Multilevel Ensemble Transform Particle Filtering | Zendy

Alastair Gregory | Zendy; Colin J. Cotter | Zendy; Sebastian Reich | Zendy

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Multilevel Ensemble Transform Particle Filtering

Author(s) -

Alastair Gregory,

Colin J. Cotter,

Sebastian Reich

Publication year - 2016

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/15m1038232

Subject(s) - particle filter , resampling , variance reduction , monte carlo method , mathematics , estimator , variance (accounting) , algorithm , filter (signal processing) , statistical physics , nonlinear system , mathematical optimization , computer science , statistics , kalman filter , physics , accounting , quantum mechanics , business , computer vision

This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.

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