大地主题解算实用算法

A Practical Algorithm for Solution of Geodetic Problem

针对目前大地主题解算中普遍存在的计算结果奇异、象限判断复杂和适用范围受限等问题,在综合高斯平均引数公式、巴乌曼投影公式、贝塞尔公式和文森特公式等多个解算公式优缺点的基础上,应用球面三角原理和文森特公式嵌套系数思想,兼顾计算机数值计算的应用,重新推算大地主题解算过程,提出正算和反算实用算法。该算法无奇异、适用任意距离,可直接应用于电算化编程实现。实际算例结果表明该算法正确、精度高,检核结果在10-12～10-16之间。

Aiming at common problems with current solution of geodetic problems,such as singularity in compute result,complexity in quadrant determining and limitation of application etc.A practical algorithm for direct and inverse solution of geodetic problem is presented.Firstly,both advantage and disadvantage of current formulas were analyzed.Then,applying with spherical triangle theory and Vincenty formula＇s nested coefficient idea,the process of solution of geodetic problem was particular.Lastly,a practical algorithm for direct and inverse solution of geodetic problem was put forward.This algorithm has none singularity value,and is suitable for any distance,and can be applied to program directly.The results of numerical computation show that the algorithm has high validity and precision,and the verified results are in the range of 10-12~10-16.