Efficient Nonlinear Uncertainty Quantification for Spaceflight Leveraging Nonlinear Expansions
It provides a fast UQ method for nonlinear astrodynamics problems, improving on linear covariance for non-Gaussian statistics.
This paper compares modern uncertainty quantification methods for spaceflight, using differential algebra and directional differential algebra to compute higher-order moments and approximate confidence bounds for non-Gaussian distributions. The method achieves only 5x the runtime of linear covariance in numerical tests.
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.