Multielement Separated Representations for Orbit Uncertainty Propagation

Abstract

Uncertainty quantification is a valuable methodology in the field of astrodynamics, but approaches are often computationally expensive or rely on assumptions that do not account for non-Gaussian posteriors or the nonlinear evolution of the a priori uncertainty. Separated representations accurately estimate posterior distributions when using a sampling-based approach. Multimodal distributions, diffuse posteriors, or discontinuities pose convergence issues for the polynomial surrogate method of separated representations. Therefore, this paper presents the technique of multielement separated representations in order to overcome potential problems, such as the assumption of smooth and continuous behavior, present in unmodified separated representations. The decomposition of the input space as well as the construction of multielement surrogates are explained. This paper provides equations for determining if an input space split is necessary and where it should occur. The resulting algorithm is applied to four test cases in order to compare performance against unmodified separated representations. The first case considers a two-dimensional iteration of the Kraichnan–Orszag problem. Next, a Molniya case is examined with 6 and 10 input directions. Lastly, a multielement surrogate is created to estimate the posterior distribution of a third-body orbit over a continuous time span.