Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem
Joint Authors
Wang, Ke
Tao, Qiuxiang
Zhai, Min
Liu, Guolin
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-02-10
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
In this work, we combine the special structure of the separable nonlinear least squares problem with a variable projection algorithm based on singular value decomposition to separate linear and nonlinear parameters.
Then, we propose finding the nonlinear parameters using the Levenberg–Marquart (LM) algorithm and either solve the linear parameters using the least squares method directly or by using an iteration method that corrects the characteristic values based on the L-curve, according to whether or not the nonlinear function coefficient matrix is ill posed.
To prove the feasibility of the proposed method, we compared its performance on three examples with that of the LM method without parameter separation.
The results show that (1) the parameter separation method reduces the number of iterations and improves computational efficiency by reducing the parameter dimensions and (2) when the coefficient matrix of the linear parameters is well-posed, using the least squares method to solve the fitting problem provides the highest fitting accuracy.
When the coefficient matrix is ill posed, the method of correcting characteristic values based on the L-curve provides the most accurate solution to the fitting problem.
American Psychological Association (APA)
Wang, Ke& Liu, Guolin& Tao, Qiuxiang& Zhai, Min. 2020. Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem. Complexity،Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1145704
Modern Language Association (MLA)
Wang, Ke…[et al.]. Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem. Complexity No. 2020 (2020), pp.1-16.
https://search.emarefa.net/detail/BIM-1145704
American Medical Association (AMA)
Wang, Ke& Liu, Guolin& Tao, Qiuxiang& Zhai, Min. Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem. Complexity. 2020. Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1145704
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1145704