Nonlinear data assimilation

by Leeuwen, Peter Jan van

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Title Statements

Full title :Nonlinear data assimilation / Peter Jan van Leeuwen, Yuan Cheng, Sebastian Reich.

Summary

This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.

Edition Statements

Publication Date:©2015

Publication Statements

Publisher(s):Springer
Place of Publication:Cham
Language:eng
Publication Date:©2015

The Physical Object

Description:1 online resource : : color illustrations

Edition Identifiers

ISBN:9783319183473, 3319183478, 331918346X, 9783319183466
DOI:10.1007/978-3-319-18347-3
oclc:ocn914355311
LC Classification:QA401
Dewey Decimal:511.8

Machine generated contents note: 1. Nonlinear Data Assimilation for high-dimensional systems / Peter Jan van Leeuwen -- 1. Introduction -- 1.1. What is data assimilation? -- 1.2. How do inverse methods fit in? -- 1.3. Issues in geophysical systems and popular present-day data-assimilation methods -- 1.4. Potential nonlinear data-assimilation methods for geophysical systems -- 1.5.Organisation of this paper -- 2. Nonlinear data-assimilation methods -- 2.1. The Gibbs sampler -- 2.2. Metropolis-Hastings sampling -- 2.3. Hybrid Monte-Carlo Sampling -- 2.4. Langevin Monte-Carlo Sampling -- 2.5. Discussion and preview -- 3.A simple Particle filter based on Importance Sampling -- 3.1. Importance Sampling -- 3.2. Basic Importance Sampling -- 4. Reducing the variance in the weights -- 4.1. Resampling -- 4.2. The Auxiliary Particle Filter -- 4.3. Localisation in particle filters -- 5. Proposal densities -- 5.1. Proposal densities: theory -- 5.2. Moving particles at observation time.

Note continued: 6. Changing the model equations -- 6.1. The `Optimal' proposal density -- 6.2. The Implicit Particle Filter -- 6.3. Variational methods as proposal densities -- 6.4. The Equivalent-Weights Parti…

Subjects

computational mathematics computerwiskunde mathematical modelling mathematical models Mathematical physics mathematics MATHEMATICS -- General mathematische natuurkunde Méthodes de simulation Modèles mathématiques Nonlinear science Numerical analysis numerical mathematics Numerieke wiskunde simulation methods wiskunde Wiskunde (algemeen)