Twoline elements are estimated onboard and downlinked to the ground station. On board the Twoline elements are employed for station contact prediction and forecasts of shadow transit times. On ground, the Twoline elements are extracted from the telemetry and used for antenna pointing predictions and station contact forecasts using Commercial-off-the-shelf (COTS) software.
The Realtime Twoline Generation (RTG) system augments the Onboard Navigation System (ONS) on the BIRD small satellite. The RTG is capable of estimating Twoline Elements (TLE) for long-term orbit prediction purposes.
While the ONS is especially suited for navigation applications with short prediction intervals, the use of an analytical orbit model can overcome these limitations. It allows off-line predictions over mid- and long-term periods (multiple revolutions to multiple days) at the expense of a decreased short-term accuracy. The analytical model used by the Real-time Twoline Generator is the SGP4 model, which is employed by the North American Aerospace Defense Command (NORAD) for the generation of Twoline elements, a widespread standard format for the exchange of orbit information for near-circular, low-altitude satellites.
RTG Objective and Conception
The major objective of the RTG is to generate onboard Twoline elements to be transmitted to a relocatable ground station on an experimental basis. Here, the Twoline elements may be applied using Commercial-off-the-Shelf (COTS) software to perform the antenna steering and upcoming pass predictions, which provides an essential prerequisite for autonomous ground station operations.
The RTG applies GPS position measurements within an epoch state Kalman filter, which updates the value of the mean epoch state vector from the difference between GPS position measurements and the predicted SGP4 position. Using a mean epoch state vector for estimation as opposed to the mean orbital elements avoids the inherent singularity of the orbital elements for near-circular orbits. In addition to the SGP4 mean state vector, the RTG also accounts for the atmospheric drag by estimating a ballistic coefficient, which is part of the SGP4 algorithm.
RTG Flight Results
The analysis of the RTG results is primarily based on a sequence of transmitted Twoline elements as well as native GEM-S position fixes, which were applied to establish a reference trajectory on ground. A RTG filter convergence has been observed within about two days in accordance with pre-flight tests. Computing the RTG-derived position and velocity residuals with respect to the reference trajectory yields maximum position and velocity errors of 1.8 km and 1.6 m/s, respectively. The associated standard deviations are 0.3 km for position and 0.3 m/s for velocity, similar to residual characteristics resulting from ground-based generation of Twoline elements.
To demonstrate the potential of the RTG for onboard long-term predictions, the maximum RTG prediction errors for various prediction arcs in dependence of the applied data arc were derived. Obviously, the data arc should be longer than 1 day to operate in the converged regime of the Kalman filter. The optimum regime of the filter applies about 1.5-3.5 d of tracking data. For a 7 day prediction arc, the maximum position errors are less than 38 km, corresponding to a 5 s timing error, which is tolerable for many applications.
Gill E., Montenbruck O., Montenegro S.;Flight Results from the BIRD Onboard Navigation System;5th International ESA Conference on Guidance, Navigation and Control Systems, 22-25 October 2002, Frascati, Italy (2002).
Gill E., Montenbruck O.;The Onboard Navigation System for the BIRD Small Satellite;DLR FB 2002-06; Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen (2002).
Gill E., Montenbruck O., Kayal H., Briess K.;A Concept for an Autonomous Space and Ground Segment Applied to the BIRD Satellite Mission;19th AIAA International Communications Satellite Systems Conference, Toulouse (2001).
Gill E., Montenbruck O.;Die Satellitenmission BIRD als Meilenstein für ein bordgestütztes autonomes Navigationssystem;DGLR Jahrestagung, Dresden (2000).
Montenbruck O., Gill E.;Real-Time Estimation of SGP4 Orbital Elements from GPS Navigation Data;15th International Symposium on Spaceflight Dynamics, 26-30 June 2000; Biarritz (2000).