椭球大地测量常用幂级数的第三扁率展开  

The Third Flattening Expansion of Power Series Commonly Used in Ellipsoid Geodesy

作　　者：汪绍航 边少锋[1] 金立新 叶彤 WANG Shaohang;BIAN Shaofeng;JIN Lixin;YE Tong(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,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：《测绘科学技术学报》2021年第6期571-578,共8页Journal of Geomatics Science and Technology

基　　金：国家自然科学基金项目(41876222,41971416,42074010);湖北省杰出青年科学基金项目(2019CFA086)。

摘　　要：针对椭球大地测量中以第一偏心率为e参数的幂级数展开式收敛速度慢、形式繁杂冗长的问题,以第三扁率n代替e作为辅助参数对部分常用幂级数展开式进行重新推导,并将结果展至n^(6)。算例分析表明:以n为参数推导所得的6种辅助纬度及复变高斯投影展开式展至n^(6)时,精度达到(10^(-13))″,优于以e为参数的展开式展至e^(12),收敛速度提升明显;且大地纬度、地心纬度和归化纬度间计算展开式由以e的幂级数形式变为以n的确定形式,关系更加严密、形式更为直观。Aimed at the problem of slow convergence speed and complicated and long form of the power series expansion with the first eccentricity e as the parameter in ellipsoid geodesy,the third flattening n is used as an auxiliary parameter to re-derive some common power series expansions and the result is expanded to n^(6).The analysis of the calculation example shows that the accuracy reaches(10^(-13))″when the expansions of 6 auxiliary latitudes and Gauss projection based on complex function derived from n as the parameter are expanded to n^(6) which is better than that of the expansion with e as the parameter to e^(12),and the convergence speed is significantly improved.The calculation expansion formula between geodetic latitude,geocentric latitude and reduced latitude is changed from a power series of e to a definite form of n,so then the relationship is more rigorous and the form is more intuitive.

关 键 词：椭球大地测量 第三扁率 第一偏心率 辅助纬度 复变高斯投影 幂级数展开式 

分 类 号：P282[天文地球—地图制图学与地理信息工程]