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Active TRL 2 (started at 2, targeting 3)
Current and planned activity in cislunar space are both increasing rapidly. NASA's Artemis program will see placement of the lunar Gateway and other assets in Near Rectilinear Halo Orbits (NRHOs), which offer clear operational benefits to the program. Despite this, orbit determination in this regime remains an open area of research. This is due to spacecraft uncertainty becoming non-Gaussian because of highly nonlinear dynamics and the types of available measurements. Because orbital Rendezvous and Proximity Operations (RPO) are crucial to the Gateway's operation, developing novel capabilities to accurately represent the non-Gaussian Probability Density Functions (PDFs) of spacecraft in NRHOs and leveraging that information for efficient guidance and maneuver optimization using robust control would greatly improve the technology readiness level (TRL) of RPO in cislunar space. Polynomial Chaos Expansions (PCEs) provide an opportunity to approximate higher-order moments of probability distributions by projecting a stochastic solution onto an orthogonal polynomial basis as a function of random inputs. PCEs show promise on the fronts of both accuracy and computational efficiency, with a subset of methods known as intrusive PCEs (iPCEs) offering the best combination of both. Through use of the Galerkin projection on the equations of motion and relevant measurement models in combination with a nonlinear polynomial based filter, analytic time and measurement updates may be performed on polynomial expansions representing a spacecraft's state, preserving information regarding the uncertainty's higher order moments. This work seeks to derive such a filter that can estimate higher order moments of a spacecraft’s PDF while remaining computationally tractable, that is robust to different measurement frameworks, and that is usable directly in support of long-term orbital rendezvous and maneuver design.
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