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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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.

Original language	English
Title of host publication	2014 IEEE 53rd Annual Conference on Decision and Control (CDC), 15-17 December 2014, Los Angeles, California
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	2636-2641
Number of pages	6
ISBN (Electronic)	978-1-4673-6090-6
ISBN (Print)	978-1-4799-7746-8
DOIs	https://doi.org/10.1109/CDC.2014.7039792
Publication status	Published - 2014
Externally published	Yes
Event	53rd IEEE Conference on Decision and Control, CDC 2014 - "J.W. Marriott Hotel", Los Angeles, United States Duration: 15 Dec 2014 → 17 Dec 2014 Conference number: 53 http://cdc2014.ieeecss.org/

Conference

Conference	53rd IEEE Conference on Decision and Control, CDC 2014
Abbreviated title	CDC
Country/Territory	United States
City	Los Angeles
Period	15/12/14 → 17/12/14
Internet address	http://cdc2014.ieeecss.org/

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10.1109/CDC.2014.7039792

Cite this

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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.",

author = "G. Bottegal and H{\aa}kan Hjalmarsson",

year = "2014",

doi = "10.1109/CDC.2014.7039792",

language = "English",

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pages = "2636--2641",

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

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "53rd IEEE Conference on Decision and Control, CDC 2014, CDC ; Conference date: 15-12-2014 Through 17-12-2014",

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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, pp. 2636-2641, 53rd IEEE Conference on Decision and Control, CDC 2014, Los Angeles, California, United States, 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. p. 2636-2641.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - On the variance of identified SIMO systems with spatially correlated output noise

AU - Bottegal, G.

AU - Hjalmarsson, Håkan

N1 - Conference code: 53

PY - 2014

Y1 - 2014

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.

U2 - 10.1109/CDC.2014.7039792

DO - 10.1109/CDC.2014.7039792

M3 - Conference contribution

SN - 978-1-4799-7746-8

SP - 2636

EP - 2641

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

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 53rd IEEE Conference on Decision and Control, CDC 2014

Y2 - 15 December 2014 through 17 December 2014

ER -

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

Abstract

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