A Tikhonov regularization method to estimate Earth's oblateness variations from global GPS observations

Earth's oblateness is varying due to the redistribution of Earth's fluid mass and the interaction of various components in the Earth system. Nowadays, continuous Global Positioning System (GPS) observations can estimate Earth's oblateness (J2) variations with the least squares method, but are subject to ill-conditioned equations with limited GPS observations and aliasing errors from truncated degrees. In this paper, a Tikhonov regularization method is used to estimate J2 variations from global continuous GPS observations. Results show that the J2 has been better estimated from GPS observations based on a Tikhonov regularization method than the usual least squares method when compared to SLR solutions. Furthermore, the amplitudes and phases of the annual and semi-annual J2 variations are closer to the SLR results with truncated degrees from 2 to 5. Higher truncated degrees will degrade the J2 estimate. Annual J2 variations are best estimated from GPS observations with truncated degree 4 and semi-annual J2 variations are best estimated with truncated degree 2.