This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can enable fast UQ in the case of non-Gaussian statistics. Higher-order moments, namely skew and kurtosis, can be computed quickly by several means. This motivates their implementation in an analytic approximation of the confidence bounds for the so-called "banana-shaped" non-Gaussian distributions encountered often in nonlinear astrodynamics problems. This method improves greatly on a linear covariance approach, with only 5x its runtime in numerical tests, even before DA methods are employed. Test problems in this work include a restricted three-body cislunar example and an Earth-return aerocapture example.
Cite
@article{arxiv.2605.24147,
title = {Efficient Nonlinear Uncertainty Quantification for Spaceflight Leveraging Nonlinear Expansions},
author = {Ethan R. Burnett and Spencer Boone},
journal= {arXiv preprint arXiv:2605.24147},
year = {2026}
}