Identification of the Wiener System Based on Instrumental Variables

  • Shaoxue JingEmail author
  • Tianhong Pan
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 582)


The Wiener system consists of a linear model followed in series with a nonlinear static element. The parameter estimation of a Wiener system, whose linear part is a finite impulse response function and nonlinear inverse function a polynomial, is considered in this paper. The system is polluted by a process noise. Traditional algorithms cost heavy computation because of the parameter product term and give a biased estimate owing to the correlation between the information vector and the noise. To solve these problems, a two-stage input prediction error algorithm is proposed. In the first stage, a least squares estimate is obtained by minimizing the input prediction error. However, this estimate is biased. To get an unbiased estimate, the estimated output of the linear part is taken as an instrumental variable. And an instrumental variable estimate is obtained unbiasedly. A numerical simulation verified the proposed algorithm.


Parameter estimation Wiener system Process noise Input prediction error Instrumental variable 



This work is supported by National Nature Science Foundation under Grant 61873113, Industry-University Cooperation Project of Jiangsu Province (BY2018231), and Natural Science Research Project of Jiangsu higher school, China (19KJD510001).


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Physics and Electronic Electrical EngineeringHuaiyin Normal UniversityHuaianChina
  2. 2.School of Electrical Engineering and AutomationAnhui UniversityHefeiChina

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