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

Lin, Tsair-Chuan; Wong, Kainam Thomas

doi:10.1016/j.sigpro.2015.09.024

Cited by 6 publications

(12 citation statements)

References 22 publications

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“…zffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl }|ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl ffl fflffl { Incidentally, the assumption in Equation (2.3) has also been made in [30,46]. 5 Incidentally, this finite impulse-response assumption has also been made of the linear subsystem in [29,39].…”

Section: A New Nonparametric Estimator Of the Nonlinear Static Subsystemmentioning

confidence: 99%

“…some linear combination of preset basis functions [6, 13, 35, 43–45, 50].…”

Section: Introductionmentioning

confidence: 99%

“… often a polynomial of a prior known order [3, 4, 7, 24, 26, 27, 32, 34, 47], or a piecewise linear function [33] or some spline interpolation [51]. some linear combination of preset basis functions [6, 13, 35, 43–45, 50]. …”

Section: Introductionmentioning

confidence: 99%

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Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation – nonparametric estimator of the static nonlinear subsystem

Lin

Wong

2021

IET Signal Processing

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This study proposes the first estimator in the open literature (to the present authors' best knowledge) to nonparametrically estimate a Hammerstein system's nonlinear static subsystem when excited by an input that is temporally self-correlated with an unknown spectrum, an unknown variance and an unknown mean (instead of the input as commonly presumed to be white and zero-mean). This proposed nonparametric estimator is analytically proved here to be asymptotically unbiased and pointwise consistent. The proposed estimate's associated finite-sample convergence rate is also derived analytically. | INTRODUCTIONA Hammerstein system comprises two subsystems in series: (i) a nonlinear, static (memoryless) subsystem, trailed by (ii) a linear, dynamic, time-invariant, asymptotically stable subsystem. Please see Figure 1 for a schematic showing these two subsystems and their associated signals, which are described in great details in Section 1.This study proposes a new estimate for the nonlinear static subsystem's input-output nonlinearity m(⋅). This estimator relies on observations of only the input and the output of the overall Hammerstein system (i.e. {(U n , Y n ), ∀n}), but not on any observation of any intrasystem signal/noise (e.g. {W n , Z n , V n , X n , P n , ∀n}).This proposed estimator also does not require any prior/simultaneous identification of the nonlinear static subsystem.This is an open access article under the terms of the Creative Commons Attribution-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited and no modifications or adaptations are made.

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Section: A New Nonparametric Estimator Of the Nonlinear Static Subsystemmentioning

confidence: 99%

“…some linear combination of preset basis functions [6, 13, 35, 43–45, 50].…”

Section: Introductionmentioning

confidence: 99%

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Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation – nonparametric estimator of the static nonlinear subsystem

Lin

Wong

2021

IET Signal Processing

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“…Incidentally, for a block-based system's identification using a spectrally coloured input as system excitation-that has been achieved also for a Wiener system in [52,53], but those methods are inapplicable to the present Hammerstein system. The Wiener system and the Hammerstein system, of course, differ by how they sequentially link the non-linear subsystem and the linear subsystem-a Wiener system has linear then non-linear, whereas a Hammerstein system has non-linear then linear.…”

Section: Contribution Of This Workmentioning

confidence: 99%

“…The non‐linearity is set as

m (u_{n}) = sign (u_{n}) ([], {(false| u_{n} false| + 1)}^{2} - 1)

, where sign (⋅) symbolizes the sign of the scalar inside the parentheses. This dynamic non‐linearity has been used in [52, 53] to model an electronic power amplifier.…”

Section: Monte Carlo Simulations Of the Proposed Estimator Of The Linear Subsystemmentioning

confidence: 99%

Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation: Identification of the dynamic linear subsystem

Lin¹,

Wong

2021

IET Signal Processing

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For a Hammerstein system subject to a stochastic input that is spectrally coloured, this study is first in the open literature (to the present authors' best knowledge) to estimate its linear dynamic subsystem. This estimation is achieved without any prior knowledge nor any prior/simultaneous estimation of the preceding non-linear static subsystem. This proposed estimator can handle any temporally self-correlated input despite its potentially unknown spectrum, unknown variance and unknown meanunlike the common assumption that the input is white and zero-mean. This proposed estimator needs observations only of the Hammerstein system's overall input and consequential output, but not any observation of any intrasubsystem signal. Furthermore, this proposed estimator can handle a linear subsystem whose input and/or output are each corrupted additively by stationary (and possibly coloured) noises of unknown probability distributions, of unknown non-zero means and of unknown autocovariances. The proposed estimate is analytically proved herein as asymptotically unbiased and as pointwise consistent; and the estimate's finite-sample convergence rate is also derived analytically.This study proposes a new estimator for the Hammerstein linear dynamic subsystem's (possibly Q-tap-non-causal) impulse response {h i , i = −Q, −Q + 1, … }. This estimator relies on observations of only the input and the output of the overall Hammerstein system (i.e. {(U n , Y n )}), but not of any intrasystem signal nor of any intrasystem noise (e.g. {P n , V n , W n , X n , Z n }). Furthermore, this is achieved with no prior knowledge and no prior/simultaneous estimation of the leading non-linear static subsystem.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Nonparametric identification of Wiener system with a subclass of wide‐sense cyclostationary excitations

Mzyk,

Maik

2023

Adaptive Control & Signal

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SummaryThe paper identifies a Wiener system, which is excited by a cyclostationary time series. To estimate the first subsystem's linear dynamic impulse response: this proposed algorithm first kernel‐windows the Wiener system's input measurements, then cross‐correlates with the output time series. To identify the second subsystem's static nonlinearity: this proposed algorithm first estimates the unobservable inter‐block internal signal (consistently in the statistical sense), and then kernel‐windows these estimates with the Wiener system output. This estimator provides the unusual capability to identify non‐invertible nonlinearities. This strategy removes any restrictive requirement for a Gaussian random excitation or a sinusoidal deterministic excitation. This paper further proves the estimator's asymptotic consistency and determines the kernel bandwidth for algorithmic convergence. The proposed algorithm's efficacy is verified in the context of two common applications: a servo mechanical system and a telecommunication channel.

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

Cited by 6 publications

References 22 publications

Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation – nonparametric estimator of the static nonlinear subsystem

Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation – nonparametric estimator of the static nonlinear subsystem

Hammerstein system with a stochastic input of arbitrary/unknown autocorrelation: Identification of the dynamic linear subsystem

Nonparametric identification of Wiener system with a subclass of wide‐sense cyclostationary excitations

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