On the variance of identified SIMO systems with spatially correlated output noise

G. Bottegal; Håkan  Hjalmarsson

doi:10.1109/CDC.2014.7039792

On the variance of identified SIMO systems with spatially correlated output noise

G. Bottegal, Håkan Hjalmarsson

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

In this paper, we study the problem of evaluating the accuracy of identified linear single-input multi-output (SIMO) dynamical models, where the disturbances affecting the output measurements are spatially correlated. Assuming that the input is an observed white noise sequence, we provide an expression for the covariance matrix of the parameter estimates when weighted least-squares (WLS) are adopted to identify the parameters. Then, we show that, by describing one of the subsystems composing the SIMO structure using less parameters than the other subsystems, substantial improvement on the accuracy of the estimates of some parameters can be obtained. The amount of such an improvement depends critically on the covariance matrix of the output noise and we provide a condition on the noise correlation structure under which the mentioned model parametrization gives the lowest variance in the identified model. We illustrate the derived results through some numerical experiments.

Originele taal-2	Engels
Titel	2014 IEEE 53rd Annual Conference on Decision and Control (CDC), 15-17 December 2014, Los Angeles, California
Plaats van productie	Piscataway
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	2636-2641
Aantal pagina's	6
ISBN van elektronische versie	978-1-4673-6090-6
ISBN van geprinte versie	978-1-4799-7746-8
DOI's	https://doi.org/10.1109/CDC.2014.7039792
Status	Gepubliceerd - 2014
Extern gepubliceerd	Ja
Evenement	53rd IEEE Conference on Decision and Control, CDC 2014 - "J.W. Marriott Hotel", Los Angeles, Verenigde Staten van Amerika Duur: 15 dec. 2014 → 17 dec. 2014 Congresnummer: 53 http://cdc2014.ieeecss.org/

Congres

Congres	53rd IEEE Conference on Decision and Control, CDC 2014
Verkorte titel	CDC
Land/Regio	Verenigde Staten van Amerika
Stad	Los Angeles
Periode	15/12/14 → 17/12/14
Ander	53rd IEEE Conference on Decision and Control
Internet adres	http://cdc2014.ieeecss.org/

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10.1109/CDC.2014.7039792

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title = "On the variance of identified SIMO systems with spatially correlated output noise",

abstract = "In this paper, we study the problem of evaluating the accuracy of identified linear single-input multi-output (SIMO) dynamical models, where the disturbances affecting the output measurements are spatially correlated. Assuming that the input is an observed white noise sequence, we provide an expression for the covariance matrix of the parameter estimates when weighted least-squares (WLS) are adopted to identify the parameters. Then, we show that, by describing one of the subsystems composing the SIMO structure using less parameters than the other subsystems, substantial improvement on the accuracy of the estimates of some parameters can be obtained. The amount of such an improvement depends critically on the covariance matrix of the output noise and we provide a condition on the noise correlation structure under which the mentioned model parametrization gives the lowest variance in the identified model. We illustrate the derived results through some numerical experiments.",

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publisher = "Institute of Electrical and Electronics Engineers",

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Bottegal, G & Hjalmarsson, H 2014, On the variance of identified SIMO systems with spatially correlated output noise. in 2014 IEEE 53rd Annual Conference on Decision and Control (CDC), 15-17 December 2014, Los Angeles, California. Institute of Electrical and Electronics Engineers, Piscataway, blz. 2636-2641, 53rd IEEE Conference on Decision and Control, CDC 2014, Los Angeles, California, Verenigde Staten van Amerika, 15/12/14. https://doi.org/10.1109/CDC.2014.7039792

On the variance of identified SIMO systems with spatially correlated output noise. / Bottegal, G.; Hjalmarsson, Håkan .
2014 IEEE 53rd Annual Conference on Decision and Control (CDC), 15-17 December 2014, Los Angeles, California. Piscataway: Institute of Electrical and Electronics Engineers, 2014. blz. 2636-2641.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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AU - Hjalmarsson, Håkan

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N2 - In this paper, we study the problem of evaluating the accuracy of identified linear single-input multi-output (SIMO) dynamical models, where the disturbances affecting the output measurements are spatially correlated. Assuming that the input is an observed white noise sequence, we provide an expression for the covariance matrix of the parameter estimates when weighted least-squares (WLS) are adopted to identify the parameters. Then, we show that, by describing one of the subsystems composing the SIMO structure using less parameters than the other subsystems, substantial improvement on the accuracy of the estimates of some parameters can be obtained. The amount of such an improvement depends critically on the covariance matrix of the output noise and we provide a condition on the noise correlation structure under which the mentioned model parametrization gives the lowest variance in the identified model. We illustrate the derived results through some numerical experiments.

AB - In this paper, we study the problem of evaluating the accuracy of identified linear single-input multi-output (SIMO) dynamical models, where the disturbances affecting the output measurements are spatially correlated. Assuming that the input is an observed white noise sequence, we provide an expression for the covariance matrix of the parameter estimates when weighted least-squares (WLS) are adopted to identify the parameters. Then, we show that, by describing one of the subsystems composing the SIMO structure using less parameters than the other subsystems, substantial improvement on the accuracy of the estimates of some parameters can be obtained. The amount of such an improvement depends critically on the covariance matrix of the output noise and we provide a condition on the noise correlation structure under which the mentioned model parametrization gives the lowest variance in the identified model. We illustrate the derived results through some numerical experiments.

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BT - 2014 IEEE 53rd Annual Conference on Decision and Control (CDC), 15-17 December 2014, Los Angeles, California

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ER -

On the variance of identified SIMO systems with spatially correlated output noise

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