The Koopman Operator (KO) theory is applied to generate an analytical solution of dynamical systems. The approach proposed in this work exploits a novel derivation of the KO with orthogonal polynomials to represent and propagate uncertainties, where the polynomials are modified to work with stochastic variables. Thus, a new uncertainty quantification technique is proposed in which 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, for which the measurements are considered as additional observables in the KO mathematics. The uncertainty propagation technique is tested by predicting the state probability density function of a spacecraft in a halo orbit. The performance of the technique is assessed with a Monte Carlo analysis and proven to obtain accurate estimates for the state covariance, skewness, and kurtosis. The novel filtering methodology is then applied to an orbit determination application regarding a Lyapunov orbit, where an analysis on the filter accuracy and consistency shows that the new KO filter outperforms other common estimators.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Uncertainty Propagation and Filtering via the Koopman Operator in Astrodynamics


    Beteiligte:

    Erschienen in:

    Erscheinungsdatum :

    2023-06-06


    Format / Umfang :

    17 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




    Koopman Operator Approach to Airdrop Mission Planning Under Uncertainty

    Leonard, Andrew / Rogers, Jonathan / Gerlach, Adam | AIAA | 2019


    Astrodynamics

    Online Contents | 1995


    Astrodynamics

    Gurfil, Pini ;Belbruno, Edward | TIBKAT | 2008


    Astrodynamics

    Online Contents | 2012


    Astrodynamics

    Online Contents | 2009