Nonlinear least squares parameter estimation problem using Levenberg-Marquardt method - Kaw, Wei Ching; Kek, Sie Long; Sim, Sy Yi (An International Peer Review E-3 Journal of Sciences and Technology, 2017)
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.