子午线弧长正反解表达式3种形式的解析  

Analysis of three forms of direct and inverse expressions of meridian arc length

作　　者：张晓平 焦晨晨 李厚朴[4] 边少锋[4,5] 张思远 ZHANG Xiaoping;JIAO Chenchen;LI Houpu;BIAN Shaofeng;ZHANG Siyuan(Information Network Center,China University of Geosciences(Beijing),Bejing 100083,China;Research Center of Graphic Communication,Printing and Packaging,Wuhan University,Wuhan 430070;School of Information and Engineering,China University of Geosciences,Wuhan 430074,China;Department of Navigation,Naval University of Engineering,Wuhan 430033,China;Key Laboratory of Geological Survey and Evaluation of Ministry of Education,Wuhan 430074,China)

机构地区：[1]中国地质大学(北京)信息网络中心,北京100083 [2]武汉大学图像传播与印刷包装研究中心,湖北武汉430070 [3]中国地质大学(武汉)地理与信息工程学院,湖北武汉430074 [4]海军工程大学导航工程系,湖北武汉430033 [5]中国地质大学(武汉)地质探测与评估教育部重点实验室,湖北武汉430074

出　　处：《海洋测绘》2023年第6期70-76,共7页Hydrographic Surveying and Charting

基　　金：国家优秀青年科学基金(42122025);国家自然科学基金(41971416;42074010);中国地质大学(北京)学科发展研究基金(2022XK207)。

摘　　要：为了分析不同表达式在计算效率方面的影响,给出了子午线弧长的3种表达形式,将其展开系数改写为第三扁率n的表达形式,并对不同形式的子午线弧长的截断误差进行计算分析,选取合适的项数,给出展开式的实用公式。结果表明,基于n表示的子午线弧长,其系数在分数形式上看起来位数更少,形式更简单,更便于推广使用;当正解精度为毫米时,展开式只需保留前4项即可满足精度,当反解精度为0.0001″时,展开式只需保留前4项即可满足精度;对于3种表达形式,二倍角形式计算效率最高,因此建议在子午线弧长正反解过程中采用二倍角形式。In order to analyze the influence of different expressions on the computational efficiency,three expressions of the meridian arc length are given in this paper.The expansion coefficients are rewritten as the third flattening n.The truncation errors of different forms of meridian arc length are calculated and analyzed,the appropriate terms are selected and the practical formulas of the expansion are given.The results show that the coefficients in the direct and inverse of the meridian arc length based on n have fewer digits in the numerical value,more concise form,and are more convenient for popularization and application.When the accuracy of the direct expression is millimeter,the expansion only needs to keep the first four items.When the inverse solution accuracy is 0.0001",the expansion only needs to keep the first four items to satisfy the accuracy.For the three expressions,the double-angle form has higher computational efficiency.Therefore,it is recommended to use the double-angle form in the process of the positive and negative solutions of the meridian arc length.

关 键 词：大地测量 子午线弧长 第三扁率 截断误差 3种表达式 

分 类 号：P282[天文地球—地图制图学与地理信息工程]