Data association for too-short arc scenarios with initial and boundary value formulations

Untraced space debris is the principal threat to the functioning of operational satellites whose services have become a fundamental part of our daily life. Small debris between 1 and 10 cm are currently too small to be cataloged and are only detectable for a limited amount of time. Indeed, when performing survey campaigns, the selected schedule and/or visibility constraints often result in short-arc observations with long observing gaps, which do not allow for precise orbit determination during a single passage of the object over an observing station. For this reason the problem of data association becomes relevant: one has to find more observations of the same resident space object to precisely determine its orbit. This paper compares different methods that build on the concept of Admissible Region and attributable to solve the problem of correlating sparse observations. The comparison is carried out on real optical observations obtained by the ZimSMART telescope on consecutive nights