A software suite for conjunction analysis assessment in Space Surveillance and Tracking applications
Authors:   Politecnico di Milano, Milan, Italy, Bonaccorsi Sergio , Felice Montaruli Marco , Di Lizia Pierluigi , Peroni Moreno , Panico Alessandro , Rigamonti Marco , del Prete Francesco 
Published: January 2024

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 Space Surveillance and Tracking (SST) related initiatives have been promoted to tackle this issue. Indeed, the presence of the so-called space debris may jeopardise the operative mission of active satellites, given that the possible impact with a space debris ranges from cumulative erosion of satellite surface to the possible satellite destruction, with the generation of thousands of additional pieces of debris and inevitable environmental drawbacks and possible cascade effects. Within this framework, the Flight Test Wing of the Italian Air Force is currently upgrading the ISOC 3.0 Suite, an integrated platform providing multiple functions and services in the SST and SSA domains. As previous versions, ISOC 3.0 Suite will be a web-based platform giving users the ability to connect and use the system both locally and remotely. The embedded softwares are being designed and implemented in partnership with industry and academia. This work describes the prototypal version of the conjunction analysis tool developed for the ISOC 3.0 Suite thanks to a collaboration involving the Italian Air Force, Leonardo Company and Politecnico di Milano. The software architecture has been designed to guarantee the highest performance in terms of computational times.
The process starts screening the catalogue of resident space objects, containing their orbital states (possibly provided with uncertainty) and other possible physical information (otherwise assumed). This phase can be run either searching for conjunctions involving a particular satellite, or to detect any sort of conjunction, regardless which objects are involved. First, a geometrical filter searches for those satellites pairs for which the larger perigee (between the two objects) is larger than the smaller apogee, according to a threshold quantity. For those pairs which pass the filter, it is checked whether the two objects cross a region of relative closeness at the same time and, for each pair satisfying such a condition, the Minimum Orbital Intersection Distance (MOID) between their orbits is computed. Both the relative distance check and the MOID computation are performed, either through an unperturbed or a perturbed model (depending on the user request). If the computed MOID satisfies a threshold quantity, the pair is returned as a possible conjunction, and it is analysed in detail.
The objects involved in a possible conjunction are propagated across a time interval defined by the user, and the relative distance is computed on a time grid. The epoch related to the minimum relative distance is taken as first guess of an optimization process aimed at computing the Time of Closest Approach (TCA), according to the assumption that at TCA the relative distance and the relative velocity are orthogonal. The algorithm can also manage cases in which multiple TCAs are identified in the analysis time window. At this point, both primary and secondary objects are propagated to the resulting TCA, together with their covariances. In this phase, if no covariance is associated to any involved catalogued object, the algorithm exploits a tailored routine to estimate it from its orbit characteristics. Based on these quantities, both the Miss Distance (MD) and the Probability of Collision (PoC) are computed for each TCA. In particular, the PoC is computed according to the short-term encounter model, that is assuming a high relative velocity between the two satellites, either through a numerical or an analytical method (in the latter case two different algorithms can be called). Furthermore, it is up to the user to select either the nominal or the maximum PoC, the latter being computed on a set of candidates retrieved by increasing and decreasing the involved objects covariance. All these quantities are later written in a Conjunction Data Message (CDM), according to the Consultative Committee for Space Data Systems (CCSDS) formats.
For those conjunctions characterized by either a MD or a PoC which overcomes alert levels, the algorithm allows the user to plan an impulsive Collision Avoidance Maneuver (CAM), given the MD and PoC thresholds to satisfy afterwards, together with a maneuvering epoch list the CAM may be planned at. If a tangential maneuver is requested, a numerical procedure computes the impulse magnitude needed to satisfy the required thresholds. Otherwise, an optimal out-of-plane CAM is computed through an analytical unperturbed approach which aims either at matching the target PoC or the target MD. The process is repeated for all the listed maneuvering epochs. The results are then verified through a perturbed propagation, and MD and PoC after the maneuver are recomputed both at the original TCA and at the one occurring after having performed the CAM. Finally, it will be up to the user to select the most suitable maneuver.
The work presents the suite, and describes the validation process through both real and synthetic data.