A stochastic approach to detect fragmentation epoch from a single fragment orbit determination

In the last decades, the growing in-orbit population of resident space objects has become one of the main concerns for space agencies and institutions worldwide. In this context, fragmentations further contribute to increase the number of space debris and, operationally, it is fundamental to identify the event epoch as soon as possible, even when just a single fragment orbital state, resulting from an Initial Orbit Determination (IOD) process, is available. This work illustrates the Fragmentation Epoch Detector (FRED) algorithm, which deals with the problem through a stochastic approach, starting from a single fragment IOD result (expressed through mean state and covariance) and parent ephemeris (assumed as deterministic). The process populates the fragment ephemeris with a multivariate normal distribution and, for each couple sample-parent, the epochs of parent transit through the Minimum Orbital Intersection Distance (MOID) are first computed on a time window and then clustered in time. For each cluster, both the three-dimensional MOID and the three-dimensional relative distance distributions are derived, and their similarity is statistically assessed. Given that, at the actual fragmentation epoch, MOID and relative distance were equal, the cluster featuring the best matching between the two distributions is considered as the optimal candidate, and the related fragmentation epoch is returned from the time of parent transit through the MOID, in terms of mean and standard deviation. FRED algorithm performance is assessed through a numerical analysis. The algorithm robustness decreases when parent and fragment orbits share a similar geometry, and results get deteriorated if the perturbations and, moreover, the IOD errors are included in the process, but the correct fragmentation epoch is always present among candidates. Overall, FRED algorithm turns out to be a valid choice in operational scenarios, and a sensitivity analysis tests the algorithm out of the nominal conditions.