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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.
1992 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 24, no 2, 412-440 p.Article in journal (Refereed) Published
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
Applied Probability Trust , 1992. Vol. 24, no 2, 412-440 p.
Keyword [en]
ARX models, Frequency domain, Linear systems, Autoregression, Identification, Almost sure convergence, Central limit theorem
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-95646OAI: diva2:637107
Available from: 2013-07-16 Created: 2013-07-16 Last updated: 2014-02-08Bibliographically approved

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Ljung, Lennart
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Automatic ControlThe Institute of Technology
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