极区不分带高斯投影的正反解表达式

doi:10.11947/j.AGCS.2017.20170009

测绘学报 ›› 2017, Vol. 46 ›› Issue (6): 780-788.doi: 10.11947/j.AGCS.2017.20170009

极区不分带高斯投影的正反解表达式

李忠美¹, 边少锋¹, 金立新^2,3, 陈成¹, 刘强^1,4

1. 海军工程大学导航工程系, 湖北武汉 430033;
2. 甘肃铁道综合工程勘察院有限公司, 甘肃兰州 730000;
3. 中铁第一勘察设计院集团有限公司, 陕西西安 710043;
4. 海军驻天津地区航保军事代表室, 天津 300042

收稿日期:2017-01-05 修回日期:2017-05-10 出版日期:2017-06-20 发布日期:2017-06-28
通讯作者: 边少锋 E-mail:sfbian@sina.com
作者简介:李忠美(1990—),女,博士生,主要研究方向为海图投影理论。E-mail:15827116839@163.com
基金资助:
国家自然科学基金（41631072；41604010；41574009）

Forward and Inverse Expressions of Polar Gauss Projection without Zoning Limitations

LI Zhongmei¹, BIAN Shaofeng¹, JIN Lixin^2,3, CHEN Cheng¹, LIU Qiang^1,4

1. Department of Navigation, Naval University of Engineering, Wuhan 430033, China;
2. The General Engineering Survey Institute of Railways of Gansu co., LTD, Lanzhou 730000, China;
3. China Railway First Survey and Design Institute Group co., LTD, Xi'an 710043, China;
4. Military Delegate Office of Naval Navigation Guarantee in Tianjin, Tianjin 300042, China

Received:2017-01-05 Revised:2017-05-10 Online:2017-06-20 Published:2017-06-28
Supported by:
The National Natural Science Foundation of China (Nos. 41631072;41604010;41574009)

摘要/Abstract

摘要： 针对传统高斯投影公式在极区难以应用的问题，通过引入等角余纬度及等量纬度的表达式，推导出严密的复数等角余纬度公式，进而得到严密的极区高斯投影正解表达式；借助符号迭代法及指数函数与三角函数间的关系式，推导出对应的极区高斯投影反解表达式；基于极区高斯投影正解表达式，推导出可用于极区的长度比、子午线收敛角公式；最后，以CGCS2000椭球为例，与实数型幂级数高斯投影公式计算的结果进行对比，验证了本文推导公式的正确性。由于本文推导公式不受带宽限制，且可用于整个极区的表示，对于编制极区地图及极区导航具有重要的参考价值。

关键词: 高斯投影, 极区, 正反解, 长度比, 子午线收敛角

Abstract: As traditional formulae of Gauss projection could not be used in polar regions, strict equation of complex conformal colatitude was derived with relationship between conformal colatitude and isometric latitude introduced, and then strict forward expressions of Gauss projection suit for polar regions were carried out. Based on relationship between exponential and trigonometric functions, inverse expressions of polar Gauss projection were derived by means of symbol iteration method. With reference to the forward expressions, corresponding equations of length ratio and meridian convergence for polar Gauss projection were achieved. Finally, Taking CGCS2000 ellipsoid for example, by comparing with results calculated by formulae of Gauss projection in power series forms, correctness of the proposed expressions was verified. Expressions in this paper are all free from bandwidth, and can be used in the entire poles, which could provide important references for polar mapping and navigation.

Key words: Gauss projection, polar region, forward and inverse solution, length ratio, meridian convergence angle

中图分类号:

P282.1

李忠美, 边少锋, 金立新, 陈成, 刘强. 极区不分带高斯投影的正反解表达式[J]. 测绘学报, 2017, 46(6): 780-788.

LI Zhongmei, BIAN Shaofeng, JIN Lixin, CHEN Cheng, LIU Qiang. Forward and Inverse Expressions of Polar Gauss Projection without Zoning Limitations[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(6): 780-788.

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极区不分带高斯投影的正反解表达式

Forward and Inverse Expressions of Polar Gauss Projection without Zoning Limitations

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