Tikhonov Regularized Variable Projection Algorithms for Separable Nonlinear Least Squares Problems
Tikhonov Regularized Variable Projection Algorithms for Separable Nonlinear Least Squares Problems
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DOI：
10.1155/2019/4861708
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Zhengqing Fu;Lanlan Guo
中科院分区：
文献类型：
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作者：
Zhengqing Fu;Lanlan Guo
本文考虑经典的可分非线性最小二乘问题。这类问题可以表示为非线性函数的线性组合，并且需要估计线性和非线性参数。在现有的结果中，病态问题较少被考虑。因此，本文重点研究病态问题的一种算法。在所提出的线性参数估计过程中，利用Tikhonov正则化降低了模型对扰动的敏感性。采用Lvenberg-MarQuardt算法对非线性参数进行估计。LM所需的雅可比矩阵由Golub、Pereyra、Kaufman和Ruano方法计算。结合非线性和线性参数估计方法，得到了三种估计模型，并论证了模型估计的可行性和稳定性。通过仿真数据和实际数据对模型进行了验证。实验结果也说明了该模型的可行性和稳定性。
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.