Analytical gravity field error analysis of multiple pair constellations

Abstract

The GRACE and GRACE-FO missions have provided monthly gravity field models for more than 20 years. The upcoming GRACE-C mission will guarantee data continuation for the next decade following the concept of a pair of satellites flying in a polar orbit for global coverage. Along with an additional satellite pair flying in an inclined orbit, the two satellite pairs will form a Bender constellation resulting in the MAGIC mission. As a result, both temporal and spatial resolution of Earth’s gravity field will improve. The novel mission configuration, however, poses new challenges for mission design, such as optimal selection of the constellation orbital parameters. In this work, the lumped coefficients theory is employed to propagate the error spectra of inter-satellite range and GNSS observations to the Stokes coefficients representing the gravity field. Noise propagation from accelerometers and attitude noise to the observations is also considered. This methodology is computationally much more efficient than error analysis studies from full end-to-end simulation. Thus, the design space can be quickly explored to determine a global optimal inclination for the second pair, for example. However, the analytical methodology presents some limitations, mainly the stationarity of observation noise. Therefore, we do not consider background model errors and temporal aliasing cannot be accounted for. Nonetheless, it can be circumvented directly observing the high-frequency signals at daily and sub-daily timescales. Multiple pair constellations are a promising mission concept in this regard. This provides a framework for leveraging the benefits of the analytical methodology. We apply the lumped coefficients theory to multiple pair constellations and analyse their spatio-temporal resolution for constellations up to 100 satellite pairs.