Direct initial orbit determination
Chee-Kheng Chng Trent Jansen-Sturgeon Timothy Payne Tat-Jun Chin
Initial orbit determination (IOD) is an important early step in the
processing chain that makes sense of and reconciles the multiple optical
observations of a resident space object. IOD methods generally operate on
line-of-sight (LOS) vectors extracted from images of the object, hence the LOS
vectors can be seen as discrete point samples of the raw optical measurements.
Typically, the number of LOS vectors used by an IOD method is much smaller than
the available measurements (\ie, the set of pixel intensity values), hence
current IOD methods arguably under-utilize the rich information present in the
data. In this paper, we propose a \emph{direct} IOD method called D-IOD that
fits the orbital parameters directly on the observed streak images, without
requiring LOS extraction. Since it does not utilize LOS vectors, D-IOD avoids
potential inaccuracies or errors due to an imperfect LOS extraction step. Two
innovations underpin our novel orbit-fitting paradigm: first, we introduce a
novel non-linear least-squares objective function that computes the loss
between the candidate-orbit-generated streak images and the observed streak
images. Second, the objective function is minimized with a gradient descent
approach that is embedded in our proposed optimization strategies designed for
streak images. We demonstrate the effectiveness of D-IOD on a variety of
simulated scenarios and challenging real streak images.