Simplified Expansions of Common Latitudes with Geodetic Latitude and Geocentric Latitude as Variables
Simplified Expansions of Common Latitudes with Geodetic Latitude and Geocentric Latitude as Variables
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DOI：
10.3390/app12157818
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
Xiaoyong Li;Houpu Li;Guohui Liu;S. Bian;Chenchen Jiao
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文献类型：
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作者：
Xiaoyong Li;Houpu Li;Guohui Liu;S. Bian;Chenchen Jiao
利用符号计算程序Mathematica，基于以大地纬度为变量的公纬度幂级数展开式，推导了以地心纬度为变量的公纬度幂级数展开式。两组公式的系数均基于椭球偏心率e和椭球三次扁率n，使得膨胀更加均匀。以CGCS2000为例，通过数值分析验证了推导的幂级数展开式的准确性和可靠性。通过分析计算基于椭球偏心率e和不同阶次的三次压扁n展开的公纬度截断误差，得到了满足测地精度要求的简化、实用的公纬度公式。此外，我们还表明，推导的实用公式具有更高的计算效率和更易于传播，丰富了地图投影理论，为更好地显示遥感图像提供了基础。
Using the symbolic calculation program Mathematica and based on the power series expansions of the common latitude with geodetic latitude as a variable, power series expansions of the common latitude with geocentric latitude as the variable are derived. The coefficients of the two groups of formulas are based on the ellipsoid eccentricity e and the ellipsoid third flattening n, which make the expansions more uniform. Taking the CGCS2000 as an example, numerical analysis is applied to verify the accuracy and reliability of the derived power series expansions. By analyzing and calculating the truncation error of the common latitude based on ellipsoidal eccentricity e and the third flattening n expansion to different orders, we obtain simplified, practical formulas for the common latitude that satisfy the requirement of geodesic accuracy. Moreover, we show that the practical formula derived has higher calculation efficiency and easier dissemination, enriches the theory of map projection, and provides a basis for better display of remote sensing images.