Probabilistic data association based on intersection of Orbit Sets

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 is going to illustrate a novel approach that exploits Differential Algebra to handle the data association problem in a completely analytical way. The paper presents an algorithm that uses the Subset Simulation to find correlated observations starting from the solution to the Initial Orbit Determination problem. Due to the different capabilities of the observatories, several observing strategies are currently being used. The algorithm is thus tested for different strategies against a well known approach from literature. Then, the performance of the data association method is tested on some real observations obtained in two consecutive nights. Finally, preliminary results for data association without Initial Orbit Determination are shown

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