Stochastic analysis of impulsive thrust uncertainties in the CR3BP

TL;DR

This paper addresses uncertainty propagation for impulsive thrust maneuvers in the circular restricted three-body problem (CR3BP) by leveraging an alternate dynamical model, the Spherical-Velocity Angles Model (S-VAM), which preserves the Jacobi constant $C$. The authors deploy Conjugate Unscented Transform (CUT) to efficiently compute higher-order state sensitivities (CUT-STTs) and to propagate the state pdf using a sparse, data-driven polynomial representation. The framework yields accurate moment estimates and fast analytical approximations of the evolving pdf, demonstrated through case studies with exaggerated thrust uncertainties and comparisons to Monte Carlo simulations. The work shows potential for rapid, reliable sensor tasking and trajectory uncertainty management in cislunar space, with future work including process noise and continuous-thrust extensions.

Abstract

This paper employs an alternate dynamical model of the circular restricted three body problem to quantify uncertainties associated with spacecraft thrusting maneuvers. A non-product quadrature scheme known as Conjugate Unscented Transform (CUT) is employed to determine the higher order system sensitivities through a computationally efficient data driven approach. Moreover, the CUT scheme, in conjunction with a sparse approximation method, is used to find an analytical representation of the time evolution of the state probability density function (pdf).

Figures (9)

• Figure 1: CR3BP schematic
• Figure 2: Reference trajectory from LEO to an $L_2$ halo orbit
• Figure 3: Two-norm error between the CUT and MC computations of the centralized statistical moments up to third order
• Figure 4: Cone of uncertainty ($\gamma$, $\beta$)
• Figure 5: Position error (in km) between MC integration and CUT approximation plotted against the initial and final Mahalanobis distances of the samples