| LS和TLS在平面坐标转换中的应用 |
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| 引用本文： | 刘立龙,姚朝龙.LS和TLS在平面坐标转换中的应用[J].测绘科学,2012,37(5):12-13,64. |
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| 作者姓名： | 刘立龙 姚朝龙 |
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| 作者单位： | 1. 广西空间信息与测绘重点实验室,广西桂林541004;桂林理工大学土木与建筑工程学院,广西桂林541004
2. 桂林理工大学土木与建筑工程学院,广西桂林,541004 |
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| 基金项目： | 国家自然科学基金资助项目(41064001);广西研究生教育创新计划项目(2010105960816M29) |
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| 摘 要： | 在超定线性方程Ax=b的解算中,最小二乘(LS)只考虑观测向量b的误差,而总体最小二乘(TLS)则同时顾及观测向量b和系数矩阵A均含误差的情况。本文以六参数模型在平面坐标转换中的应用为例,分别采用LS和TLS进行模型参数的求解。结果表明,2种方法所求参数并无显著差异,但是总体最小二乘更好地改善了坐标转换的内部精度,是一种更为合理的计算方法。
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| 关 键 词： | 总体最小二乘 最小二乘 坐标转换 六参数模型 精度分析 |
Application of LS and TLS in plane coordination transformation |
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| LIU Li-long
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YAO Chao-long.Application of LS and TLS in plane coordination transformation[J].Science of Surveying and Mapping,2012,37(5):12-13,64. |
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| Authors: | LIU Li-long YAO Chao-long |
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| Institution: | ②(①Guangxi Key Laboratory for Spatial Information and Geomatics,Guangxi Guilin 541004,China;②College of Civil Engineering,Guilin University of Technology,Guangxi Guilin 541004,China) |
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| Abstract: | For the solution of the overdetermined set of linear equation Αx=b,the errors in observation vector b is only considered in the least squares(LS) approach,while observation vector b errors and data matrix A errors are both considered in total least squares(TLS).Taking the application of six-parameter model in plane coordinate transformation as an example,the paper used LS and TLS to estimate the parameters of the model respectively.The results showed that although there is no significant difference in transformation parameters by the two approaches,TLS could improve the accuracy in interior precision and be taken as a more reasonable method of calculation. |
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| Keywords: | Total Least Squares Least Squares coordinate transformation six-parameter model analysis accuracy |
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