Metrics on space of closed orbits for near-Earth objects identification

In the characterization of the space debris environment, the computation of the orbit of the debris objects is usually conducted by considering the association of short sequences of observations called tracklets. In case the orbits can be already determined with sufficient accuracy from single tracklets, it is necessary to define a criterion to decide if two calculated orbits correspond to the same object. One possibility is to introduce a definition of distance between orbits and to consider a threshold below which the two orbits are considered to be originating from the same object. The concept of distance is quite general and leaves room to different definitions. There are different ways to describe and to parameterize the space of the possible orbits. In this article, new metrics are proposed which extend distance definitions suggested in previous works. In these metrics in addition to orbital plane and orbital shape, also the position of the object along the orbit is taken into account. The obtained distances are scaled according to the orbit covariance. This has the advantage that the distance between orbits with different accuracy can be evaluated. The proposed metrics are then compared with existing common metrics to assess their applicability.