| 三维坐标转换的通用整体最小二乘算法 |
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| 引用本文： | 方兴,曾文宪,刘经南,姚宜斌.三维坐标转换的通用整体最小二乘算法[J].测绘学报,2014,43(11):1139-1143. |
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| 作者姓名： | 方兴 曾文宪 刘经南 姚宜斌 |
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| 作者单位： | 1. 武汉大学测绘学院;
2. 武汉大学卫星定位导航技术研究中心;
3. 武汉大学 测绘学院 |
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| 基金项目： | 国家自然科学基金(41474006；41404005；41231174；41174012)；中央高校基本科研基金 |
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| 摘 要： | 三维坐标转换模型属于非线性EIV（errors-in-variables）模型，现有整体最小二乘算法均设定了某些特殊假设条件，如仅适用于小角度或者属于非统计意义上的数值解，并且不能用于结构性的系数矩阵等，算法适用性受到极大限制。本文提出了三维坐标转换模型的通用加权整体最小二乘算法，该算法适用于任意旋转角度以及一般性的权矩阵情况下的三维坐标转换模型，并且将结构性系数矩阵、同时包含随机和非随机元素的系数矩阵等情况纳入到了统一的坐标转换模型算法。实例计算表明，本文提出的算法具有通用性，适用于实际应用中的各类三维坐标转换模型。
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| 关 键 词： | 整体最小二乘估计 三维坐标转换模 EIV模型 非线性算法 |
| 收稿时间： | 2014-01-08 |
| 修稿时间： | 2014-04-07 |
A General Total Least Squares Algorithm for Three-dimensional Coordinate Transformations |
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| FANG Xing,ZENG Wenxian,LIU Jingnan,YAO Yibin.A General Total Least Squares Algorithm for Three-dimensional Coordinate Transformations[J].Acta Geodaetica et Cartographica Sinica,2014,43(11):1139-1143. |
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| Authors: | FANG Xing ZENG Wenxian LIU Jingnan YAO Yibin |
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| Institution: | 1. School of Geodesy and Geomatics, Wuhan University;
2. Research Center of GNSS, Wuhan University |
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| Abstract: | The model of three-dimensional coordinate transformation is a nonlinear EIV (errors-in-variables) model. The methods proposed in published literatures are always restricted in practice for their special assumptions, such as size of rotation angles, structured design matrix and special weight matrix. In this paper, a general weighted TLS algorithm of a three-dimensional coordinate transformation is investigated. The new algorithm can be applied in transformations with an arbitrary rotation angles and any applicable weights of the observations, as well as the structured design matrix or the design matrix with both random and fixed elements. The example given in this paper illustrates that this algorithm is general and suits to all kinds of three-dimensional coordinate transformations in practice. |
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| Keywords: | total least-squares method three-dimensional coordinate transformations errors-in-variables model nonlinear program |
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