Alessia De Riz, Politecnico di Milano; Riccardo Cipollone, Politecnico di Milano; Pierluigi Di Lizia, Politecnico di Milano
Keywords: SST, track-to-track correlation, optimal control, optical measurements, uncertainty propagation
Abstract:
In recent decades, the concern surrounding the increase of resident space objects (RSOs) within the near-Earth environment has gained extensive attention. Continuous efforts are underway to pioneer innovative techniques and solutions aimed at improving the surveillance and monitoring of RSOs. However, with the growing interest in cislunar space, the scientific community is actively mobilizing to extend Space Situational Awareness (SSA) and Space Surveillance and Tracking (SST) activities to this novel domain, avoiding the near-Earth precedent. In this context, object catalog maintenance and update stand as essential. Emphasis is placed on track-to-track correlation, a pivotal component within the framework of preserving a reliable catalog.
As part of the SST pipeline, track-to-track correlation or association steps in when a new RSO is detected and needs to be included in the catalog. At the core of this process lies the concept of track, which denotes a series of consecutive observations of the same target taken by a single sensor within a restrained timeframe, usually not sufficient to estimate a reliable orbit. When it comes to measurement processing, an acquired track is generally labeled as uncorrelated (UCT) until a cataloged object is identified to have generated it. While well-established techniques exist to tackle this issue in the two-body dynamics framework, many of them rely on its specific features, making their possible extension to the cislunar domain unfeasible. A control distance metric-based formulation, explored in the literature as a maneuver detection and correlation metric, emerges as the most suitable method as it is free from strong a priori approximations. This technique is commonly paired with an admissible region approach, though defining the constraints to bound such a region proves challenging in scenarios different from the two-body ones.
In this regard, this work aims to explore a novel procedure that leverages an energy optimal control metric, tailoring it to the application via its typical transversality conditions, used as a workaround for the definition of a proper admissible region. This technique offers a dual advantage: on one hand, it enables the association of tracks linked by purely ballistic dynamics, while it concurrently allows for robustness to maneuvers. This capability significantly aids catalog maintenance, effectively mitigating the occurrence of duplicated objects. Furthermore, such a technique implies no assumption on the target orbital dynamics, enabling the possibility of its extension to a cislunar framework.
The workflow of the proposed methodology is described in detail hereafter. The problem to be solved consists in the correlation of two optical tracks belonging to different time instants, therefore the initial and final states are only partially defined by the related angular measurement sets (condensed into attributables). They represent the boundary conditions (BCs) of the mentioned minimum-energy optimal control problem exploited to retrieve the expense linking them. As for the cost, it is expressed as thrust energy, accounting for a given reference dynamics. The OCP is solved by means of an indirect formulation, augmenting the state with an adjoint one linked to the control acceleration. From the problem characteristics, specific transversality conditions are exploited to set up a non-linear system embedding the available measurement information that can then be solved via simple shooting. BC uncertainty is taken into account and propagated across the pipeline to retrieve the solution distributions in terms of state and control expense, exploited in turn to design a statistically significant metric and set up the correlation test. The score is based on the comparison between the obtained solution distribution and a background one, encoding the only expense due to the problem’s uncertainty.
To assess the performance of this preliminary version of the algorithm, a numerical testing campaign is carried out on ballistic scenarios only. The involved data comprises realistically simulated measurements sampled from a reference ground station given the related target orbital state and the accuracy declared by the sensor. The latter information is leveraged to properly integrate uncertainty into the pipeline as well. The tests show promising results, hinting at the flexibility required to extend the approach to the cislunar dynamical framework.
Date of Conference: September 17-20, 2024
Track: Cislunar SDA