Separable nonlinear least squares algorithm based on finite difference

Ke Wang; Baomin Han

doi:10.1117/12.2682631

1 June 2023 Separable nonlinear least squares algorithm based on finite difference

Ke Wang, Baomin Han

Proceedings Volume 12710, International Conference on Remote Sensing, Surveying, and Mapping (RSSM 2023); 1271006 (2023) https://doi.org/10.1117/12.2682631
Event: International Conference on Remote Sensing, Surveying, and Mapping (RSSM 2023), 2023, Changsha, China

Abstract

The problem of parameter estimation widely exists in the field of surveying and mapping. In view of the special form of linear combination of nonlinear functions as the parameter model, the linear parameters are eliminated by variable projection operators, which reduces the dimension of the parameters to be solved and increases the possibility of convergence. Then, the Jacobian matrix of the residual vector is numerically approximated by the finite difference method, and the nonlinear function matrix in the iterative objective function is decomposed by QR and SVD. It can simplify the difficulty of matrix calculation and ensure the stability and efficiency of pseudo inverse matrix solution. The experiment is carried out through the full waveform decomposition of the height measurement LiDAR of ICEsat-1 satellite. The results show that under the same optimal solution, the method of approximating Jacobian matrix with finite difference effectively reduces the calculation time, improves the calculation efficiency, and provides a new idea for improving the separable nonlinear least squares variable projection algorithm.

Citation Download Citation

Ke Wang and Baomin Han "Separable nonlinear least squares algorithm based on finite difference", Proc. SPIE 12710, International Conference on Remote Sensing, Surveying, and Mapping (RSSM 2023), 1271006 (1 June 2023); https://doi.org/10.1117/12.2682631

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KEYWORDS

Matrices

Finite difference methods

LIDAR

Signal to noise ratio

Algorithm development

Bismuth

Nonlinear optimization

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