| 子午线弧长公式的简化及其泰勒级数解释 |
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| 引用本文： | 过家春.子午线弧长公式的简化及其泰勒级数解释[J].测绘学报,2014,43(2):125. |
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| 作者姓名： | 过家春 |
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| 作者单位： | 安徽农业大学 |
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| 基金项目： | 江西省数字国土重点实验室开放研究基金(DLLJ201211);安徽农业大学学科学位点建设项目(XKXWD2013022) |
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| 摘 要： | 通过引入椭球的第三扁率及高斯超几何函数，推导得到子午线弧长解算公式的简化形式，并给出其泰勒级数解释，进而根据拉格朗日余项理论估计其误差。以WGS-84椭球参数为例进行验证分析，结果表明简化后的子午线弧长公式精度提高显著，误差估计理论正确。
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| 关 键 词： | 子午线弧长 第三扁率 高斯超几何函数 泰勒级数 误差估计 |
| 收稿时间： | 2012-12-10 |
| 修稿时间： | 2013-01-27 |
A Simplification of The Meridian Formula and Its Taylor-series Interpretation |
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| Abstract: | A more concise formula of the meridian arc length was obtained by introduced two new parameters: the third flattening and the Gauss hypergeometric function. From another perspective, the simplified formula is also can be explained by a Taylor series expansion. By this, we got error estimate of the formula in terms of the Lagrange form of the remainder. For numerical verification of the error estimate theory, application example was presented by using the WGS84 data. The results show that experimental data are consistent with the error estimate theory and the simplified formula is more precise than the standard one. |
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