子午线弧长的计算方法及精度分析
发布时间：2019-05-29 10:39
【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。
[Abstract]:In addition to the classical series expansion algorithm, the meridian arc length can also be solved by numerical integration and numerical solution of ordinary differential equations. In order to evaluate the accuracy of various algorithms, this paper selects three sets of sample data with latitude from 0 掳to 90 掳and interval distance of 1 掳, 1 掳and 1 ", respectively, based on the traditional algorithm. Numerical integration algorithm and ordinary differential equation numerical algorithm are used to calculate the meridian arc length corresponding to each sample, and the accuracy and speed of the algorithm are analyzed and evaluated. The example shows that the third-order and fourth-order Runge-Kutta algorithms are not only accurate, but also more than twice as efficient as other algorithms. The research results provide an effective algorithm model for calculating meridian arc length.
【作者单位】： 河南省中纬测绘规划信息工程有限公司;郑州工业贸易学校;
【基金】：2016年国家重点研发计划(2016YFC0803103) 河南省高校创新团队支持计划(14IRTSTHN026) 河南省创新型科技创新团队支持计划
【分类号】：P226
本文编号：2487876
[Abstract]:In addition to the classical series expansion algorithm, the meridian arc length can also be solved by numerical integration and numerical solution of ordinary differential equations. In order to evaluate the accuracy of various algorithms, this paper selects three sets of sample data with latitude from 0 掳to 90 掳and interval distance of 1 掳, 1 掳and 1 ", respectively, based on the traditional algorithm. Numerical integration algorithm and ordinary differential equation numerical algorithm are used to calculate the meridian arc length corresponding to each sample, and the accuracy and speed of the algorithm are analyzed and evaluated. The example shows that the third-order and fourth-order Runge-Kutta algorithms are not only accurate, but also more than twice as efficient as other algorithms. The research results provide an effective algorithm model for calculating meridian arc length.
【作者单位】： 河南省中纬测绘规划信息工程有限公司;郑州工业贸易学校;
【基金】：2016年国家重点研发计划(2016YFC0803103) 河南省高校创新团队支持计划(14IRTSTHN026) 河南省创新型科技创新团队支持计划
【分类号】：P226
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，本文编号：2487876
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