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Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method

Least squares method, which is a statistical method with minimum sum squares of errors (SSE), is used for curve fitting and parameter estimation. In general, the Gauss-Newton (GN) and the Levenberg-Marquardt (LM) methods are the popular least squares method. In this paper, a nonlinear least squares...

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主要な著者: Kaw, Wei Ching, Kek, Sie Long, Sim, Sy Yi
フォーマット: 論文
言語:English
出版事項: An International Peer Review E-3 Journal of Sciences and Technology 2017
主題:
L Education (General)
オンライン･アクセス:http://eprints.uthm.edu.my/5098/1/AJ%202017%20%28261%29%20Nonlinear%20least%20squares%20parameter%20estimation.pdf
http://eprints.uthm.edu.my/5098/
http://dx.doi.org/10.24214/jecet.C.6.3.30313
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spelling my.uthm.eprints.50982022-01-05T08:24:04Z http://eprints.uthm.edu.my/5098/ Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method Kaw, Wei Ching Kek, Sie Long Sim, Sy Yi L Education (General) Least squares method, which is a statistical method with minimum sum squares of errors (SSE), is used for curve fitting and parameter estimation. In general, the Gauss-Newton (GN) and the Levenberg-Marquardt (LM) methods are the popular least squares method. In this paper, a nonlinear least squares problem and the LM method are discussed. In our study, the derivation of the LM algorithm is briefly described and the relevant necessary condition is satisfied. During the calculation procedure, the optimal solution, which is the optimal parameter estimate, is obtained once the convergence is achieved. For illustration, the related models for an exponential distribution with two unknown parameters, and for the average monthly high temperature with four unknown parameters are constructed. Their respective unknown parameters are estimated by applying the LM method. Besides, the best model selection is suggested to represent the dataset of the concentration of a blood sample. Moreover, a numerical comparison between the methods of LM and GN is carried out. By virtue of these examples studied, the results show the applicability of the LM method in solving the nonlinear least squares problem. In conclusion, the efficiency of the LM method is highly presented. An International Peer Review E-3 Journal of Sciences and Technology 2017 Article PeerReviewed text en http://eprints.uthm.edu.my/5098/1/AJ%202017%20%28261%29%20Nonlinear%20least%20squares%20parameter%20estimation.pdf Kaw, Wei Ching and Kek, Sie Long and Sim, Sy Yi (2017) Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method. Journal of Environmental Science, Computer Science and Engineering & Technology, 6 (3). pp. 202-313. ISSN 2278–179X http://dx.doi.org/10.24214/jecet.C.6.3.30313
institution Universiti Tun Hussein Onn Malaysia
building UTHM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tun Hussein Onn Malaysia
content_source UTHM Institutional Repository
url_provider http://eprints.uthm.edu.my/
language English
topic L Education (General)
spellingShingle L Education (General)
Kaw, Wei Ching
Kek, Sie Long
Sim, Sy Yi
Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method
description Least squares method, which is a statistical method with minimum sum squares of errors (SSE), is used for curve fitting and parameter estimation. In general, the Gauss-Newton (GN) and the Levenberg-Marquardt (LM) methods are the popular least squares method. In this paper, a nonlinear least squares problem and the LM method are discussed. In our study, the derivation of the LM algorithm is briefly described and the relevant necessary condition is satisfied. During the calculation procedure, the optimal solution, which is the optimal parameter estimate, is obtained once the convergence is achieved. For illustration, the related models for an exponential distribution with two unknown parameters, and for the average monthly high temperature with four unknown parameters are constructed. Their respective unknown parameters are estimated by applying the LM method. Besides, the best model selection is suggested to represent the dataset of the concentration of a blood sample. Moreover, a numerical comparison between the methods of LM and GN is carried out. By virtue of these examples studied, the results show the applicability of the LM method in solving the nonlinear least squares problem. In conclusion, the efficiency of the LM method is highly presented.
format Article
author Kaw, Wei Ching
Kek, Sie Long
Sim, Sy Yi
author_facet Kaw, Wei Ching
Kek, Sie Long
Sim, Sy Yi
author_sort Kaw, Wei Ching
title Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method
title_short Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method
title_full Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method
title_fullStr Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method
title_full_unstemmed Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method
title_sort nonlinear least squares parameter estimation problem using levenberg-marquardt method
publisher An International Peer Review E-3 Journal of Sciences and Technology
publishDate 2017
url http://eprints.uthm.edu.my/5098/1/AJ%202017%20%28261%29%20Nonlinear%20least%20squares%20parameter%20estimation.pdf
http://eprints.uthm.edu.my/5098/
http://dx.doi.org/10.24214/jecet.C.6.3.30313
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score 13.251813

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