| 子午线弧长的计算方法及精度分析 |
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| 引用本文： | 刘学杰,杨丽坤.子午线弧长的计算方法及精度分析[J].测绘通报,2017,0(8):106. |
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| 作者姓名： | 刘学杰 杨丽坤 |
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| 作者单位： | 1. 河南省中纬测绘规划信息工程有限公司, 河南 焦作 454000;2. 郑州工业贸易学校, 河南 郑州 450007 |
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| 基金项目： | 2016年国家重点研发计划，河南省高校创新团队支持计划，河南省创新型科技创新团队支持计划 |
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| 摘 要： | 计算子午线弧长除了采用经典的级数展开算法之外，还可通过数值积分与常微分方程数值解法进行求解。为评价各种算法的精度，本文选取大地纬度自0°-90°、间隔距离为1°、1'、1″的3组样本数据，分别基于传统算法、数值积分算法和常微分方程数值算法3大类11种算法计算得到各组样本所对应的子午线弧长结果，并从算法精度和运算速度两个方面对各种数值算法进行了分析与评价。实例表明三阶、四阶Runge-Kutta算法不仅精度高，而且运算效率是其他算法的2倍多，研究结果为计算子午线弧长的提供了有效的算法模型。
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| 关 键 词： | 子午线弧长 数值积分 常微分方程 展开算法 |
| 收稿时间： | 2017-02-20 |
Calculation Methods and Accuracy Analysis of Meridian Arc Length |
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| LIU Xuejie,YANG Likun.Calculation Methods and Accuracy Analysis of Meridian Arc Length[J].Bulletin of Surveying and Mapping,2017,0(8):106. |
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| Authors: | LIU Xuejie YANG Likun |
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| Institution: | 1. Zhongwei Surveying and Planning Information Engineering Co., Ltd. of Henan Province, Jiaozuo 454000, China;2. Zhengzhou Industry and Trade School, Zhengzhou 450007, China |
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| Abstract: | There are several kinds of algorithms for calculating the meridian arc length except the classical expanded algorithm, such as numerical integration and ordinary differential equations numerical solution.In order to study the accuracy of each algorithm, this paper selected 3 sets of sample data within the geodetic latitude from 0° to 90°, whose intervals are 1°,1′,1″, respectively.Based on the traditional expanded algorithms, numerical integral algorithms and numerical solution of ordinary differential equations, the corresponding meridian arc length results were calculated and the quality of each numerical algorithm with regard to algorithm accuracy and computation speed were evaluated.The results show that the 3 and 4 order Runge-Kutta algorithm not only have high precision but the computing speed is twice more than other algorithms.This paper provides new, reliable algorithm with high speed for meridian arc length calculation.The results provide an effective algorithm for calculating the meridian arc length. |
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| Keywords: | meridian arc length numerical integral ordinary differential equations expanded algorithm |
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