Tikhonov Regularized Variable Projection Algorithms for Separable Nonlinear Least Squares Problems

This paper considers the classical separable nonlinear least squares problem. Such problems can be expressed as a linear combination of nonlinear functions, and both linear and nonlinear parameters are to be estimated. Among the existing results, ill-conditioned problems are less often considered. H...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2019, Vol.2019 (2019), p.1-9
Main Authors: Fu, Zhengqing, Guo, Lanlan
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Computer simulation
Economic models
Efficiency
Feasibility
Ill-conditioned problems (mathematics)
Jacobi matrix method
Jacobian matrix
Least squares method
Linear programming
Mathematical models
Methods
Parameter estimation
Parameter sensitivity
Process parameters
Regularization
Stability
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Summary:This paper considers the classical separable nonlinear least squares problem. Such problems can be expressed as a linear combination of nonlinear functions, and both linear and nonlinear parameters are to be estimated. Among the existing results, ill-conditioned problems are less often considered. Hence, this paper focuses on an algorithm for ill-conditioned problems. In the proposed linear parameter estimation process, the sensitivity of the model to disturbance is reduced using Tikhonov regularisation. The Levenberg–Marquardt algorithm is used to estimate the nonlinear parameters. The Jacobian matrix required by LM is calculated by the Golub and Pereyra, Kaufman, and Ruano methods. Combining the nonlinear and linear parameter estimation methods, three estimation models are obtained and the feasibility and stability of the model estimation are demonstrated. The model is validated by simulation data and real data. The experimental results also illustrate the feasibility and stability of the model.
ISSN:1076-2787
1099-0526
DOI:10.1155/2019/4861708