MINQUE Method Variance Component Estimation for the Mixed Additive and Multiplicative Random Error Model
Publication: Journal of Surveying Engineering
Volume 149, Issue 4
Abstract
To address the problem of inaccurate mixed additive and multiplicative random error stochastic model weighting, we apply the minimum norm quadratic unbiased estimator (MINQUE) to a mixed additive and multiplicative random error model (TMAMM). Then we construct the corresponding calculation formula and iterative algorithm. Based on the formula and algorithm, we estimate the corresponding additive error variance and multiplicative error variance components. The MINQUE variance component estimation (VCE) method is based on (1) invariance, (2) unbiasedness, and (3) minimum normality. Therefore, the variance component estimates derived from the MINQUE method for the mixed additive and multiplicative random error stochastic model also have unbiased and least norm properties. The mixed additive and multiplicative random error stochastic model is modified based on an estimated variance component valuation to obtain a more reasonable parameter valuation. Numerical simulation experiments, digital terrain model (DTM) experiments, and side net measurement are used to verify the effectiveness of the proposed method.
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Data Availability Statement
All data, models, and code generated or used during the study are available from the corresponding author by reasonable request. The data can be provided in a .mat file.
Acknowledgments
The authors are grateful to the anonymous reviewers and editors for their comprehensive and insightful comments, which have improved the resulting presentation. This study is supported by the National Natural Science Foundation of China (Grant Nos. 42174011 and 41874001), and the Innovation Fund Designated for Graduate Students of JiangXi Province (Grant No. YC-2022-S607).
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Published In
Journal of Surveying Engineering
Volume 149 • Issue 4 • November 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Aug 13, 2022
Accepted: Jun 12, 2023
Published online: Aug 4, 2023
Published in print: Nov 1, 2023
Discussion open until: Jan 4, 2024
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