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Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method

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. 303-313. ISSN 2278179X

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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.

Item Type: Article
Uncontrolled Keywords: Nonlinear least squares; sum squares of error; parameter estimation; curve fitting; model selection
Subjects: Q Science > QA Mathematics > QA76 Computer software
Divisions: Faculty of Applied Science and Technology > Department of Mathematics and Statistic
Depositing User: Mr. Mohammad Shaifulrip Ithnin
Date Deposited: 30 Apr 2019 01:05
Last Modified: 30 Apr 2019 01:05
URI: http://eprints.uthm.edu.my/id/eprint/10962
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