An epoch state filter for use with analytical orbit models of low earth satellites

Kalman filters provide a well established means for satellite orbit determination. In combination with space based sensors like GPS, DORIS or PRARE, accurate estimates of the spacecraft position and velocity can be obtained in real-time on-board the space vehicle. Traditionally, numerical methods of varying complexity are applied for propagating the state vector between measurements and updates of the state vector are referred to the epoch of the latest sensor output. In the present study a different approach is followed, which offers increased on-board autonomy and is particularly promising for small satellites with moderate accuracy requirements. An analytical orbit model is used to describe the spacecraft trajectory and mean elements at epoch are estimated instead of the instantaneous, osculating state vector. This adds the capability of performing on-board orbit prediction over time scales of up to one week, which is required, for instance, for the autonomous forecast of eclipse times or station contacts. Making use of the SGP4 orbit model that is compatible with NORAD twoline elements, an epoch state Kalman filter has been implemented and tested with GPS flight data of GPS/MET (MicroLab-1) and MOMSNAV (MIR). It is demonstrated that the proposed method provides an accuracy compatible with that of the analytical model and is robust enough to handle large data gaps in case of limited on-board resources for GPS operations. By adjusting the ballistic coefficient along with the mean elements, a considerable improvement of mid-term orbit predictions is achieved over methods that are restricted to the estimation of the state vector alone.