Ensemble transform algorithms for nonlinear smoothing problems
- Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence ofSeveral numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.…
Author details: | Jana de WiljesORCiDGND, Sahani Darschika PathirajaORCiD, Sebastian ReichORCiDGND |
---|---|
DOI: | https://doi.org/10.1137/19M1239544 |
ISSN: | 1064-8275 |
ISSN: | 1095-7197 |
Title of parent work (English): | SIAM journal on scientific computing |
Publisher: | Society for Industrial and Applied Mathematics |
Place of publishing: | Philadelphia |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/10/28 |
Publication year: | 2020 |
Release date: | 2023/03/13 |
Tag: | adaptive; data assimilation; localization; optimal transport; smoother; spread correction |
Volume: | 42 |
Issue: | 1 |
Number of pages: | 28 |
First page: | A87 |
Last Page: | A114 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG); [CRC 1294] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik | |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |