Linear Time-Varying Parameter Estimation: Maximum A Posteriori Approach via Semidefinite Programming

Sasan Vakili; Mohammad Khosravi; Peyman Mohajerin Esfahani; Manuel Mazo

doi:10.1109/LCSYS.2023.3347198

Linear Time-Varying Parameter Estimation: Maximum A Posteriori Approach via Semidefinite Programming

Sasan Vakili^*, Mohammad Khosravi, Peyman Mohajerin Esfahani, Manuel Mazo

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

Original language	English
Pages (from-to)	73-78
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	8
DOIs	https://doi.org/10.1109/LCSYS.2023.3347198
Publication status	Published - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Estimation
identification
linear matrix inequalities
optimization
semidefinite programming

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10.1109/LCSYS.2023.3347198

Cite this

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title = "Linear Time-Varying Parameter Estimation: Maximum A Posteriori Approach via Semidefinite Programming",

abstract = "We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.",

keywords = "Estimation, identification, linear matrix inequalities, optimization, semidefinite programming",

author = "Sasan Vakili and Mohammad Khosravi and Esfahani, {Peyman Mohajerin} and Manuel Mazo",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.",

year = "2024",

doi = "10.1109/LCSYS.2023.3347198",

language = "English",

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journal = "IEEE Control Systems Letters",

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T2 - Maximum A Posteriori Approach via Semidefinite Programming

AU - Vakili, Sasan

AU - Khosravi, Mohammad

AU - Esfahani, Peyman Mohajerin

AU - Mazo, Manuel

N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2024

Y1 - 2024

N2 - We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

AB - We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

KW - Estimation

KW - identification

KW - linear matrix inequalities

KW - optimization

KW - semidefinite programming

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DO - 10.1109/LCSYS.2023.3347198

M3 - Article

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SN - 2475-1456

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EP - 78

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -

Linear Time-Varying Parameter Estimation: Maximum A Posteriori Approach via Semidefinite Programming

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