大地测量与地球动力学2026，Vol.46Issue(9)：1039-1045,7.DOI:10.14075/j.jgg.2026.02.043
子午线弧长多项式函数模型的最小二乘估计
Least Squares Method for Polynomial Function Model of Meridian Arc Length
摘要
Abstract
To address the limitations of the algebraic expansion of the meridian arc length,this study is based on the principles of equivalent transformation and order-increment invariance.Using the first ec-centricity or the third flattening,this study reconstructs polynomial function models for the meridian arc length and the meridian radius of curvature,respectively.Additionally,a constrained least squares method is derived for the direct estimation of the model constant coefficients.The results indicate that,regardless of whether the first eccentricity or the third flattening is used,the polynomial func-tion models facilitate the high-order expansion and correctness verification of the algebraic expansion of the meridian arc length.Furthermore,their estimation accuracy can meet the requirements of prac-tical applications such as high-precision geodesy and map projection.关键词
子午线弧长/代数展开式/阶次递增不变性/多项式函数模型/最小二乘Key words
meridian arc length/algebraic expansion/order-increment invariance/polynomial function model/least squares分类
天文与地球科学引用本文复制引用
刘志平,苗路政,庄乾乐,沈瑞虹..子午线弧长多项式函数模型的最小二乘估计[J].大地测量与地球动力学,2026,46(9):1039-1045,7.基金项目
国家自然科学基金(42404016,42271460). （42404016,42271460）
