测绘学报 ›› 2014, Vol. 43 ›› Issue (8): 778-785.

• 学术论文 • 上一篇    下一篇

块对角最小二乘方法在确定全球重力场模型中的应用

李新星1,吴晓平1,李姗姗2,刘晓刚3,崔志伟4   

  1. 1. 解放军信息工程大学地理空间信息学院
    2. 信息工程大学测绘学院
    3. 西安测绘研究所
    4. 解放军61206部队
  • 收稿日期:2013-12-06 修回日期:2014-05-12 出版日期:2014-08-20 发布日期:2014-08-27
  • 通讯作者: 李新星 E-mail:minibad@126.com

The Application of Block-diagonal Least-squares Methods in Geopotential Model Determination

  • Received:2013-12-06 Revised:2014-05-12 Online:2014-08-20 Published:2014-08-27

摘要:

分析研究了最小二乘求解重力场模型的六种位系数排列方式下的块对角形态及三种不同条件下的块对角近似:BD-1、BD-2、BD-3,探讨了块对角最小二乘方法在联合早期卫星重力场模型和最新GRACE-only模型中的应用,通过实验计算,结果表明,块对角最小二乘方法较之于积分方法,能更好的提高所恢复模型的精度,说明在卫星重力飞速发展、地面重力数据不断完善的今天,块对角最小二乘法在超高阶地球重力场模型构建方面的优势逐渐突出。

关键词: 块对角矩阵, 最小二乘, 超高阶地球重力场模型, EGM2008, 正交性

Abstract:

Six kind of permutations of spherical harmonic coefficients and their block diagonal form of corresponding normal matrixes were studied as well as three kinds of approximation BDs: BD-1, BD-2, BD-3. The application of block-diagonal least-squares methods in geopotential model determination was analyzed and its advantage to quadrature formulas was showed by a simulated calculation. It illustrated that, with the global terrestrial gravity data and the satellite gravity field model whose accuracy was being improved continuously, block-diagonal least-squares methods are playing an increasingly important role in the calculation of the ultra-high-degree gravity field model.

Key words: block-diagonal, least-squares, ultra-high-degree geopotential model determination, EGM2008, orthogonality

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