2000国家大地坐标系坐标转换精度检测

地理空间信息
GEOSPATIAL INFORMATION
2020年8月第18卷第8期
Aug.,2020Vol.18,
No.8
2000国家大地坐标系坐标转换精度检测
方郧农1，王　博1，李　婉1
（1.湖北省测绘质量监督检验站，湖北 武汉430074）
摘 要：对相关坐标转换方法及相关理论进行论述，结合以往对此类项目的检查验收情况，总结出一些经验方法，旨在对目前城市坐标转换项目成果的检查验收和质量评定工作有所帮助。

关键词：2000国家大地坐标系；坐标转换；二维平面四参数；精度检测；内业检测；外业检测中图分类号：P226 文献标志码：B
文章编号：1672-4623（2020）08-0129-02
遵照国务院推广使用2000国家大地坐标系的要求，各市、县级自然资源主管部门按照“统一组织、分级实施、立足实际、全面推进”的原则，依据相关规范和技术要求，根据实际需要，组织完成支撑第三次土地调查工作和自然资源日常管理工作的各类存量空间数据向2000国家大地坐标系转换工作。

目前市、县各类存量空间数据主要以大比例尺4D 数据成果为主，坐标系统基本采用城市相对独立的平面坐标系，建立城市相对独立的平面坐标系统与2000国家大地坐标系联系时，坐标转换模型要同时适用于地方控制点转换和城市数字地图的转换，一般采用二维平面四参数转换模型，重合点较多时可采用多元逐步回归模型。

相对独立的平面坐标系统下数字地形图转换采用点对点转换法完成相对独立的平面坐标系统下数字地形图到2000国家大地坐标系的转换，转换后相邻图幅不存在接边问题。

1坐标转换参数求取方法
1）重合点选取。

选用具有原坐标系坐标和 2000
国家大地坐标系坐标的控制点作为重合点（实测、收集），重合点选取的基本原则为等级高、精度高、分布均匀、覆盖整个转换区域、局部变形小。

重合点要分布均匀，包围城市区域，并在城市内部选定若干个均匀分布的重合点对坐标转换精度进行检核，检核点数量一般不少于6个[1]。

2）转换参数计算。

城市局部区域一般采用二维四参数平面坐标转换模型
[2]
，重合点坐标为x 和y ，共
4个转换参数，即2个平移参数、1个旋转参数和1个尺度参数。

计算转换参数应有多余条件，用于计算转换参数的重合点数量与转换区域的大小有关，重合点
数量一般不少于5个。

用所确定的重合点坐标，根据坐标转换模型利用最小二乘法计算模型参数。

最终采用哪些重合点，需根据所计算的转换参数计算重合点坐标残差，分析比较残差值的大小，剔除残差大于3倍中误差的重合点（粗差），粗差率应控制在20%以内，重新计算坐标转换参数，直到满足精度要求为止。

2坐标转换参数精度检测
1）重合点如果是实测控制点，首先按相关规范
[3]
要求检查控制测量成果，需检验合格。

2）内业根据相关资料核查分析坐标转换参数计算的内符合和外符合精度。

内符合精度依据计算坐标转换模型参数的重合点的残差中误差评估坐标转换精度。

对于n 个点，坐标转换精度估计公式为：重合点残差V =重合点转换坐标－重合点已知坐标，中误差为一组控制点的均方根Mp ，最大误差限允限=2Mp ，是一组控制点中个别点最大误差的允许限差，大于3倍中误差的点为含有粗差的点，应该剔除。

外符合精度选择部分重合点作为外部检核点，不参与转换参数计算，用转换参数计算这些点的转换坐标，与已知坐标进行比较、进行外部检核，检查点中误差应不大于点位中误差的2倍。

即m M s p =×2。

平面四参数坐标转换精度估计公式如下：x
残差中误差M x =收稿日期：2020-01-14。

doi:10.3969/j.issn.1672-4623.2020.08.035
地理空间信息·130·
第18卷第8期
y
残差中误差M y =点位中误差M M M p x y =
±+22。

3）外业检测。

①静态测量，选取部分相对独立平面坐标系下未参与参数计算的控制点（非重合点）组网进行实地观测，联测2000国家大地坐标系坐标，施测方法、精度等级应不低于实测重合点控制测量精度等级
[3]
，用转换参数计算这些点的转换坐标，与实测
坐标进行比较，按同精度计算检测中误差。

计算公式
如下：
M =检测点n 的数量应大于等于20，小于20时以误差的算术平均值代替中误差[4]。

②RTK 测量，可分为单基准站RTK 测量和网络RTK 测量两种检测方法
[5]，选取部分相对独立平面坐
标系下未参与参数计算的控制点（非重合点）进行实地观测获得其2000国家大地坐标系坐标，与转换坐标进行比较。

施测方法应按照CH /T 2009-2010《全球定位系统实时动态测量（RTK ）技术规范》[5]
要求执行，按同精度计算检测中误差，计算公式同静态测量检测方法。

上述2种外业检测方法，静态测量检测精度高、准确可靠，但效率低、可操作性不强。

目前各地均建立了省、市、县级CORS 网，平面定位精度均在 3～5 cm ，符合CJJ /T 8-2011《城市测量规范》
[6]
第
4.1.6条和CH /T 2014-2016《大地测量控制点坐标转换技术规范》[2]
第6.2条精度要求，所以，一般情况下建议采用RTK 测量方法效率更高也易于操作，检测精度也可得到保证，条件允许的情况下也可采用第一种方法进行检测。

3大比例尺数字地形图转换精度检测
3.1 内业检测方法
1）内业量取转换前样本原图内部分地物点坐标
（检测点一般选取20～50个），可适当扩大统计范围（若干样本图幅组成区域，以区域为单位进行统计）。

2）通过省级CORS 转换参数线上转换成2000国家大地坐标系坐标，这是基于原坐标系为新1954年北京坐标系和1980西安坐标系下相对独立的坐标系可进行转换，如不是上述坐标系，则这些检测点只能使用坐标转换软件并采用生产单位求取的坐标转换参数转
换成2000国家大地坐标系坐标。

3）量取转换后的相应图幅成果内同名点坐标，最后对较差进行精度统计，按高精度计算检测中误差。

计算公式如下：
M =±
按照技术要求规定，中误差小于或等于图上 0.1 mm 。

根据以往检查验收情况，图幅和数据库坐标转换精度远小于图上0.1 mm 的规定，与坐标转换参数计算精度相当。

3.2 外业检测方法
坐标转换后图幅地物点平面位置精度包含原图地物点误差和坐标转换误差，但坐标转换误差相对于地物点误差很小，可忽略不计，所以转换后图幅地物点平面位置精度应与转换前图幅精度要求一致。

因此外业精度检测可按照GB /T 24356-2009《测绘成果质量检查与验收》[4]
第4.3条规定执行，直接检测转换后图幅的平面位置精度即可，如满足相应规范要求，可判定图幅转换精度符合要求。

4结　语
相对独立平面坐标系转换到2000国家大地坐标系的坐标转换精度、数字地形图的坐标转换精度检测和精度评定采取上述方法进行检验，经对几个城市坐标转换项目的检验后，实践证明切实可行，检测精度可靠，精度判定准确，可对类似项目的检查验收提供参考，亦可保证转换成果数据能有效服务于自然资源的调查和管理工作。

参考文献
[1] 国土资源部,国家测绘地理信息局.国土资源数据2000国家
大地坐标系转换技术要求[Z ]. 北京:国土资源部,2017
[2] 中国测绘科学研究院,国家测绘产品质量检验测试中心,广
州市城市规划勘测设计研究院.CH /T 2014-2016大地测量控制点坐标转换技术规范[S ].
[3] 国家测绘局测绘标准化研究所,国家测绘局第一大地测量
队,国家基础地理信息中心. GB /T18314-2009 全球定位系统(GPS )测量规范[S ].
[4] GB /T24356-2009测绘成果质量检查与验收[S ].
[5] 浙江省测绘局 国家测绘局重庆测绘院. CH /T 2009-2010全
球定位系统实时动态测量(RTK )技术规范[S ].
[6] 北京市测绘设计研究院. CJJ /T 8-2011城市测量规范[S ].[7] 北京市测绘设计研究院. CJJ /T 73-2010卫星定位城市测量
技术规范[S ].第一作者简介：方郧农，高级工程师，注册测绘师，现主要从事测绘地理信息质量检查与评价应用研究工作。

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