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.
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