Orbit Propagation and Validation with Angle-Only Observations

Abstract

With the growing number of resident space objects (RSOs) precise orbit determination and prediction plays an increasingly important role. In the scope of protecting o perational spacecraft very accurate orbit prediction is a prerequisite. Predicting close conjunctions and a ssessing collision probabilities well in advance on a reliable confidence level enables planning and performing o f collision avoidance manoeuvres. With sophisticated post-processing methods, when all information is available accuracies in the order of centimeters can be achieved. Post-processing of surveillance data (optica l, radar) is still assumed to be in the order of meters. The accuracy of orbit prediction rather than a post-fit of dat a of common operational products is inferior by orders of magnitudes. This paper addresses the task of orbit propagation based on angle-only observations of RSOs in geostationary and high eccentricity orbits. The focus is on objects which do not perform manoeuvres, to clearly separate the effects of manoeuvre data ‐ which is probably unavailable and/or inaccurate ‐ from modeling the natural forces. The angle-only observations stem from the one-meter ZIMmerwald Laser and Astrometry Telescope (ZIMLAT), the 18-cm Zimmerwald SMall Robotic Telescope (ZimSMART), both located in Zimmerwald, close to Bern, Switzerland, and from the one-meter ESA Space Debris Telescope (ESASDT) located on Tenerife, Spain. The one-meter telescopes have been used for RSO surveys and for so-called follow-up observations over the past decade by the Astronomical Institute of the University of Bern, which is a prime contractor of the European Space Agency (ESA) in the fields of Surveillance and Tracking. Supplementary observations are provided by the courtesy of the International Scientific Optical Network (ISON). Orbit determination and propagation is performed with an enhanced version of the CelMech tool (Beutler, Methods of Celestial Mechanics , Springer 2001). The force model used includes Earth’s pote ntial coefficients up to order and degree 12, perturbations due to earth tides, and corrections due to general relativity. Earth shadow passages are modeled. In addition, a model for estimating the direct radiation pressure (DRP) is used, which allows an estimate of the area to mass ratio as a scaling factor, as well as the osculating elements. Optionally, biases, which account inter alia for asymmetries in the observed object, e.g. misalignment of solar panels, can be estimated. Orbit propagation is perfor med using the determined osculating elements, the estimated area to mass ratio, and the reflection coefficie nt within the force model mentioned above. The estimated biases are not available for orbit propagation. T he ephemerides of the propagated orbits are compared to observations of the same object, which were not used for orbit determination. Those additional angle-only observations serve as ground truth. The additional observations that belong to the same object are validated by a further orbit determination including all ob servations. The influence of the temporal spacing of observations and the effect of fusing data of different ob servation sites is investigated. As a reference, two line element data (TLEs) of the US Strategic Command (USSTRATCOM) catalogue are propagated with the SDP4 propagator and the resulting ephemerides are compared to the angle-only observations. Covariances for the TLE data are then estimated.