Direct Initial Orbit Determination

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 (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i>, 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">direct</i> 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 proposed orbit-fitting paradigm: first, we introduce a 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 the 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.