Approach for Determining Satellite Gravity Model from GOCE Gravitational Gradient Tensor Invariant Observations

A semi-analytical (SA) approach is proposed to recover a gravity field model from the GOCE tensor invariant observations. The SA approach is more efficient than the least-squares method, and could provide the posterior variance of estimated coefficients. The formulas for gravity field model determination from tensor invariant observations based on SA approach were derived and a corresponding procedure for estimation of the satellite gravity model from satellite gravity gradient observations are described. Testing results from the simulated error free observations along the circular orbit with the inclination 89.5° show that applying the SA approach to process tensor invariant observations is theoretically rigorous. Using the simulated observations with or without errors in gradiometer reference frame (GRF) along the one repeat cycle GOCE real orbit, we recovered the gravity field models from the I₂ and V_zz components respectively. Numerical analysis results show that the solution from I₂ was slightly better than the one from V_zz component, which verified the feasibility of the method.