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Finite Sample Confidence Region for EIV Systems Using Regression Model

  • Masoud Moravej KhorasaniEmail author
  • Erik Weyer
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)

Abstract

Errors-In-Variables (EIV) models in which both input and output data are contaminated by noise have applications in signal processing. We propose a method for constructing non-asymptotic confidence regions for the parameters of EIV models. The method is based on the Leave-out Sign-dominant Correlation Regions (LSCR) principle which gives probabilistically guaranteed confidence region when the input is measured without noise. A regression model is utilized to extend LSCR to EIV systems. The newly established regression vector contains the past outputs and the estimated past inputs. It is shown that the corresponding prediction error has the desired properties such that it can be used to form correlation functions from which confidence regions can be constructed. For any finite number of data points it is proved that the region contains the true parameter with a user-chosen probability.

References

  1. 1.
    Campi, M., Weyer, E.: Guaranteed non-asymptotic confidence regions in system identification. Automatica 41, 1751–1764 (2005)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Campi, M., Weyer, E.: Non-asymptotic confidence sets for the parameters of linear transfer functions. IEEE Trans. Autom. Control. 55, 2708–2720 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Garatti, S., Campi, M., Bittanti, S.: Assessing the quality of identified models through the asymptotic theory-when is the result reliable? Automatica 40, 1319–1332 (2004)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Khorasani, M.M., Weyer, E.: Non-asymptotic confidence regions for error-in-variables system. In: 18th IFAC Symposium on System Identification, pp. 2115–2120. IFAC, Stockholm (2018)CrossRefGoogle Scholar
  5. 5.
    Ljung, L.: System Identification-Theory for the User. Prentice Hall, Upper Saddle River (1999)Google Scholar
  6. 6.
    Söderström, T.: Identification of stochastic linear systems in presence of input noise. Automatica 17, 713–725 (1981)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Söderström, T.: Errors-in-variables methods in system identification. Automatica 43, 939–958 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Söderström, T.: Errors-in-variables methods in system identification. Springer, Cham (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringThe University of MelbourneParkvilleAustralia

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