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

• 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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

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

Publikations- och innehållstyp

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