On the accuracy in errors-in-variables identification compared to prediction-error identification

Hjalmarsson, Håkan,1962-KTH,Reglerteknik,ACCESS Linnaeus Centre,System Identification Group (author)

QC 20121019
Errors-in-variables estimation problems for single-inputsingle-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle's formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.

TEKNIK OCH TEKNOLOGIER Elektroteknik och elektronik Reglerteknik hsv//swe
ENGINEERING AND TECHNOLOGY Electrical Engineering, Electronic Engineering, Information Engineering Control Engineering hsv//eng
Accuracy of identification
Asymptotic variance expressions
Error-in-variables identification
System identification
Asymptotic covariance matrix
Asymptotic variance
Asymptotically efficient
Errors in variables
Estimation problem
Explicit expressions
Gaussian signals
Geometric representation
Gramians
Input noise
Measurement Noise
Noise spectra
Noise variance
Parameter estimate
System Dynamics
Underlying systems
Asymptotic analysis
Covariance matrix
Errors
Estimation
Identification (control systems)
Parameter estimation
Spurious signal noise
Fisher information matrix
SRA - ICT
SRA - Informations- och kommunikationsteknik

Mårtensson, JonasKTH,Reglerteknik,ACCESS Linnaeus Centre,System Identification Group(Swepub:kth)u1576kww (author)
Rojas, Cristian R.,1980-KTH,Reglerteknik,ACCESS Linnaeus Centre,System Identification Group(Swepub:kth)u10v97p2 (author)
Söderström, TorstenUppsala universitet,Avdelningen för systemteknik,Reglerteknik(Swepub:uu)torssode (author)
KTHReglerteknik (creator_code:org_t)

By the author/editor: Hjalmarsson, Håk ...; Mårtensson, Jona ...; Rojas, Cristian ...; Söderström, Tors ...

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