An analysis of geopotential difference determination from satellite-to-satellite tracking

The determination of the Earth’ s gravitational field from a dedicated
satellite-to-satellite (SST) tracking mission has been considered for more than two
decades. The usual assumed approach to gravitational field modeling from SST data
is by spherical harmonic series development. On the other hand, many feasibility
studies based on covariance analyses have assumed a direct relationship between
geopotential and intersatellite range-rate. The latter would make local gravity field
determination possible, without the need for computationally massive global
spherical harmonic solutions. However, the relationship between the actual
observable and the potential is not as simple as assumed in previous studies.
Alternatively, three-dimensional velocity differences may be determined with GPS
baseline tracking, and then the relationship to potential is, in fact, straightforward.
But the measurement accuracy of the observable is less than with intersatellite
ranging. This paper examines in detail the relationship between geopotential
differences and the observables in intersatellite ranging and in GPS relative velocity
measurements. Error analyses and simulations based on the GRACE mission are
presented to show the feasibility for local gravity field determination in either case.