基于Romberg积分与牛顿迭代的高斯投影坐标正反算算法  

Algorithm of Gaussian Projection Coordinate Forward and Backward Calculation Based on Romberg Integration and Newton Iteration Method

作　　者：翟高鹏 李文彬 ZHAI Gaopeng;LI Wenbin(Quality Supervision and Inspection of Surveying and Mapping Products Station of Hebei Province,Shijiazhuang 050031,China;Institute of Land Resource and Urban and Rural Planning,Hebei GEO University,Shijiazhuang 050031,China)

机构地区：[1]河北省测绘产品质量监督检验站,河北石家庄050031 [2]河北地质大学土地资源与城乡规划学院,河北石家庄050031

出　　处：《测绘地理信息》2020年第5期51-53,共3页Journal of Geomatics

基　　金：国家自然科学基金(41774032)。

摘　　要：提出一种基于Romberg积分和牛顿迭代的高斯投影坐标正反算算法,对子午线弧长数学模型进行求解,由子午线弧长数学模型构造求底点纬度的牛顿迭代算法。通过C#编程实现了高斯投影坐标正反算,并用一组模拟数据对其计算结果的精度进行了验证。经实例验证,该算法计算精度可靠,能够满足高斯投影坐标正反算工作需求。The forward and backward calculation of Gaussian projection coordinates is an important surveying problem in geodesy. In this paper, an algorithm of forward and backward calculation of Gaussian projection coordinates based on Romberg integral and Newton iteration is proposed to solve the methematic model of the meridian arc length. Newton iterative algorithm for calculating the latitude of the bottom point is constructed by the solution of methematic model of the meridian arc length via Romberg integral, the forward and backward calculation of Gaussian projection coordinates program is realized by C # programming, and the accuracy of calculation results is verified by simulation data. It has been proved that the algorithm is accurate, reliable and can meet the requirements of forward and backward calculation of Gaussian projection coordinates.

关 键 词：子午线弧长 底点纬度 Romberg积分 牛顿迭代 

分 类 号：P226[天文地球—大地测量学与测量工程]