卫星重力梯度数据确定地球重力场的正则化方法研究

Regularization of the earth gravity field determination using satellite gravity gradiometry data

在卫星重力梯度数据确定地球重力场时,观测数据有色噪声及极空白问题导致法方程呈现病态性.本文基于严密的卫星重力梯度数据确定地球重力场的直接解法,对零次、一次Tikhonov正则化和Kaula正则化等多种正则化技术,以及用于确定正则化参数的L曲线法、GCV法、MSE法等三种方法进行了适用性分析.研究结果表明,Tikhonov正则化和Kaula正则化方法能够有效改善法方程求解的稳定性,提高大地水准面的恢复精度,Kaula正则化方法较之Tikhonov正则化要稍优.以大地水准面误差均方差最小为标准,GCV方法的精度要优于L曲线法,更适于卫星重力梯度实测数据的解算.

When determining the earth's gravity field using the satellite gravity gradiometry data,the normal equation is illconditioned because of the colored noise and the polar gaps in the observation data.In the paper,using the direct approach of the earth's gravity field determination with satellite gravity gradiometry data,the zero-order,the first-order Tikhonov regularization and Kaula regularization,as well as the three methods of determining the regularization parameter including L-curve method,GCV method and MSE method are compared and analyzed in numerical simulation.The results show that,both Tikhonov regularization and Kaula regularization could effectively improve the solution stability of the normal equation and the recovery accuracy of the geoid.The solution after Kaula regularization is slightly better than that after Tikhonov regularization.According to the minimum mean square error of the geoid,the accuracy of the GCV method is better than the L-curve method,which is more suitable for the processing of the real satellite gravity gradiometry data.