子午线弧长多项式函数模型的最小二乘估计OA

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.