基于空域最小二乘法求解GOCE卫星重力场的模拟研究

Simulation Study for Recovering GOCE Satellite Gravity Model Based on Space-wise LS Method

论述最小二乘过程中有色噪声的处理方法,提出使用自回归模型对GOCE梯度观测值中的有色噪声进行时域滤波,数值模拟结果验证该方法的有效性。利用数值模拟验证直接求逆方法和PCCG法求解大型法方程的有效性,后者的效率远远高于前者。联合加入噪声(有色噪声和白噪声)的卫星重力梯度张量径向分量观测值Vzz和SST观测值,分别使用空域最小二乘法和半解析法恢复180阶全球重力场模型,前者求解重力场模型的大地水准面和重力异常在180阶次的精度分别为3.01 cm和0.75 mGal(1 mGal=10-5 m/s2),优于半解析法求解模型的精度。

The approach to deal with the colored noise in space-wiseLSisdiscussed. Theautoregressive（AR） filter is proposed to process the colored noise in the GOCE satellite gravity gradiometry, which is validated by the numerical results. The preconditioned conjugate gradient （PCCG） method and the direct inverse for solving the large normal equation are also verified by the numerical analysis. And the former approach is much faster than the latterone. Combing theradial component Vzz of the simulated gravity gradient tensor with colored noise and SST observation with white noise, the global gravity field model up to degree and order 180 is estimated by the spacewise LS method and thesemi-analytical（SA） approach respectively. The accuracies of geoid and gravity anomaly of the global gravity field model estimated from the space-wise LS method are 3. 01 cm and 0. 75 mGal（1 Gal= l0 ^-2 m/s^2） respectively, which are better than them from the SA approach.