基于改进的预处理共轭梯度法和三维插值法精确和快速解算GRACE地球重力场

Accurate and rapid determination of the GRACE Earth's gravitational field using the improved pre-conditioned conjugate-gradient approach and three-dimensional interpolation method

本文首先对比分析了基于直接最小二乘法(DLSP),预处理共轭梯度法(PCCG)和三维插值法(TDIM)解算卫星观测方程的优缺点;其次,基于能量守恒法分别利用改进的PCCG和TDIM反演了120阶GRACE地球重力场,在120阶处累计大地水准面精度为17.316 cm和15.421 cm;最后,通过和德国波兹坦地学研究中心(GFZ)公布的EIGEN-GRACE02S地球重力场模型的符合性验证了基于PCCG和TDIM解算高精度和高空间分辨率地球重力场的有效性,同时提出TDIM可作为将来有效解算中高频地球重力场(如GRACE Follow-On,360阶)的优选方法之一.

Firstly, the advantages and disadvantages of calculating satellite observation equation using the Direct Least-Squares Principle （DLSP）, Pre-Conditioned Conjugate-Gradient approach （PCCG） and Three-Dimensional Interpolation Method （TDIM） are comparatively analyzed. Secondly, the GRACE Earth＇s gravitational field completed up to degree and order 120 is recovered using the PCCG and TDIM based on the energy conservation principle, and cumulative geoid height errors are 17. 316 cm and 15.421 cm at the degree 120, respectively. Finally, the availability of the high-accuracy and high-resolution Earth＇s gravitational field recovery based on the PCCG and TDIM is verified by preferably according with the Earthrs gravitational field model EIGEN-GRACE02S released bythe German GeoForsehungsZentrum Potsdam （GFZ）, and the TDIM will promisingly be one of the future optimal methods in the efficient measurement of the medium-high frequency Earth＇s gravitational field （e. g. GRACE Follow- On, 360 degrees）.