| 加权总体最小二乘的效率优化算法 |
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| 引用本文： | 倪福泽,王建民.加权总体最小二乘的效率优化算法[J].测绘通报,2020,0(11):90. |
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| 作者姓名： | 倪福泽 王建民 |
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| 作者单位： | 太原理工大学矿业工程学院, 山西 太原 030024 |
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| 基金项目： | 地质灾害防治与地质环境保护国家重点实验室开放基金（SKLGP2020K027）；山西省自然科学基金（201901D111048） |
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| 摘 要： | 加权总体最小二乘法是理论上估计EIV模型参数相对严密的方法，其迭代过程中涉及的矩阵运算较为耗时，在处理大量级数据时尤其明显。PEIV模型有助于提高加权总体最小二乘法的计算效率。本文基于PEIV模型和经典最小二乘准则给出了一种加权总体最小二乘法算法，算法的推导过程简洁，易于理解，迭代过程中无需重构矩阵，减少了矩阵运算量。最后通过仿真试验验证了算法的可靠性。试验结果表明，本文算法可以取得与现有算法相同的参数估计精度且计算效率更高。
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| 关 键 词： | 最小二乘 加权总体最小二乘 PEIV模型 计算效率 坐标转换 |
| 收稿时间： | 2020-01-03 |
| 修稿时间： | 2020-04-14 |
An optimization algorithm to enhance efficiency of weighted total least squares |
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| NI Fuze,WANG Jianmin.An optimization algorithm to enhance efficiency of weighted total least squares[J].Bulletin of Surveying and Mapping,2020,0(11):90. |
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| Authors: | NI Fuze WANG Jianmin |
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| Institution: | College of Mining Technology, Taiyuan University of Technology, Taiyuan 030024, China |
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| Abstract: | At present, the weighted total least-squares (WTLS) adjustment is a relatively rigorous method used for estimating parameters in the errors-in-variables (EIV) model. However, the required matrix operations involved in the iteration process are extremely time-consuming, particularly when processing large data sets. Using partial errors-in-variables (PEIV) is conducive to improve the computational efficiency of WTLS. Based on the PEIV model and the least squares criterion, this study derived an algorithm for weighted total least squares problemin a concise way. The algorithm is simple in the concept and involves fewer matrix operations because it doesn't demand matrix reconstruction in the iteration process. Finally, simulated experiment is used to test the performance of the proposed algorithm. The results show that the proposed algorithm can achieve the same results as the existing algorithms and has higher computational efficiency. |
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| Keywords: | least squares weighted total least squares partial errors-in-variables model computational efficiency coordinate transformation |
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