Virtual Observation Iteration Solution and A-Optimal Design Method for Ill-Posed Mixed Additive and Multiplicative Random Error Model in Geodetic Measurement
Publication: Journal of Surveying Engineering
Volume 147, Issue 4
Abstract
The mixed additive and multiplicative random error model is a combination of the additive error random model and multiplicative random error model. Weakness is an attribute of the mixed additive and multiplicative random error model, and the ill-posed problem of the coefficient matrix is ignored in the existing parameter estimation methods for addressing the model, which will result in an unstable or nonconvergent solution. Aiming at solving this problem, this paper first derives the virtual observation iterative solution (VOIS) formula for the ill-posed mixed additive and multiplicative random error model by combining the observation equation of the mixed additive and multiplicative random error model and the virtual observation equation. Furthermore, based on the principle of the A-optimal design, the A-optimal design method is proposed to determine the regularization parameter of the ill-posed model. Finally, the VOIS method is applied in simulated and actual data for verification and analysis and is compared with existing methods. The experimental results show that the A-optimal design method can determine reasonable regularization parameters and that the VOIS method can obtain more accurate parameter estimations than existing methods and has strong feasibility and applicability.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (i.e., raw data of the digital elevation models of Examples 2, 3, and 4 can be provided as.mat files).
Acknowledgments
The authors are grateful to all of the anonymous reviewers and editors for their careful review and valuable suggestions, which improved the quality of this paper. This research is supported by the National Natural Science Foundation of China, Grant Nos. 41874001 and 41664001, National Key Research and Development Program, Grant No. 2016YFB0501405, and Innovation Found Designated for Graduate Students of ECUT, Grant No. DHYC-202020.
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Published In
Journal of Surveying Engineering
Volume 147 • Issue 4 • November 2021
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© 2021 American Society of Civil Engineers.
History
Received: Jul 28, 2020
Accepted: Apr 5, 2021
Published online: Jun 30, 2021
Published in print: Nov 1, 2021
Discussion open until: Nov 30, 2021
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