On identification of block orientated systems by non-parametric techniques

Krzyżak, Adam; Partyka, Marian A.

doi:10.1080/00207729308949543

Cited by 11 publications

(13 citation statements)

References 26 publications

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“…This convergent rate of the proposed linear subsystem estimate subject to any arbitrarily coloured input is not inferior to but same as that in [44,45,47,49,50,56] with simply a white input. 27 With regard to the above proof for a coloured input, that proof non-trivially generalizes the spectrally white case, for which the inequality's right side would simply be…”

Section: Asymptotic Analysis Of the Estimator Proposed In Section 3 For The Linear Subsystemsupporting

confidence: 69%

“…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.…”

Section: Contribution Of This Workmentioning

confidence: 99%

“…This is unlike [39][40][41][42][43][44][45][46][47][48][49][50][51], which are restricted to spectrally white inputs.…”

Section: Contribution Of This Workmentioning

confidence: 99%

“… To the aforementioned non‐linear subsystem's unobserved output { W n }, a temporally wide‐sense stationary noise { Z n } may possibly be added. This { Z n } may be Gaussian or non‐Gaussian, with a possibly unknown and possibly non‐zero mean of μ z (unlike the μ z = 0 assumption in [45, 72]), a possibly unknown autocovariance function and statistical independence from the system's input { U n }. This { Z n } produces the corrupted output V n ≔ W n + Z n , which becomes input to the linear subsystem. The linear dynamic subsystem's impulse response

({}, h_{i}, i = - Q, - Q + 1, …, - Q + I - 1)

may have a finite or an infinite number ( I ) of taps, with I known prior 19 .…”

Section: Mathematical Model Of the Subsystems And Their Associated Time Seriesmentioning

confidence: 99%

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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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Section: Asymptotic Analysis Of the Estimator Proposed In Section 3 For The Linear Subsystemsupporting

confidence: 69%

“…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.…”

Section: Contribution Of This Workmentioning

confidence: 99%

“…This is unlike [39][40][41][42][43][44][45][46][47][48][49][50][51], which are restricted to spectrally white inputs.…”

Section: Contribution Of This Workmentioning

confidence: 99%

({}, h_{i}, i = - Q, - Q + 1, …, - Q + I - 1)

may have a finite or an infinite number ( I ) of taps, with I known prior 19 .…”

Section: Mathematical Model Of the Subsystems And Their Associated Time Seriesmentioning

confidence: 99%

See 2 more Smart Citations

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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show abstract

“…It is known that the estimate is consistent, i.e., that μ(u) → μ(u) as n → ∞ in probability (7) at every point u at which both m and f are continuous and, moreover, f (u) > 0, see Greblicki and Pawlak [1986], Greblicki and Pawlak [1987], and also Greblicki and Pawlak [1989], Greblicki and Pawlak [1994], Krzyżak [1990], Krzyżak and Partyka [1993]. Moreover, if both m and f are differentiable at a point u and…”

Section: Nonparametric Kernel Algorithmmentioning

confidence: 96%