An efficient and global method for orbit uncertainty propagation near irregular-shaped asteroids

Asteroid close-proximity missions, such as orbiting, hovering, and landing, face significant dynamical challenges owing to the irregular and highly perturbed gravitational field. Orbital uncertainty plays a key role in close-proximity operations around asteroids. This study seeks to develop an efficient and global approach for dealing with orbit uncertainty propagation in an asteroid dynamical environment. First, to achieve global applicability and enhance efficiency, the quadrature-based polyhedral model is employed to represent the gravity of the irregularly shaped asteroid. The solar radiation pressure and the Sun's third-body gravity are considered to ensure the accuracy of the dynamic model. Second, the Analytic Continuation technique, originally developed for the perturbed two-body problem, is expanded to compute higher-order State Transition Tensors (STTs) of the high-fidelity dynamics. Recursive formulas for the time derivatives of STTs are obtained using the Leibniz product rule, enabling the STTs to be conveniently approximated through arbitrary-order Taylor series. Finally, by incorporating adaptive time steps and expansion order, an efficient algorithm for predicting the orbit state probability density function is developed. The orbit near the irregularly shaped, dog-bone-like asteroid 216 Kleopatra is used to demonstrate the effectiveness of the proposed method. Numerical simulations confirm the global applicability of the proposed method for uncertainty propagation, even for orbits involving multiple close flybys over the asteroid. Using only the fourth-order STT achieves results similar to full-scale Monte Carlo simulations with 50,000 samples but only needs 3% of the computational effort. These results strongly demonstrate that the proposed algorithm is a suitable tool for uncertainty propagation in asteroid exploration mission analysis.