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On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-8655-2655
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2012 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 8, 1525-1535 p.Article in journal (Refereed) Published
Abstract [en]

Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements. We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression. The main issue is how to determine a suitable regularization matrix (Bayesian prior or kernel). Several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets. Our findings based on the data bank are as follows. The classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach - the prediction error method/maximum likelihood (PEM/ML) approach. If the goal is to estimate a model of given order as well as possible, a low order model is often better estimated by the PEM/ML approach, and a higher order model is often better estimated by model reduction on a high order regularized FIR model estimated with careful regularization. Moreover, an optimal regularization matrix that minimizes the mean square error matrix is derived and studied. The importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach.

Place, publisher, year, edition, pages
Elsevier, 2012. Vol. 48, no 8, 1525-1535 p.
Keyword [en]
System identification, Transfer function estimation, Regularization, Bayesian inference, Gaussian process, Mean square error, Bias-variance trade-off
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-81831DOI: 10.1016/j.automatica.2012.05.026ISI: 000307688200005OAI: oai:DiVA.org:liu-81831DiVA: diva2:556599
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Swedish Foundation for Strategic Research Swedish Research Council
Available from: 2012-09-25 Created: 2012-09-24 Last updated: 2017-12-07

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Chen, TianshiOhlsson, HenrikLjung, Lennart

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