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arXiv · 1712.00895

Localised sequential state estimation for advection dominated flows with non-Gaussian uncertainty description

Emanuele Ragnoli·Mykhaylo Zayats·Fearghal O'Donncha·Sergiy Zhuk
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Abstract

This paper presents a new iterative state estimation algorithm for advection dominated flows with non-Gaussian uncertainty description of $L^\infty$-type: uncertain initial condition and model error are assumed to be pointvise bounded in space and time, and the observation noise has uncertain but bounded second moments. The algorithm approximates this $L^\infty$-type bounding set by a union of possibly overlapping ellipsoids, which are localized (in space) on a number of sub-domains. On each sub-domain the state of the original system is estimated by the standard $L^2$-type filter (e.g. Kalman/minimax filter) which uses Gaussian/ellipsoidal uncertainty description and observations (if any) which correspond to this sub-domain. The resulting local state estimates are stitched together by the iterative d-ADN Schwartz method to reconstruct the state of the original system. The efficacy of the proposed method is demonstrated with a set of numerical examples.

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Emanuele Ragnoli, Mykhaylo Zayats, Fearghal O'Donncha, Sergiy Zhuk. 2017-12-04. Localised sequential state estimation for advection dominated flows with non-Gaussian uncertainty description. https://arxiv.org/abs/1712.00895

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