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.

翻译：Koopman算子（KO）通过正交多项式为动力系统提供解析解。本研究利用该表示方法引入不确定性传播机制，通过修正多项式以处理随机变量。由此提出一种新的不确定性量化技术，将KO解扩展至任意阶中心矩的预测。进一步将不确定性传播拓展至新型滤波算法设计，其中测量值被视作KO数学框架中的附加可观测量。通过天体动力学数值仿真验证了新方法的精度与性能。