| 三维坐标转换的稳健加权总体最小二乘算法 |
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| 引用本文： | 王乐洋,许冉冉.三维坐标转换的稳健加权总体最小二乘算法[J].大地测量与地球动力学,2020,40(10):1027-1033. |
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| 作者姓名： | 王乐洋 许冉冉 |
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| 摘 要： | 针对当前加权对称相似变换中仅考虑观测值含有随机误差，而不考虑观测值含有粗差的情况，基于加权对称相似变换进一步验证其不具有抗差性，并在此基础上采用选权迭代法进行稳健加权对称相似变换。由中位数法求解具有抗差性的单位权中误差，构造标准化残差，求解权因子，进而求得可靠的参数解。实验结果表明，当观测值含有4~6个粗差时，采用该方法能够探测出更多可能存在粗差的数据，给出的权因子更合理，所得参数解精度更高、稳定性更强。
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| 关 键 词： | 坐标转换 总体最小二乘 稳健估计 中位数法 |
Robust Weighted Total Least Squares Algorithm for Three-DimensionalCoordinate Transformation |
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| WANG Leyang,XU Ranran.Robust Weighted Total Least Squares Algorithm for Three-DimensionalCoordinate Transformation[J].Journal of Geodesy and Geodynamics,2020,40(10):1027-1033. |
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| Authors: | WANG Leyang XU Ranran |
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| Abstract: | Based on the existing weighted symmetric similarity transformation, only the case where the observation value contains random error is considered, and the case where the observation value contains the gross error is not considered. This paper further verifies that the weighted symmetric similarity transformation is not robust. Based on the weighted symmetric similarity transformation, the method of selecting weight iteration is adopted to make the robust weighted symmetric similarity transformation. The model obtains unit weight mean square error with robustness by the median method and utilizes the standardized residual to construct the weight factor function, to obtain a reliable parametric solution. Comparative analysis shows that: when the observations contain 4-6 gross errors, the method of this paper can be used to detect more data that may have gross errors, the weighting factors given are more reasonable, and the obtained parameter solution has higher accuracy and stronger stability. |
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| Keywords: | coordinate transformation total least squares robust estimation median method |
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