重力场数学拟合模型解的影响因素探究  

Exploration of influence factors on solution of gravitational field mathematical fitting models

作　　者：鹿荻 陈锴 

机构地区：[1]贵阳市测绘院,贵阳550000 [2]贵州毕节经济开发区规划建设局,贵州毕节551700

出　　处：《测绘科学》2016年第3期28-33,共6页Science of Surveying and Mapping

摘　　要：为了提高地球重力场模型不适定方程求解的精度,该文采用谱分析方法从级数展开阶数、数据采样率及数据缺失量3个方面探索影响数学拟合效果的根本因素:从常用的三角级数及勒让德级数模型出发,引出重力场拟合模型球谐函数模型,观察在改变级数展开阶数、数据采样率及数据缺失量等情况下所对应设计矩阵谱结构的变化,并从微观上研究影响误差分配的有关因素及最小奇异值对误差的决定性作用,为探求重力场模型解不准的原因及实现更高精度的全球重力场模型的建立提供参考。In order to improve the solution accuracy of ill-posed functions of the Global Gravitational Field, the paper adopted the spectrum analysis method to explore the basic factors which affect the fitting effect from the following three aspects, series expansion order, data sampling rate and the amount of data missing： from trigonometric series and Legendre series, the spherical harmonic model always used in gravitational field mathematical fitting was introduced, the spectrum structure changes of design matrix while changing series expansion order, sampling rate or the amount of data missing were observed, and the relevant factors that influence the error distribution and the decisive role of least singular value were discussed in a microscopically way, which would provide a reference for exploring the reason that the gravitational field model was not accurately determined and achieving higher accuracy in global gravitation- al field model constructing.

关 键 词：不适定问题 地球重力场 球谐函数 谱结构 误差分配 

分 类 号：P223.0[天文地球—大地测量学与测量工程]