AI 中文总结
研究受摄航天器动力学中非高斯不确定性，引入全解析无样本框架提取高阶矩，用双积投影策略克服计算瓶颈，所提方法在高保真环境验证，实现高精度并大幅减少计算时间。
AI 中文摘要
本文研究受摄天体动力学中的非线性不确定性传播，聚焦非高斯分布的快速表征及三维“香蕉形”置信边界的构建。为弥合计算量大的高保真方法与不准确的线性近似之间的差距，引入全解析、无样本的高阶矩提取框架。利用微分代数绕过重复数值积分，通过伊瑟利斯定理和单项式到埃尔米特基变换解析提取统计矩。采用双积投影策略克服全四阶张量收缩的严重计算瓶颈，仅计算相关项。提取的偏度和峰度分量直接参数化非椭圆置信几何，捕捉天体动力学中典型非高斯分布的空间弯曲和面外耦合。该方法在包括地月近直线晕轨道和地球飞越阿波菲斯附近近距离轨迹等高保真环境中得到验证，解析方法实现了与昂贵的蒙特卡罗模拟相当的几何精度，同时将计算运行时间减少了几个数量级。
英文摘要
This work investigates nonlinear uncertainty propagation in perturbed astrodynamics, focusing on the rapid characterization of non-Gaussian distributions and the construction of three-dimensional "banana-shaped" confidence boundaries. To bridge the gap between computationally intensive high-fidelity methods and inaccurate linear approximations, this paper introduces a fully analytical, sample-free framework for higher-order moments extraction. Leveraging Differential Algebra to bypass repeated numerical integration, statistical moments are extracted analytically via Isserlis' theorem and a monomial-to-Hermite basis transformation. A pair-product projection strategy is exploited to overcome the severe computational bottleneck of full fourth-order tensor contractions and compute only relevant terms via efficient polynomial algebra. The extracted skewness and kurtosis components directly parameterize non-elliptical confidence geometries that capture spatial bending and out-of-plane coupling of typical non-Gaussian distributions in astrodynamics. The approach is validated in high-fidelity environments including a cislunar Near-Rectilinear Halo Orbit and close-proximity trajectories around Apophis during Earth's flyby, where the analytical approach achieves geometric accuracy comparable to expensive Monte Carlo simulations while reducing computational runtime by orders of magnitude.
Comments2026 AAS Astrodynamics Specialist Conference. 21 pages, 9 figures
