高斯投影长度比和子午线收敛角公式改化  

Modification of Gaussian projection length ratio and meridian convergence angle

作　　者：汪绍航 李厚朴[1] 金立新 卞鸿巍[1] WANG Shaohang;LI Houpu;JIN Lixin;BIAN Hongwei(Department of Navigation,Naval University of Engineering,Wuhan 430033,China;The General Engineering Survey Institute of Railways of Gansu Co.Ltd.,Lanzhou 730000,China)

机构地区：[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

出　　处：《海洋测绘》2021年第5期32-36,共5页Hydrographic Surveying and Charting

基　　金：国家自然科学基金(41876222,41871376,41971416);湖北省杰出青年科学基金(2019CFA086)。

摘　　要：为导出兼顾高精度与形式直观的高斯投影长度比与子午线收敛角公式,借助球面情况下的高斯投影正算、投影长度比、子午线收敛角公式都为闭合公式的优点,利用传统椭球面高斯投影公式对其进行适当改化。改化后以球面高斯投影闭合公式为主项,将改化项附加在主项后,得到改化后的高斯投影长度比和子午线收敛角公式,且改化项直观反映了球面高斯投影和椭球面高斯投影之间的差值关系,能一定程度上体现两者之间的内在联系。经算例验证,在高斯投影分带内,该改化公式兼具精度高、适应性好、表示形式简单的特点。In order to derive the formula of Gaussian projection length ratio and meridian convergence angle with both high precision and intuitive form, with the help of closed formulas of the positive calculation of Gaussian projection, projection length ratio and meridian convergence angle in the case of a spherical surface, use the traditional ellipsoidal Gaussian projection formula to modify it appropriately.After the modification, the spherical Gaussian projection closed formula is used as the main item, and the modified item is appended to the main item to obtain the modified Gaussian projection length ratio and the meridian convergence angle formula, and the modified item intuitively reflects the difference relationship between the spherical Gaussian projection and the ellipsoidal Gaussian projection, and can reflect the internal connection between the two to a certain extent.The calculation example shows that in the Gaussian projection sub-band, the modified formula obtained in this paper has the characteristics of high accuracy, good adaptability and simple representation.

关 键 词：球面高斯投影 椭球面高斯投影 投影正算公式 长度比 子午线收敛角 投影公式改化 

分 类 号：P282[天文地球—地图制图学与地理信息工程]