块对角最小二乘方法在确定全球重力场模型中的应用

摘要

分析研究最小二乘求解重力场模型的6种位系数排列方式下的块对角形态及3种不同条件下的块对角近似：BD-1、BD-2、BD-3,探讨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。试验结果表明,块对角最小二乘方法较之于积分方法,能更好地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。%Six kinds 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 illustrates that, with the global terrestrial gravity data and the satellite gravity field model whose accuracy is 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.