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

  • Authors:

  • Håkan Hjalmarsson;Jonas Mårtensson;Cristian R. Rojas;Torsten Söderström

  • Affiliations:

  • ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden;ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden;ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden;Division of Systems and Control, Department of Information Technology, Uppsala University, P.O. Box 337, SE-751 05 Uppsala, Sweden

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

Errors-in-variables estimation problems for single-input-single-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.