关键词: 最小二乘配置法, 大地水准面, Tikhonov正则化法, GCV法

Abstract:

LSC method (least squares collocation method) attracted widespread attention due to the integration of different types of gravity observation data to determine the geoid. But the observation errors are amplified by the small singular values of the ill-posed covariance matrix, leading to the unstable and low-accuracy collocation results. This paper proposed the Tikhonov-LSC method, namely in the LSC method to introduce the Tikhonov regularization algorithm, based on the GCV method to select the regularization parameter of the covariance matrix, and using the parameter to modify the small singular values of the ill-posed covariance matrix, in order to inhibit its observational error amplification impact. Using the Tikhonov_LSC method to determining the Geoid can effectively improve the stability and accuracy. The experiments using gravity anomalies based on the EGM2008 in three different regions such as mountainous region, hill and ocean region to determine the geoid verify the validity of the method.

Key words: Least-squares combination, Geoid, Tikhonov regulation algorithm, GCV method