| 加权和不加权TLS方法及其在不等精度坐标变换中的应用 |
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| 引用本文： | 周拥军,邓才华.加权和不加权TLS方法及其在不等精度坐标变换中的应用[J].武汉大学学报(信息科学版),2012,37(8):976-979,1007. |
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| 作者姓名： | 周拥军 邓才华 |
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| 作者单位： | 1. 上海交通大学船舶海洋与建筑工程学院,上海市东川路800号,上海200240
2. 中南大学测绘与国土信息工程系,长沙市麓山南路932号,长沙410083 |
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| 基金项目： | 国家自然科学基金资助项目，中国博士后基金资助项目 |
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| 摘 要： | 以重合点坐标独立但不等精度的三维坐标变换问题为基础,采用不加权和加权的TLS方法进行解算。模拟算例表明,未加权的简单TLS方法与基于残差的LS方法的估计结果一致。在加权方法中,按行分块独立的WTLS方法能达到最大似然估计精度,而EWTLS方法由于未考虑元素间的相关性,估计精度略低。
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| 关 键 词： | 三维坐标变换 不等精度 加权总体最小二乘 最大似然估计 |
Weighted and Unweighted Total Least Square Methods and Applications to Heteroscedastic 3D Coordinate Transformation |
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| ZHOU Yongjun,DENG Caihua.Weighted and Unweighted Total Least Square Methods and Applications to Heteroscedastic 3D Coordinate Transformation[J].Geomatics and Information Science of Wuhan University,2012,37(8):976-979,1007. |
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| Authors: | ZHOU Yongjun DENG Caihua |
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| Institution: | 1 School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiaotong University, 800 Dongchuan Road,Shanghai 200240,China)(2 Department of Surveying and Geo-informatics,Central South University,932 South Lushan Road,Changsha 410083,China) |
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| Abstract: | Traditional solution to 3D coordinate transformation problem is the optimal estimation at the cost function of the least squares(LS)for residual vector without consideration of point covariance.Whereas ordinary least squares and total least squares methods can not work well in the heteroscedastic cases.Then unweighted and weighted TLS methods are introduced and compared.The data experiments indicate that unweighted TLS method and LS method have the consistent results and the block row-wised WTLS method has the same results as the maximum likelihood estimator(MLE),and the element-wised method is not so accurate as MLE due to neglecting the correlations of the matrix elements. |
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| Keywords: | three-dimensional coordinate transformation~ heteroseedastic weighted totalleast squares maximum likelihood estimation |
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