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首页> 外文期刊>Journal of Geosciences and Geomatics >Accuracy Assessment of Cartesian (X, Y, Z) to Geodetic Coordinates (φ, λ, h) Transformation Procedures in Precise 3D Coordinate Transformation – A Case Study of Ghana Geodetic Reference Network
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Accuracy Assessment of Cartesian (X, Y, Z) to Geodetic Coordinates (φ, λ, h) Transformation Procedures in Precise 3D Coordinate Transformation – A Case Study of Ghana Geodetic Reference Network

机译：精确3D坐标转换中笛卡尔（X，Y，Z）到大地坐标（φ，λ，h）转换过程的准确性评估–以加纳大地测量参考网为例

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Ghana a developing country still adopt the non-geocentric ellipsoid known as the War Office 1926 as its horizontal datum for all surveying and mapping activities. Currently, the Survey and Mapping Division of Lands Commission in Ghana has adopted the satellite positioning technology such as Global Positioning System based on a geocentric ellipsoid (World Geodetic System 1984 (WGS84)) for its geodetic surveys. It is therefore necessary to establish a functional relationship between these two different reference frames. To accomplish this task, the Bursa-Wolf transformation model was applied in this study to obtain seven transformation parameters namely; three translations, three rotations and a scale factor. These parameters were then used to transform the WGS84 data into the War office system. However, Ghana’s national coordinate system is a projected grid coordinate and thus the new War Office coordinates (X, Y, Z) obtained are not applicable. There is therefore the need to project these coordinates onto the transverse Mercator of Ghana. To do this, the new war office data (X, Y, Z) attained must first be transformed into geodetic coordinates. The reverse conversion from cartesian (X, Y, Z) to its corresponding geodetic coordinate (φ, λ, h) is computation intensive with respect to the estimation of geodetic latitude and height. This study aimed at evaluating the performance of seven methods in transforming from cartesian coordinates to geodetic coordinates within the Ghana Geodetic Reference Network. The seven reverse techniques considered are Simple Iteration, Bowring Inverse equation, method of successive substitution, Paul’s method, Lin and Wang, Newton Raphson and Borkowski’s method. The obtained results were then projected onto the transverse Mercator projection to get the new projected grid coordinates in the Ghana national coordinate system. These results were compared with the existing coordinates to assess their performance. The authors proposed the Paul’s method to be a better fit for the Ghana geodetic reference network based on statistical indicators used to evaluate the reverse methods performance.
机译：加纳是一个发展中国家，在所有测绘活动中，仍采用非地心椭球体（称为1926年战争办公室）作为其水平基准面。目前，加纳土地委员会的测绘处已采用卫星定位技术，例如基于地心椭球的全球定位系统（世界大地测量系统1984（WGS84））进行大地测量。因此，有必要在这两个不同的参考系之间建立功能关系。为了完成这一任务，本研究采用Bursa-Wolf变换模型，获得了七个变换参数。三个平移，三个旋转和一个比例因子。然后使用这些参数将WGS84数据转换为War office系统。但是，加纳的国家坐标系是投影的网格坐标，因此，新获得的战争办公室坐标（X，Y，Z）不适用。因此，需要将这些坐标投影到加纳的横向墨卡托上。为此，必须首先将获得的新的战争办公室数据（X，Y，Z）转换为大地坐标。从笛卡尔（X，Y，Z）到其对应的大地坐标（φ，λ，h）的逆向转换相对于大地纬度和高度的估计来说是计算密集的。这项研究旨在评估在加纳大地参考网络中从笛卡尔坐标转换到大地坐标的七种方法的性能。考虑的7种反向技术分别为：简单迭代，Bowring逆方程，连续替换方法，Paul方法，Lin和Wang，Newton Raphson和Borkowski方法。然后将获得的结果投影到墨卡托横向投影上，以在加纳国家坐标系中获得新的投影网格坐标。将这些结果与现有坐标进行比较以评估其性能。作者基于用于评估反演方法性能的统计指标，提出了Paul的方法更适合加纳大地测量参考网络。

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