Gravity Estimation from Satellite-Satellite Tracking using Total Variation Regularization

The problem of gravity estimation from satellite-satellite tracking measurements is fundamentally ill-posed due to upward continuation, which results in poor observability of the high-frequency components of the potential. Additionally, the ground track orientation and orbital resonance introduce poor observability along certain directions and spectral bands of the solution. Consequently, the gravity estimates obtained by direct inversion exhibit non-physical noise features. Regularization schemes are employed in the solution of ill-posed problems, wherein pseudo-information is added to the optimization cost function to stabilize the inversion. The preferred regularization scheme for spaceborne gravity estimation has been L2-Tikhonov regularization with a heuristic constraint matrix.

Regularization schemes based on the spatial gradient of the solution field, such as H1 and Total Variation (TV), produce a penalty that naturally increases with frequency. Thus, they are effective in countering the ill-posedness due to poor observability of higher frequencies. Additionally, the TV penalty has the unique feature of promoting sharp edges, which could limit signal leakage in the solution. We previously reported results from the application of gradient regularization schemes as post-processing to the GRACE/GRACE-FO problem, as well as preliminary results from the application of these techniques to the full problem.

Here, we present the time series of solutions obtained by the application of gradient regularization methods to the full GRACE/GRACE-FO gravity estimation problem. The edge-preserving nature of the TV penalty facilitates recovery of sharp edges and signal localization in the solution, without the need for explicit spatial constraints. Additionally, we present results from the application of higher order generalizations of the TV penalty (Total Generalized Variation), which allows for recovery of sharp edges while limiting the undesirable peak-flattening effect induced by the TV penalty.