Nonparametric identification of a Wiener system using a stochastic excitation of arbitrarily unknown spectrum

Tsair Chuan Lin, Kainam Thomas Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


A Wiener system consists of two sequential sub-systems: (i) a linear, dynamic, time-invariant, asymptotically stable sub-system, followed by (ii) a nonlinear, static (i.e. memoryless), invertible sub-system. Both sub-systems will be identified non-parametrically in this paper, based on observations at only the overall Wiener systems input and output, without any observation of any internal signal inter-connecting the two sub-systems, and without any prior parametric assumption on either sub-system. This proposed estimation allows the input to be temporally correlated, with a mean/variance/spectrum that are a priori unknown (instead of being white and zero-mean, as in much of the relevant literature). Moreover, the nonlinear sub-systems input and output may be corrupted additively by Gaussian noises of non-zero means and unknown variances. For the above-described set-up, this paper is first in the open literature (to the best of the present authors knowledge) to estimate the linear dynamic sub-system non-parametrically. This presently proposed linear system estimator is analytically proved as asymptotically unbiased and consistent. Moreover, the proposed nonlinear sub-systems estimate is assured of invertibility (unlike earlier methods), asymptotic unbiasedness, and pointwise consistence. Furthermore, both sub-systems estimates finite-sample convergence is also derived analytically. Monte Carlo simulations verify the efficacy of the proposed estimators and the correctness of the derived convergence rates.
Original languageEnglish
Pages (from-to)422-437
Number of pages16
JournalSignal Processing
Publication statusPublished - 1 Mar 2016


  • Estimation
  • Linear systems
  • Nonlinear estimation
  • Nonlinear filters
  • Nonlinear systems
  • Nonlinearities
  • Recursive estimation
  • Regression analysis
  • Stochastic systems
  • System identification
  • Time series analysis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


Dive into the research topics of 'Nonparametric identification of a Wiener system using a stochastic excitation of arbitrarily unknown spectrum'. Together they form a unique fingerprint.

Cite this