Uncertainty Propagation and Filtering via the Koopman Operator in Astrodynamics

TL;DR

This paper introduces a novel uncertainty propagation and filtering method in astrodynamics using the Koopman Operator, enabling analytical prediction of moments and incorporating measurements as observables.

Contribution

It develops a new uncertainty quantification technique and filtering algorithm based on the Koopman Operator, extending its application to stochastic variables and measurements.

Findings

Accurate propagation of uncertainties in astrodynamics models.

Effective filtering method incorporating measurements as observables.

Numerical simulations demonstrate improved performance over traditional methods.

Abstract

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. Numerical simulations in astrodynamics assess the accuracy and performance of the new methodologies.