A geometrical approach to association of space-based very short-arc LEO tracks

Conventional methods of association between uncorrelated tracks (UCTs) require knowledge of UCT covariance and their accurate propagations, which are difficult to achieve in some cases. For space-based angles-only very short-arc (SBVSA) LEO tracks, errors of initial tracks determined through the initial orbit determination (IOD) could be very large, for example, the semi-major axes (SMA) could have errors exceeding 100 km. Therefore, the conventional methods may fail if two tracks are apart by tens of orbital periods because of the need to correctly propagate the errors over the time span. In this paper, a geometrical approach to associating the SBVSA LEO tracks is proposed. This approach uses an analytical orbital propagator to propagate two UCTs to the middle of the time interval, and then adjust the SMA of one UCT to minimise position difference between the two UCTs at the middle point. After several iterations, an acceptable along track bias is obtained and a judgement on whether the two UCTs are associated is made. Preliminary simulations show that, the true positive rate is about 90% for LEO near-circular UCT associations. Furthermore, the geometrical method is tested on the non-circular LEO track association problem, the true positive rate is about 80%. A comparison with the Covariance Based Track Association (CBTA) method is also presented in the paper.