High-precision dynamic orbit integration for spaceborne gravimetry

Future gravity missions like GRACE Follow-On and beyond will deliver low-low satellite-to-satellite ranging measurements of much increased precision. To prepare for the new challenges and opportunities involved in processing this new data, it is necessary to perform a systematic review and re-evaluation of current algorithms and assumptions used in gravity field determination from GRACE data.
In this context, this study investigates the computation of dynamic orbits from GRACE accelerometer measurements and background models, which are used at multiple steps in gravity recovery. They are, for example, used in computing linearised observation equations for the low-low satellite-to-satellite tracking instruments, or to evaluate potential models like static fields or dealiasing products. It is thus desirable for the precision at which the dynamic orbits are determined to surpass the precision of the ranging observations.

We computed dynamic orbits for GRACE, both in a simple simulation and for real observational data. We observed the differences between successive iterations of orbit determination and used these as a benchmark for the quality of the orbit solution. We implemented a numerically stable orbit determination algorithm employing Encke's method, in which we use a novel reference trajectory determined through rigorous optimization. This reference trajectory was parameterised and computed using equinoctial elements to minimize orbit errors resulting from imprecision in the reference motion. We present the effects of these two optimizations on the dynamic orbits, and show that the resulting orbits are self-consistent to below the expected precision of the GRACE Follow-On ranging instruments.