Analysis of Non-Gaussian Uncertainty Evolution in the Cislunar Domain

Recent years have seen an explosion of interest in the exploration and use of cislunar space. In contrast with near-Earth-Keplerian orbits, trajectories within cislunar space are highly sensitive to small deviations with perturbing effects often manifesting as diverging trajectories. Because of this, characterizing the evolution of uncertainty is particularly challenging. This manuscript explores this evolution, seeking to draw connection between particular orbits or regions of space and the rate at which uncertainties become non-Gaussian through the study of metrics that include covariance growth, multivariate skewness, and multivariate kurtosis. These metrics and their evolution through time is evaluated through Monte Carlo sampling as well as samples generated from the Conjugate Unscented Transform method (CUT). Particular emphasis is placed on assessment of the planar translunar and L₁´ L₂corridor as well as L₂halo orbits, which are important for current and planned lunar operations.