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Identification of Semi-Linear Models within an Errors-In-Variables Framework

In: Total Least Squares and Errors-in-Variables Modeling

Author

Listed:
  • Rik Pintelon

    (Vrije Universiteit Brussel, department ELEC)

  • Johan Schoukens

    (Vrije Universiteit Brussel, department ELEC)

Abstract

Semi-linear models are models which are linear-in-the-observations and (non)linear in the model parameters. Assuming that all observations are noisy (errors-in-variables framework), the Cramér-Rao lower bound of the model parameters is calculated, and the stochastic properties (strong convergence, convergence rate, strong consistency, asymptotic normality, asymptotic efficiency) of the Markov estimator are analyzed. It follows that in general the Markov estimator is strongly consistent, and asymptotically inefficient (in case of Gaussian errors the estimator does not reach the Cramér-Rao lower bound). Sufficient conditions for the asymptotic efficiency of the Markov estimator are given. The theory is applicable to, for example, signal modelling and multivariable system identification, both in time and frequency domains.

Suggested Citation

  • Rik Pintelon & Johan Schoukens, 2002. "Identification of Semi-Linear Models within an Errors-In-Variables Framework," Springer Books, in: Sabine Van Huffel & Philippe Lemmerling (ed.), Total Least Squares and Errors-in-Variables Modeling, pages 165-177, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3552-0_15
    DOI: 10.1007/978-94-017-3552-0_15
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