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Asymptotic Properties of the Least Squares Method for Estimating Transfer Functions and Disturbance Spectra
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Royal Institute of Technology, Sweden.
1989 (English)Report (Other academic)
Abstract [en]

The problem of estimating the transfer function of a linear system, together with the spectral density of an additive disturbance, is considered. The set of models used consists of linear rational transfer functions and the spectral densities are estimated from a finite-order autoregressive disturbance description. The true system and disturbance spectrum are, however, not necessarily of finite order. We investigate the properties of the estimates obtained as the number of observations tends to ∞ at the same time as the model order employed tends to ∞ . It is shown that the estimates are strongly consistent and asymptotically normal, and an expression for the asymptotic variances is also given. The variance of the transfer function estimate at a certain frequency is related to the signal/noise ratio at that frequency and the model orders used, as well as the number of observations. The variance of the noise spectral estimate relates in a similar way to the squared value of the true spectrum.

Place, publisher, year, edition, pages
Linköping: Linköping University , 1989. , 32 p.
Series
LiTH-ISY-I, ISSN 8765-4321 ; 1008
Keyword [en]
ARX models, Frequency domain, Linear systems, Autoregression, Identification, Almost sure convergence, Central limit theorem
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-104095OAI: oai:DiVA.org:liu-104095DiVA: diva2:694544
Available from: 2014-02-06 Created: 2014-02-06 Last updated: 2014-02-06

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Ljung, Lennart

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  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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Language
  • de-DE
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  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
  • rtf