联合GOCE卫星轨道和重力梯度数据严密求解重力场的模拟研究

Simulation Study of Rigorous Gravity Field Recovery by Combining GOCE Satellite Orbit and Gravity Gradient Data

论述了联合卫星轨道和重力梯度数据严密求解重力场的方法及数据处理方案,研究了GOCE重力场反演中有色噪声的AR去相关滤波、病态法方程的Kaula正则化和观测值最优加权的方差分量估计等关键问题。模拟结果表明:①极空白问题会降低法方程求解的稳定性,导致低次位系数的求解精度较低,而Kaula正则化可有效用于GOCE病态法方程的求解,并得到合理稳定的解;②重力梯度有色噪声会降低GOCE重力场求解的整体精度,特别是对低阶位系数的影响最为明显,而AR去相关滤波法可有效处理有色噪声,但解算结果仍含有低频误差;③方差分量估计可有效确定SST和SGG两类观测值的最优权比,并且有色噪声造成的低频误差经过联合求解后得到了抑制;④利用30d、5s采样的GOCE模拟数据恢复200阶次的重力场模型,其大地水准面和重力异常精度在纬度±83°范围内分别为±3.81cm和±1.056mGal。

The combined adjustment method and its data processing scheme for rigorous gravity field recovery by combining GOCE satellite orbit and gravity gradient data are discussed.The AR decorrelation filtering method for processing of colored noise,Kaula regularization method for solving the morbid normal equations,and variance component estimation（VCE） method for determining the optimal weight of SST and SGG data are studied.The results show that： Firstly,the polar gaps of SGG data will decrease the stability of the solution,and lead to a lower accuracy of low-order geopotential coefficients.Kaula regularization can be effectively used to solve the GOCE morbid equations and obtain a stable solution.Secondly,SGG colored noises degrade the total accuracy of GOCE gravity field model,especially for the low-degree of geopotential coefficients.The AR decorrelation filtering can handle the colored noise,but the solution still contains significant low-frequency errors.Thirdly,the VCE method can effectively determine the optimal weights of SST and SGG data,and it shows that the low-frequency errors caused by colored noise are effectively inhibited.Finally,the GOCE gravity field with degree of 200 is recovered from 30 days of simulated GOCE data with 5s sampling interval,and its accuracy of geoid heights and gravity anomalies between±83°latitude areas are ±3.81 cm and ±1.056 mGal,respectively.