全球定位系统2026，Vol.51Issue(4)：47-54,8.DOI:10.12265/j.gnss.2026195
长波甚长波定位中大地线正解的符号迭代法
Symbolic iterative method for forward solution of geodetic line in long-wave and very long-wave positioning
摘要
Abstract
Based on the geometric definitions of geodetic line and the Bessel projection on an ellipsoid,this paper establishes a unified notation system to resolve previous inconsistencies.Using computer algebra and the concept of symbolic iteration,a direct expression for the forward solution of the geodetic line is derived.This approach offers a simplified,non-iterative representation of the geodetic line,eliminating the need for repeated numerical iterations in subsequent calculations.Consequently,three equivalent formulations of the exact direct solution are presented.Numerical experiments show that,compared to conventional iterative methods,the computational error in long-distance geodetic lines remains below 0.6 m,meeting the accuracy demands of high-precision applications.Validation using the long-wave navigation stations in Dunhuang,Naqu,and Korla further demonstrates the practicality of the proposed algorithm,as evidenced by verifying the exact solution for a 1 000 km geodetic line.关键词
长波及甚长波定位/符号迭代法/大地线/计算机代数/验证分析Key words
long-wave and very long-wave positioning/symbolic iteration method/geodetic line/computer algebra/verification analysis分类
天文与地球科学引用本文复制引用
周东权,边少锋,李兆权..长波甚长波定位中大地线正解的符号迭代法[J].全球定位系统,2026,51(4):47-54,8.基金项目
国家自然科学基金(42430101) （42430101）
