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Particle Filtering for Stochastic Navier–Stokes Observed with Linear Additive Noise

Llopis, FP; Kantas, N; Beskos, A; Jasra, A; (2018) Particle Filtering for Stochastic Navier–Stokes Observed with Linear Additive Noise. SIAM Journal on Scientific Computing , 40 (3) A1544-A1565. 10.1137/17M1151900. Green open access

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Abstract

We consider a nonlinear filtering problem whereby the signal obeys the stochastic Navier–Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather prediction and climate modeling, where similar models are used for unknown ocean or wind velocities. We present a particle filtering methodology that uses likelihood-informed importance proposals, adaptive tempering, and a small number of appropriate Markov chain Monte Carlo steps. We provide a detailed design for each of these steps and show in our numerical examples that they are all crucial in terms of achieving good performance and efficiency.

Type: Article
Title: Particle Filtering for Stochastic Navier–Stokes Observed with Linear Additive Noise
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/17M1151900
Publisher version: https://doi.org/10.1137/17M1151900
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: stochastic Navier–Stokes, stochastic filtering, particle filters, preconditioned Crank–Nicolson Markov chain Monte Carlo
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10045962
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