Bias Reduction Method for Parameter Inversion of Ill-Posed Surveying Model
Publication: Journal of Surveying Engineering
Volume 146, Issue 3
Abstract
Because of ill-posed problems, inverted parameters of ill-posed models always have large variances. The regularization method is widely used to solve this problem. Based on the mean square error (MSE) criterion, the regularization method reduces the parameter estimation variances through introducing biases. However, excessive biases will increase the MSE and the unreliability of the estimates. To improve this situation, this paper first analyzes the calculation of the MSE through the singular value decomposition (SVD) method and then proposes a bias reduction method. Based on this method, a bias-reduced regularization method is proposed to improve the MSE of regularized model parameter estimations. Simulation and practical examples are respectively displayed to demonstrate the effectiveness of the new method. In the simulation example, the root-mean-square error (RMSE) of the regularized model parameter estimates is reduced by 78%. In the polarimetric interferometric synthetic aperture radar (PolInSAR) surveying example, the RMSE of the inverted vegetation height is improved by 23%. Both examples clearly show the effectiveness of the new method.
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Data Availability Statement
Some data, models, or code generated or used during the study are available from the corresponding author by request (generated Fredholm integral equation data and code).
Acknowledgments
The work presented in the paper was supported by the Provincial Key Research and Development Program of Hunan (No. 2018GK2015), Research Project of the Education Department of Hunan Province (No. 18C0312), Open Fund of Hunan International Scientific and Technological Innovation Cooperation Base of Advanced Construction and Maintenance Technology of Highway (Changsha University of Science & Technology, No. kfj190805), National Nature Science Foundation of China (No. 41674012), and Scientific Research Project of Hunan University of Science and Technology (No. CXTD004).
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Published In
Journal of Surveying Engineering
Volume 146 • Issue 3 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jun 21, 2019
Accepted: Jan 27, 2020
Published online: May 7, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 7, 2020
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