Absolute Orbit and Gravity Determination Using Relative Position Measurements Between Two Satellites

Abstract

A method has been developed to use a time series of relative position measurements to estimate the orbits of two satellites along with corrections to the gravity model of the celestial body about which they orbit. This system provides autonomy or near autonomy and could be used for gravity recovery at the Moon or a planet. This system eliminates the need for a third spacecraft that maintains a constant link with Earth-based tracking stations when the two probe spacecraft pass to the far side of the body whose gravity model is being estimated. The system uses a radio cross link to measure the relative range between the two satellites. It uses an optical imaging device on one of the satellites, such as a star camera, and a light beacon on the other satellite in order to measure the relative bearing between the satellites referenced to inertial coordinates. The two satellites’ orbits and corrections to the gravity field model are shown to be absolutely observable in cases where the two orbital altitude time histories are not identical. An extended Kalman filter for this system is developed, and it is tested using data from a truth-model simulation. The resulting system can achieve absolute RMS position accuracies of 3.5 m, absolute RMS velocity accuracies of 0.003 m/s, and RMS gravity accuracies of 3x10 -7 m/s 2 when operating on a month’s worth of data from a pair of Lunar orbiting spacecraft.