引用本文: 刘文超, 温朝江, 卞鸿巍, 郑小兵. 利用双重投影改进横墨卡托投影极区应用方法[J]. 武汉大学学报 ( 信息科学版), 2019, 44(8): 1138-1143.
LIU Wenchao, WEN Chaojiang, BIAN Hongwei, ZHENG Xiaobing. An Improved Method of Polar Ellipsoid Transverse Mercator Projection Based on Double Projection[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1138-1143.
 Citation: LIU Wenchao, WEN Chaojiang, BIAN Hongwei, ZHENG Xiaobing. An Improved Method of Polar Ellipsoid Transverse Mercator Projection Based on Double Projection[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1138-1143.

## An Improved Method of Polar Ellipsoid Transverse Mercator Projection Based on Double Projection

• 摘要: 针对球体横墨卡托投影与基于地球椭球体的导航设备结合使用存在误差以及传统椭球横墨卡托投影依据经差分带不适用于极区的问题，在分析双重投影可用于极区存在计算奇异和计算溢出问题的基础上，研究了一种基于双重投影的横墨卡托投影极区应用改进方法。首先利用函数等效变换和经线长度比计算公式推导出椭球投影到球体上的坐标变换、球体半径和长度比计算公式，然后利用分段函数的方法研究了球体横墨卡托投影计算公式，综合两个阶段给出了完整的坐标变换公式和长度比计算公式，最后推导了子午线收敛角计算公式。理论分析和算例仿真表明，该改进方法能够解决极区投影计算奇异和计算溢出问题，近极点地区长度变形较小，且与导航设备采用的地球模型一致，可消除由于地球模型不同引起的误差，提高航海绘算精度。

Abstract: Due to the problems that there are deviances when sphere transverse Mercator projection and navigation equipment based on ellipsoid are used together and that traditional ellipsoid transverse Mercator projections which are based on longitude difference to zone the regions are not applicable to polar regions, an improved method of transverse Mercator projection based on double projection has been studied on the basis of analyzing the existence of the problems which are calculation singular and overflow when double projection is used. Firstly, equivalent transformation functions and meridian length ratio formula have been used to deduce coordinate transformations of ellipsoid projection on a sphere, radius of the sphere, and the length ratio formula. Then the sphere transverse Mercator projection formula has been generated by using the piecewise function; the complete coordinate transformation formula and the length ratio formula are all derived from the previous stages. Finally, the meridian convergent angle formula is deduced. From theoretical analysis and simulations, the improved method can solve the problems of calculation singular and overflow. The length deformation when the areas are near the poles is relatively small and it is in accordance with the earth model adopted by the navigation equipment, which can remove the deviances caused by the different earth models and improve the precision of navigation plotting.

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