三轴椭球上笛卡尔坐标到大地坐标的直接变换
Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid
摘要：
本文提出了两种将直角坐标转换为大地坐标的新的符号-数值直接算法。在这两个算法的问题是减少到寻找一个真正的正根的六次多项式。第一种方法包括代数操作的方程描述的几何问题和第二个使用Gröbner基地。为了进行数值试验和准确地比较效率和可靠性，我们的算法与M。Ligas（2012）和J. Feltens（2009）已经在C++中实现。数值试验已经完成，考虑10个天体，在现有的文献中引用。所得到的结果清楚地表明，我们的算法改进了上述迭代法，在效率和精度方面。
英文摘要：
This paper presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxial reference ellipsoid. The problem in both algorithms is reduced to finding a real positive root of a sixth degree polynomial. The first approach consists of algebraic manipulations of the equations describing the geometry of the problem and the second one uses Gröbner bases. In order to perform numerical tests and accurately compare efficiency and reliability, our algorithms together with the iterative methods presented by M. Ligas (2012) and J. Feltens (2009) have been implemented in C++. The numerical tests have been accomplished by considering 10 celestial bodies, referenced in the available literature. The obtained results clearly show that our algorithms improve the aforementioned iterative methods, in terms of both efficiency and accuracy.
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