On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited [Elektronisk resurs]
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Chen, Tianshi (författare)
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Ohlsson, Henrik 1981- (författare)
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Ljung, Lennart 1946- (författare)
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- Linköpings universitet Institutionen för systemteknik (utgivare)
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Alternativt namn: ISY
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Alternativt namn: Engelska: Linköping University. Department of Electrical Engineering
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- Linköpings universitet Tekniska högskolan (utgivare)
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Alternativt namn: Linköpings universitet. Tekniska fakulteten
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Alternativt namn: Linköpings tekniska högskola
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Alternativt namn: Tekniska högskolan vid Linköpings universtiet
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Alternativt namn: LiTH
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Alternativt namn: Linköping University. Institute of Technology
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Se även: Universitet i Linköping Tekniska högskolan
- Elsevier 2012
- Engelska.
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Ingår i: Automatica. - 0005-1098. ; 48:8, 1525-1535
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Sammanfattning
Ämnesord
Stäng
- 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.
Ämnesord
- Engineering and Technology (hsv)
- Electrical Engineering, Electronic Engineering, Information Engineering (hsv)
- Control Engineering (hsv)
- Teknik och teknologier (hsv)
- Elektroteknik och elektronik (hsv)
- Reglerteknik (hsv)
- TECHNOLOGY (svep)
- Information technology (svep)
- Automatic control (svep)
- TEKNIKVETENSKAP (svep)
- Informationsteknik (svep)
- Reglerteknik (svep)
Indexterm och SAB-rubrik
- System identification
- Transfer function estimation
- Regularization
- Bayesian inference
- Gaussian process
- Mean square error
- Bias-variance trade-off
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