Kernel Adaptive Hammerstein Filter

Zheng, Yunfei; Dong, Jiyao; Ma, Wentao; Chen, Badong

doi:10.23919/eusipco.2018.8553381

Cited by 4 publications

(2 citation statements)

References 30 publications

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“…Section 4 will theoretically prove this proposed nonlinear subsystem estimator as statistically consistent and asymptotically unbiased. Section 5 will present Monte Carlo simulations to verify the efficacy of the nonparametric estimation algorithm proposed in Section 3, to affirm the validity of the new theoretical performance analysis in Section 4, and to demonstrate the proposed estimator's better finite-sample accuracy over the open literature's only other nonparametric estimator that has appeared multiple times in [12,15,17,25,28,29,36,38,49,53] of the Hammerstein nonlinear static subsystem. (That only other nonparametric estimator is developed assuming a temporally white stochastic input.)…”

Section: Organization Of This Studymentioning

confidence: 90%

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: Organization Of This Studymentioning

confidence: 90%

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 is unlike [39][40][41][42][43][44][45][46][47][48][49][50][51][54][55][56][57][58][59][60][61][62][63][64][65][66][67], which require causality.…”

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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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Identification of Hammerstein Systems with Random Fourier Features and Kernel Risk Sensitive Loss

Zheng

Wang

Chen

2023

Neural Process Lett

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Kernel Adaptive Hammerstein Filter

Cited by 4 publications

References 30 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

Identification of Hammerstein Systems with Random Fourier Features and Kernel Risk Sensitive Loss

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