New First-Order Approximate Precision Estimation Method for Parameters in an Errors-in-Variables Model
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VIEW THE REPLYPublication: Journal of Surveying Engineering
Volume 147, Issue 1
Abstract
To evaluate the posterior precision of weighted total least-squares (WTLS) estimates in an errors-in-variables model, first-order approximate precision estimation (FOA) methods are usually used. However, FOAs might not be valid if the underlying assumption is invalid, and this assumption has not been sufficiently proven. Therefore, this paper investigates the validity of the latent assumption and proposes a new first-order approximate (NFOA) precision estimation method to avoid the underlying assumption and design a corresponding algorithm. The difference between NFOA and FOA is formulated and analyzed. The proposed NFOA method is tested by a simulated classic straight-line fitting example with six scenarios and a simulated three-dimensional (3D) affine transformation experiment with four scenarios, and the mean values of the standard deviation of true errors (MSDTE) and FOA are also calculated for comparison. The results numerically indicate that NFOA works better than FOA and is close to the MSDTE, which means that NFOA can evaluate the precision of estimated parameters more reasonably and accurately.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
| Data | SLT_True Data.mat |
| SLT_DesignedSimulatedPriorVariance_Data1.mat (Scenario I) | |
| SLT_DesignedSimulatedPriorVariance _Data2.mat (Scenario II) | |
| SLT_DesignedSimulatedPriorVariance _Data3.mat (Scenario III) | |
| SLT_DesignedSimulatedPriorVariance _Data4.mat (Scenario IV) | |
| SLT_DesignedSimulatedPriorVariance _Data5.mat (Scenario V) | |
| SLT_DesignedSimulatedPriorVariance _Data6.mat (Scenario VI) | |
| 3DAT_Resource_Cood.mat3DAT_Target_Cood.mat | |
| Code | 1. PEIV.m |
| 2. Demo.m (Example 1: Straight-line Fitting) | |
| 3. Demo1.m (Example 2: 3D Affine Transformation) |
Acknowledgments
The authors thank Professor Amiri-Simkooei and Lecturer Farzaneh for providing the MATLAB code to allow the authors to improve the quality of this paper. The work described in this paper is supported by the Shanghai Municipal Natural Science Foundation (19ZR1459700), the National Key R&D Program of China (2017YFB0502700), and the Key Laboratory of Advanced Engineering Surveying of the National Administration of Surveying, Mapping and Geoinformation (TJES1802).
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Journal of Surveying Engineering
Volume 147 • Issue 1 • February 2021
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© 2020 American Society of Civil Engineers.
History
Received: Sep 19, 2019
Accepted: Jun 24, 2020
Published online: Oct 31, 2020
Published in print: Feb 1, 2021
Discussion open until: Mar 31, 2021
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