航空重力向下延拓病态问题的求解

提出将广义岭估计用于求解航空重力向下延拓病态问题，研究了求解逆Poisson积分问题的3种正则化方法：Tikhonov正则化、岭估计和广义岭估计。利用EGM2008地球位模型设计模拟数值实验，将飞行高度处含白噪声的2.5′×2.5′重力扰动向下延拓至大地水准面上，与参考值作外部检验，全面检验、比较了各向下延拓方法的可靠性、精度和稳定性，数值结果表明基于多个最优正则化参数的广义岭估计在延拓精度、稳定性和抗差性等方面要显著优于基于单个正则化参数的Tikhonov法和岭估计。

Solution of Ill-posed Problem in Downward Continuation of Airborne Gravity

Generalized ridge estimate is suggested for solving the ill-posed problem in downward continuation(DWC) of airborne gravity.Three regularization methods are studied to solve the inverse Poisson problem,which are Tikhonov regularization,ridge estimate and generalized ridge estimate.By conducting a simulated numerical experiment designed based on EGM2008 Earth gravitational model,the 2.5′×2.5′gravity disturbances with white noise at the flight levels are downward continued to the Geoid.The accuracy and stability of the DWC methods are tested and compared.The numerical results show that,in terms of continued accuracy,stability and robustness,the generalized ridge estimate based on multiple optimal regularization parameters performs significantly well.