Object correlation and orbit determination in the geostationary orbit using optical measurements

Abstract

Due to the increasing threat of space debris to active satellites, space object catalogs must be build up and maintained. Accurate and up-to-date catalog data allow the prediction of close conjunctions and consecutively the planning of avoidance maneuvers. Objects in lower altitudes are typically observed with radars. Objects in higher orbits, such as the geostationary one, are observed with optical telescopes due to the limiting range capabilities of radars. The geostationary orbit is extensively used in various applications, e.g. communication, navigation, and weather monitoring. Hence, it needs special protection and should be regularly scanned in order to assure accuracy and currentness of data. The German Space Operations Center builds up a ground-based telescope network for that purpose and to protect its own assets. Due to the limited number of telescopes which regularly scan the complete region around the geostationary orbit in a limited observation time, each object can only be observed for a short duration. The possible observation time is limited by the length of the night and visibility constraints such as clouds covering the sky. The short observation arcs, so-called tracklets, must be either associated to already cataloged objects or used for an initial orbit determination to create new catalog entries. However, the tracklets contain incomplete state information and cannot be used alone to calculate an orbital solution. Hence, they are correlated against other tracklets, i.e. tested if they belong to a common object. After a successful association, the tracklet pairs provide enough information to determine the full orbital state. This thesis develops a methodology to perform this association and initial orbit determination using the available information of two tracklets, namely the line-of-sight and its time derivative. The method is formulated as an initial-value and boundary-value problem corresponding to the two orbital representations. The association is performed by minimizing a loss function, which describes the statistical distance between the measured arc and the combined orbital solution. If the minimum distance is below a threshold, the two tracklets are associated. The sensitivity to errors is compared for both formulations, where the symmetric boundary-value formulation is shown to use the available information better and is generally more robust than the initial-value formulation. It offers an easier calibration, i.e. a threshold can be defined, using a set of observations, which assures that a certain percentage of the measurement distribution is successfully associated. Additionally, the expected accuracy of the found solutions is assessed and shows promising results as well. Lastly, an observability analysis is performed to find out which re-observation time is advantageous for the successful association.