Analytical Uncertainty Propagation and Maximum A Posteriori Filtering with the Koopman Operato
Date
2025-05-02
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Abstract
This paper proposes a method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the system, where the dynamics have been projected on a well-defined set of basis functions. The prediction technique is derived following both the analytical (Galerkin) and numerical (EDMD) derivation of the KO, and a least square reduction algorithm assures the recursivity of the proposed methodology. Furthermore, a complete filtering algorithm is proposed, where the predicted uncertainties are updated analytically using the likelihood function, following Bayes’ formulation. Estimates are provided after optimization according to the Maximum A Posteriori formulation, where a backtracking Newton solver identifies the global most likely posterior state.
Series Number
Journal Issue
Is Version Of
Versions
Series
Academic or Administrative Unit
Type
Article
Comments
This is a manuscript of an article published as Servadio, Simone, Giovanni Lavezzi, Christian Hofmann, Di Wu, and Richard Linares. "Analytical Uncertainty Propagation and Maximum A Posteriori Filtering with the Koopman Operator." IEEE Transactions on Aerospace and Electronic Systems (2025). doi: https://doi.org/10.1109/TAES.2025.3566685.
Rights Statement
© 2025 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.