Uncertainty Propagation and Filtering via the Koopman Operator in Astrodynamics

Understand

The Koopman Operator (KO) provides an analytical solution of dynamical systems in terms of orthogonal polynomials.

• This work exploits this representation to include the propagation of uncertainties, where the polynomials are modified to work with stochastic variables.
• Thus, a new uncertainty quantification technique is proposed, where the KO solution is expanded to include the prediction of central moments, up to an arbitrary order.
• The propagation of uncertainties is then expanded to develop a new filtering algorithm, where measurements are considered as additional observables in the KO mathematics.