This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions, our approach leverages the relationship between MGFs and distribution moments to extend high-order uncertainty propagation techniques to non-Gaussian scenarios. This significantly broadens the applicability of these methods to a wider range of problems and uncertainty types. High-order moment computations are performed one-off and symbolically, reducing the computational burden of the technique to the calculation of Taylor series coefficients around a nominal trajectory, achieved by efficiently integrating the system's variational equations. Furthermore, the use of the proposed approach in combination with event transition tensors, allows for accurate propagation of uncertainties at specific events, such as the landing surface of a celestial body, the crossing of a predefined Poincar\'e section, or the trigger of an arbitrary event during the propagation. Via numerical simulations we demonstrate the effectiveness of our method in various astrodynamics applications, including the unperturbed and perturbed two-body problem, and the circular restricted three-body problem, showing that it accurately propagates non-Gaussian uncertainties both at future times and at event manifolds.

翻译：本文提出了一种基于流和矩生成函数高阶泰勒展开的动态系统不确定性传播新方法。与以往主要关注高斯分布的方法不同，本方法利用矩生成函数与分布矩之间的关系，将高阶不确定性传播技术扩展至非高斯情形。这显著拓宽了此类方法对更广泛问题及不确定性类型的适用性。高阶矩计算采用一次性符号化处理，将技术计算负担简化为沿标称轨迹的泰勒级数系数计算，这通过高效积分系统变分方程实现。此外，所提方法与事件转移张量相结合，能够精确传播特定事件（如天体着陆表面、预定庞加莱截面的穿越或传播过程中任意事件的触发）处的不确定性。通过数值仿真，我们在多种天体动力学应用中验证了本方法的有效性，包括无摄动与受摄动二体问题、圆型限制性三体问题，结果表明该方法能精确传播未来时刻及事件流形上的非高斯不确定性。