Marco Felice Montaruli, Politecnico di Milano; Pierluigi Di Lizia, Politecnico di Milano; Emiliano Cordelli, GMV; Hélène Ma, RHEA System GmbH; Jan Siminski, European Space Agency European Space Operations Centre (ESA/ESOC)
Keywords: Fragmentations, orbit determination, SST, surveillance radar, MOID, clustering, non-normal distributions
Abstract:
In the last decades, the growing in-orbit population of resident objects has become one of the main concerns for space agencies and institutions worldwide, and several initiatives have been promoted to tackle this issue. In the resulting Space Surveillance and Tracking (SST) services, orbiting objects are observed through ground-based sensors, which are radars, optical telescopes and laser stations. In particular, a distinction between tracking and survey radars exists: the former observe the target by tracking it, so requiring pass prediction, whereas the latter detect it during the cross of the sensor field of view and, hence, they are suitable for an Initial Orbit Determination (IOD).
In this context, break-ups, explosions, collisions and anomalous events resulting in fragmentations further contribute to increase the number of space debris. Operationally, after the event, the fragmentation epoch shall be identified as soon as possible, such that the fragments cloud evolution is accurately modelled, and the observations can be properly planned. Multiple works have been conducted in the past for this purpose. Yet many of them rely on the availability of ephemerides of many fragments, which are not always available, especially few hours after the event. Furthermore, the uncertainty associated to the fragment ephemerides is not always negligible, especially when the fragment orbital state is the result of an IOD process (as it is reasonable to happen right after the event). Thus, the present work aims at providing an operational methodology to identify the fragmentation epoch from a single non-deterministic fragment orbital state resulting from an IOD process conducted few hours after the event. To this purpose, the Fragmentation Epoch Detector (FRED) algorithm deals with the problem through a statistical approach, described hereafter.
Given a fragment orbital state, obtained through an IOD conducted by a surveillance radar and whose uncertainty is assumed to be Gaussian, a multivariate normal distribution can be created from its mean state and covariance, resulting in multiple six-dimensional samples, which represent the fragment orbital state and account for its uncertainty. The algorithm proceeds by computing the Minimum Orbital Intersection Distances (MOIDs) between each six-dimensional sample and the last available ephemerides of the parent object (assumed as a deterministic quantity, given its supposed accuracy), as well as the epochs of the transit through it, both for parent and fragment sample. It is important to stress that also the epoch of parent transit through the MOID changes from sample to sample. This operation is conducted on a specified time window, which is limited by the epoch of the last available ephemerides of the parent object and the one of the first fragmentation alert. In this way, multiple MOIDs (and related epochs of transit) are attributed to each 6-dimensional sample.
After a filtering phase aiming at removing unfeasible solutions, all the evaluations are clustered based on the epoch of parent transit through the MOID. For each cluster, a fragmentation epoch candidate is identified in terms of mean and standard deviation, and, in addition, two distributions of the 3-dimensional distance between the parent and the fragment sample are created, which are generally non-normal: the 3-dimensional MOID distribution, that is the distance considering both fragment sample and parent transiting through the MOID, and the 3-dimensional relative distance distribution, that is the distance computed at the epoch of the parent transit through the MOID. The cluster linked to the correct fragmentation epoch is expected to be the one featuring the best matching between these two distributions.
The work presents FRED algorithm, and a numerical analysis is conducted to assess its performance. The analysed scenario is the one of the ASAT test COSMOS 1408 satellite, occurred in the night of the November 15th, 2021, and a dataset of 231 fragments, created according to a NASA Standard Breakup Model, is considered. The analysis highlights that the algorithm properly works but in some situations in which the fragment and parent orbits are very similarly oriented (the MOID computation turns out to be unstable) or have a similar shape (which make the relative distance distributions pretty similar among clusters, basically because of the close orbital periods). Finally, an operational case which also embeds the IOD process starting from radar measurements is presented and discussed.
Date of Conference: September 27-20, 2022
Track: Space Debris