Identification of Wiener State-Space Models utilizing Gaussian Sum Smoothing

Angel L. Cedeño; Rodrigo González; Rodrigo Carvajal; Juan Carlos Aguero

doi:10.1016/j.automatica.2024.111707

Identification of Wiener State-Space Models utilizing Gaussian Sum Smoothing

Angel L. Cedeño (Corresponding author), Rodrigo González, Rodrigo Carvajal, Juan Carlos Aguero

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4 Citations (Scopus)

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Abstract

In this paper, we address the problem of system identification for Wiener state-space models. Our approach is based on the Maximum Likelihood method and the Expectation-Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation-Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state-space systems in which the output is produced by a known quantizer.

Original language	English
Article number	111707
Number of pages	9
Journal	Automatica
Volume	166
Early online date	18 May 2024
DOIs	https://doi.org/10.1016/j.automatica.2024.111707
Publication status	Published - Aug 2024

Funding

This work was supported in part by the Chilean National Agency for Research and Development (ANID) Scholarship Program/Doctorado Nacional/2020-21202410 , in part by the grants ANID-Fondecyt 3240181 , 1211630 and 11201187 , ANID-ECOS 210008 , ANID-Basal Project FB0008 (AC3E), and in part by the research program VIDI 15698, which is financed by the Netherlands Organization for Scientific Research (NWO) .

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
National Agency for Research and Development	11201187, ANID-ECOS 210008, 3240181, 1211630
National Agency for Research and Development	FB0008
National Agency for Research and Development	ANID-Fondecyt3240181, Program/DoctoradoNacional/2020-21202410
National Agency for Research and Development
Advanced Center for Electrical and Electronic Engineering	VIDI 15698

Keywords

Wiener System Identification
EM Algorithm
Maximum Likelihood
Piecewise Polynomial
Piecewise polynomial
Wiener system identification
Maximum likelihood
EM algorithm

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10.1016/j.automatica.2024.111707

Cedeno_Gonzalez_Carvajal_Aguero_Automatica_2024Final author version , 765 KBLicence: CC BY-NC-ND
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title = "Identification of Wiener State-Space Models utilizing Gaussian Sum Smoothing",

abstract = "In this paper, we address the problem of system identification for Wiener state-space models. Our approach is based on the Maximum Likelihood method and the Expectation-Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation-Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state-space systems in which the output is produced by a known quantizer.",

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author = "Cede{\~n}o, {Angel L.} and Rodrigo Gonz{\'a}lez and Rodrigo Carvajal and Aguero, {Juan Carlos}",

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AU - Cedeño, Angel L.

AU - González, Rodrigo

AU - Carvajal, Rodrigo

AU - Aguero, Juan Carlos

PY - 2024/8

Y1 - 2024/8

N2 - In this paper, we address the problem of system identification for Wiener state-space models. Our approach is based on the Maximum Likelihood method and the Expectation-Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation-Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state-space systems in which the output is produced by a known quantizer.

AB - In this paper, we address the problem of system identification for Wiener state-space models. Our approach is based on the Maximum Likelihood method and the Expectation-Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation-Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state-space systems in which the output is produced by a known quantizer.

KW - Wiener System Identification

KW - EM Algorithm

KW - Maximum Likelihood

KW - Piecewise Polynomial

KW - Piecewise polynomial

KW - Wiener system identification

KW - Maximum likelihood

KW - EM algorithm

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DO - 10.1016/j.automatica.2024.111707

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VL - 166

JO - Automatica

JF - Automatica

M1 - 111707

ER -

Identification of Wiener State-Space Models utilizing Gaussian Sum Smoothing

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Keywords

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