Penalized ensemble Kalman filters for high dimensional non-linear systems.
The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when...
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Public Library of Science (PLoS)
2021-01-01
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| Series: | PLoS ONE |
| Online Access: | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0248046&type=printable |
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| author | Elizabeth Hou Earl Lawrence Alfred O Hero |
| author_facet | Elizabeth Hou Earl Lawrence Alfred O Hero |
| author_sort | Elizabeth Hou |
| collection | DOAJ |
| description | The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems. |
| format | Article |
| id | doaj-art-4a3dae8e8db841369f9e7ecafd710aa6 |
| institution | DOAJ |
| issn | 1932-6203 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-4a3dae8e8db841369f9e7ecafd710aa62025-08-20T02:55:28ZengPublic Library of Science (PLoS)PLoS ONE1932-62032021-01-01163e024804610.1371/journal.pone.0248046Penalized ensemble Kalman filters for high dimensional non-linear systems.Elizabeth HouEarl LawrenceAlfred O HeroThe ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems.https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0248046&type=printable |
| spellingShingle | Elizabeth Hou Earl Lawrence Alfred O Hero Penalized ensemble Kalman filters for high dimensional non-linear systems. PLoS ONE |
| title | Penalized ensemble Kalman filters for high dimensional non-linear systems. |
| title_full | Penalized ensemble Kalman filters for high dimensional non-linear systems. |
| title_fullStr | Penalized ensemble Kalman filters for high dimensional non-linear systems. |
| title_full_unstemmed | Penalized ensemble Kalman filters for high dimensional non-linear systems. |
| title_short | Penalized ensemble Kalman filters for high dimensional non-linear systems. |
| title_sort | penalized ensemble kalman filters for high dimensional non linear systems |
| url | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0248046&type=printable |
| work_keys_str_mv | AT elizabethhou penalizedensemblekalmanfiltersforhighdimensionalnonlinearsystems AT earllawrence penalizedensemblekalmanfiltersforhighdimensionalnonlinearsystems AT alfredohero penalizedensemblekalmanfiltersforhighdimensionalnonlinearsystems |