Differential algebra enabled multi-target tracking for too-short arcs

Untracked space debris is the principal threat to operational satellites’ functioning whose services have become a fundamental part of our daily life. Though some specialised sensors can detect objects down to sub-cm sizes in geostationary Earth orbit, only objects larger than 30 cm are currently being catalogued. Thus, small debris are only seldom observed, typically for a short amount of time when surveying the sky. Having to deal with short arcs, the data association’s problem becomes relevant: one must find more observations of the same resident space object to precisely determine its orbit. This paper develops a new method enabled by differential algebra for track initialisation and catalogue build-up, within the framework of multi-target tracking. This is compared to literature methods that build on the concept of the admissible region and attributable to solve the problem of correlating sparse observations. The comparison is carried out on synthetic measurements and real optical observations obtained by the ZimSMART telescope on consecutive nights. Furthermore, simulated observations are used to assess whether raw data in the tracklets can be exploited to reduce the admissible region’s size. Though the gain in computational efficiency is only limited, this paper effectively shows an alternative method to the Mahalanobis distance, where the success of correlation is less affected by the time separation of two observations.