Error analysis for satellite gravity field determination based on   two-dimensional Fourier methods
  The time-wise and space-wise approaches are generally applied to data processing and error analysis for satellite gravimetry missions. But both the approaches, which are based on least-squares collocation, address the whole effect of measurement errors and estimate the resolution of gravity field models mainly from a numerical point of indirect view. Moreover, requirement for higher accuracy and resolution gravity field models could make the computation more difficult, and serious numerical instabilities arise. In order to overcome the problems, this study focuses on constructing a direct relationship between power spectral density of the satellite gravimetry measurements and coefficients of the Earth's gravity potential. Based on two-dimensional Fourier transform, the relationship is analytically concluded. By taking advantage of the analytical expression, it is efficient and distinct for parameter estimation and error analysis of missions. From the relationship and the simulations, it is analytically confirmed that the low-frequency noise affects the gravity field recovery in all degrees for the instance of satellite gradiometer recovery mission. Furthermore, some other results and suggestions are also described. 
Lin Cai, Zebing Zhou, Houtse Hsu, Fang Gao, Zhu Zhu, Jun Luo
physics.geo-ph