, Lovera et al 2000. Other methods for Wiener system identification require the non-linearity to be known, invertible, monotonic, odd, even, or require the use of specially designed input sequences.…”

Section: Resultsmentioning

confidence: 99%

“…Many methods for Wiener system identification require the non-linearity to be known, invertible, differentiable, odd or require specially designed input sequences. In particular, the Wiener identification problem has been considered in Brillinger (1970), Pajunen (1985), Hasiewicz (1987), Greblicki (1992Greblicki ( , 1994Greblicki ( , 1997Greblicki ( , 1998, Westwick and Kearney (1992), Wigren (1994), Westwick and Verhaegen (1996), Bai (1998), and Lovera et al (2000) under the assumption that the non-linearity is unknown but one-to-one. This assumption simplifies the problem considerably since the inverse system can be viewed as a Hammerstein system wherein the input to the nonlinearity is measured.…”

Section: Introductionmentioning

confidence: 99%

“…Numerous approaches have been developed for this problem, including black box and grey box techniques (Bayard and Eslami 1984, Pajunen 1985, Hunter and Korenberg 1986, Korenberg and Hunter 1986, Hasiewicz 1987, Chen and Fassois 1992, 1997, Greblicki 1992, 1997, Westwick and Kearney 1992, Wigren 1994, Westwick and Verhaegen 1996, Bai 1998, Lovera et al 2000, Van Pelt and Bernstein 2000, Nelles 2001. The grey box case includes the identification of block-structured models, such as the Hammerstein model (linear system with input non-linearity) and Weiner model (linear system with output non-linearity) (Haber and Keviczky 1999 a, b).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities

Lacy

Bernstein

2003

International Journal of Control

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Wiener systems consist of a linear dynamic system whose output is measured through a static non-linearity. In this paper we study the identification of single-input single-output Wiener systems with finite impulse response dynamics and polynomial output non-linearities. Using multi-index notation, we solve a least squares problem to estimate products of the coefficients of the non-linearity and the impulse response of the linear system. We then consider four methods for extracting the coefficients of the non-linearity and impulse response: direct algebraic solution, singular value decomposition, multi-dimensional singular value decomposition and prediction error optimization.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities

Lacy

Bernstein

2003

International Journal of Control

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“…Stegemann et al, 2012Stegemann et al, , 2011 invertible nonlinearity (cf. Greblicki, 1992) (Pintelon and Schoukens, 2001). In comparison with the classical distortion theory described in (Weiner and Spina, 1980) or (Wambacq and Sansen, 1998), the model can be used for EMI induced distortion analysis at nonsignal inputs, e.g.…”

Section: Introductionmentioning

confidence: 99%

An identification procedure of multi-input Wiener models for the distortion analysis of nonlinear circuits

Weng

Stegemann

John³

et al. 2013

Adv. Radio Sci.

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Abstract. In this contribution, a system identification procedure of a two-input Wiener model suitable for the analysis of the disturbance behavior of integrated nonlinear circuits is presented. The identified block model is comprised of two linear dynamic and one static nonlinear block, which are determined using an parameterized approach. In order to characterize the linear blocks, an correlation analysis using a white noise input in combination with a model reduction scheme is adopted. After having characterized the linear blocks, from the output spectrum under single tone excitation at each input a linear set of equations will be set up, whose solution gives the coefficients of the nonlinear block. By this data based black box approach, the distortion behavior of a nonlinear circuit under the influence of an interfering signal at an arbitrary input port can be determined. Such an interfering signal can be, for example, an electromagnetic interference signal which conductively couples into the port of consideration.

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“…Fundamental to the identification and control of the Wiener system is the characterization/representation of the unknown nonlinear static function. Various approaches have been researched including the nonparametric method [7], subspace model identification methods [8], [6], fuzzy modelling [9] and the parametric method [10], [3], [4], [2]. For the parametric method, the unknown nonlinear function is restricted by some parametric representation with a finite number of parameters, and the system identification includes the estimation of the unknown parameters using nonlinear optimization algorithms based on input/output observational data Based on the approximation theory, the polynomial functions are appropriate in approximating the unknown nonlinear static functions.…”

Section: Introductionmentioning

confidence: 99%

Wiener system identification using B-spline functions with De Boor recursion

Hong

Mitchell

Chen

2011

Sensor Signal Processing for Defence (SSPD 2011)

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Abstract-A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

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Nonparametric identification of Wiener systems

Cited by 178 publications

References 26 publications

Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities

Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities

An identification procedure of multi-input Wiener models for the distortion analysis of nonlinear circuits

Wiener system identification using B-spline functions with De Boor recursion

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