Abstract
Untraced space debris are 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 when surveying the sky. The very-short arc nature of the observations makes it very difficult to perform precise orbit determination with only one passage of the object over the 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 focuses on multitarget tracking, which is part of the data association problem and deals with the challenge of jointly estimating the number of observed targets and their states from sensor data. We propose a new method that builds on the admissible region approach and exploits differential algebra to efficiently estimate uncertainty ranges to discriminate between correlated and uncorrelated observations. The multi-target tracking problem is formulated with two different mathematical conditions: as initial-value problem and as boundary-value problem. The first one allows us to define the constraints as a six-dimensional region at a single epoch for each observation, while the second one, instead, allows us to consider the two-by-two comparison as a Lamberts problem thus constraining the position vectors at the two epochs. The efficiency and success rate of the two formulations is then evaluated.