Burnett and Boone's new method speeds nonlinear UQ for spaceflight

Uncertainty quantification in spaceflight often grapples with non-Gaussian, 'banana-shaped' distributions that linear covariance methods cannot capture. In a new paper on arXiv, researchers Ethan R. Burnett and Spencer Boone present a comparative study of modern UQ methods, introducing an efficient approach that leverages differential algebra (DA) and directional differential algebra (DDA). These techniques allow fast computation of higher-order moments like skew and kurtosis, which are used to build analytic confidence bounds for those nonlinear distributions. The method is designed for real-time performance, a key requirement for onboard spaceflight systems.

Numerical tests show the nonlinear method runs only 5x slower than a standard linear covariance approach—already impressive before applying DA acceleration. The authors validated their method on two challenging astrodynamics problems: a restricted three-body cislunar scenario and an Earth-return aerocapture trajectory. By accurately quantifying uncertainty in these highly nonlinear regimes, the method could significantly improve mission safety and autonomy. The work is detailed in arXiv:2605.24147, with 8 pages and 3 figures.