Sampling free iterative PCE filter for state and parameter estimation of nonlinear dynamical systems

W. van Dijk, W.B.J. Hakvoort, B. Rosić*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We present a novel filter for state and parameter estimation in non-linear dynamical systems, based on a generalised Kalman filter formulation. To achieve a sampling-free implementation, polynomial chaos expansion (PCE) and a Galerkin projection method are utilized for the propagation of uncertainties through the system dynamics. The non-linear dynamics of the system are then linearised by a sequence of Gauss-Newton iterations in combination with linear Kalman updates. Additionally, we introduce a new square root implementation of the PCE-based filter. The proposed filter is evaluated on the Lorenz-63 and Lorenz-84 models for the task of simultaneous state and parameter estimation and is compared with two related approaches. Finally, the computational complexity of our square-root implementation is compared against two existing square root approaches.

Original languageEnglish
Article number113118
Number of pages15
JournalJournal of computational physics
Volume511
Early online date22 May 2024
DOIs
Publication statusE-pub ahead of print/First online - 22 May 2024

Keywords

  • 2024 OA procedure
  • Gauss Newton
  • Kalman filter
  • Polynomial chaos expansion
  • Square root filter
  • Bayesian estimation

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