Unscented Filtering for LEO Satellite Orbit Determination

Abstract

The specific interest of Telespazio towards spacecraft radio-assisted navigation does not only concern with the traditional “user segment”, but the development as well of ground segment components able to support the space missions with an accurate orbit determination. Spacecraft platforms already exist, and are planned to be launched, including on board GPS receivers, thus providing the capability of processing related raw data to attain a quite precise reconstruction of the satellite dynamics. In the proposed application, it is assumed that measurements z(k) are provided of a non-linear dynamic system that represents the orbit motion of a LEO spacecraft; the observation samples originate from a dual-frequency (L1/L2) GPS receiver available on-board. The described solution allows to estimate the state vector x, that includes at least position and velocity of the satellite, with a sequential processing which avoids the calculation of any Jacobian or design matrix and thus suppresses the need of reconstructing any derivatives of plant model equations. It is attained through the use of the so called “Unscented Filter” (UF). The proposed algorithm is tested with real data, consisting of raw navigation observables and post-processed reference orbits available from Champ satellite mission. CHAMP (CHAllenging Minisatellite Payload) is a German small satellite characterised by near polar, low altitude orbit for geoscientific and atmospheric research and applications. Among the other problems, a critical aspect to be faced is that one of “outliers” detection and elimination from the orbit determination process; the selection of “proper” signals to be treated is performed in the frame of the sequential calculation, so that only a single “pass” is performed on available raw data. This means that the overall approach is a good candidate as well for a real-time determination of the state vector. As a conclusion, the UF algorithm has proven to be a working and robust solution, even starting from a bad initial approximation of the state vector, whilst this is typically not the case for an Extended Kalman Filter (EKF).