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.
The accuracy of differential interferometric synthetic aperture radar (DInSAR) in monitoring the ground subsidence is a major challenge to be addressed urgently. Using the repeat track DInSAR and GIS spatial analysis tools, eight C-band Sentinel-1A SAR images of the Guotun coal mine (China) were processed to determine the mining subsidence from November 27, 2015 to July 24, 2016. The mining data of 13 working faces and the DInSAR- and leveling-monitored results were compared. A method was proposed to solve the problem of time inconsistency between DInSAR- and leveling-monitored results. The location, spatial distribution, scope, and variations of mining subsidence monitored by Sentinel-1A repeat track DInSAR were consistent with the mining progress of the working faces. The accuracy of the DInSAR-monitored subsidence values was directly related to the coherence of the subsidence zones, and the absolute difference from the leveling-monitored values was small at the subsidence edge but large at the subsidence center.
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