Adaptive ensemble Kalman filtering of non-linear systems
A necessary ingredient of an ensemble Kalman filter (EnKF) is covariance inflation, used to control filter divergence and compensate for model error. There is an on-going search for inflation tunings that can be learned adaptively. Early in the development of Kalman filtering, Mehra (1970, 1972) ena...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Stockholm University Press
2013-07-01
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| Series: | Tellus: Series A, Dynamic Meteorology and Oceanography |
| Subjects: | |
| Online Access: | http://www.tellusa.net/index.php/tellusa/article/download/20331/pdf_1 |
| _version_ | 1811302391803281408 |
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| author | Tyrus Berry Timothy Sauer |
| author_facet | Tyrus Berry Timothy Sauer |
| author_sort | Tyrus Berry |
| collection | DOAJ |
| description | A necessary ingredient of an ensemble Kalman filter (EnKF) is covariance inflation, used to control filter divergence and compensate for model error. There is an on-going search for inflation tunings that can be learned adaptively. Early in the development of Kalman filtering, Mehra (1970, 1972) enabled adaptivity in the context of linear dynamics with white noise model errors by showing how to estimate the model error and observation covariances. We propose an adaptive scheme, based on lifting Mehra's idea to the non-linear case, that recovers the model error and observation noise covariances in simple cases, and in more complicated cases, results in a natural additive inflation that improves state estimation. It can be incorporated into non-linear filters such as the extended Kalman filter (EKF), the EnKF and their localised versions. We test the adaptive EnKF on a 40-dimensional Lorenz96 model and show the significant improvements in state estimation that are possible. We also discuss the extent to which such an adaptive filter can compensate for model error, and demonstrate the use of localisation to reduce ensemble sizes for large problems. |
| first_indexed | 2024-04-13T07:28:26Z |
| format | Article |
| id | doaj.art-c3bc46ef7d994dda847218ce9faaf861 |
| institution | Directory Open Access Journal |
| issn | 0280-6495 1600-0870 |
| language | English |
| last_indexed | 2024-04-13T07:28:26Z |
| publishDate | 2013-07-01 |
| publisher | Stockholm University Press |
| record_format | Article |
| series | Tellus: Series A, Dynamic Meteorology and Oceanography |
| spelling | doaj.art-c3bc46ef7d994dda847218ce9faaf8612022-12-22T02:56:26ZengStockholm University PressTellus: Series A, Dynamic Meteorology and Oceanography0280-64951600-08702013-07-0165011610.3402/tellusa.v65i0.20331Adaptive ensemble Kalman filtering of non-linear systemsTyrus BerryTimothy SauerA necessary ingredient of an ensemble Kalman filter (EnKF) is covariance inflation, used to control filter divergence and compensate for model error. There is an on-going search for inflation tunings that can be learned adaptively. Early in the development of Kalman filtering, Mehra (1970, 1972) enabled adaptivity in the context of linear dynamics with white noise model errors by showing how to estimate the model error and observation covariances. We propose an adaptive scheme, based on lifting Mehra's idea to the non-linear case, that recovers the model error and observation noise covariances in simple cases, and in more complicated cases, results in a natural additive inflation that improves state estimation. It can be incorporated into non-linear filters such as the extended Kalman filter (EKF), the EnKF and their localised versions. We test the adaptive EnKF on a 40-dimensional Lorenz96 model and show the significant improvements in state estimation that are possible. We also discuss the extent to which such an adaptive filter can compensate for model error, and demonstrate the use of localisation to reduce ensemble sizes for large problems.www.tellusa.net/index.php/tellusa/article/download/20331/pdf_1ensemble Kalman filterdata assimilationnon-linear dynamicscovariance inflationadaptive filtering |
| spellingShingle | Tyrus Berry Timothy Sauer Adaptive ensemble Kalman filtering of non-linear systems Tellus: Series A, Dynamic Meteorology and Oceanography ensemble Kalman filter data assimilation non-linear dynamics covariance inflation adaptive filtering |
| title | Adaptive ensemble Kalman filtering of non-linear systems |
| title_full | Adaptive ensemble Kalman filtering of non-linear systems |
| title_fullStr | Adaptive ensemble Kalman filtering of non-linear systems |
| title_full_unstemmed | Adaptive ensemble Kalman filtering of non-linear systems |
| title_short | Adaptive ensemble Kalman filtering of non-linear systems |
| title_sort | adaptive ensemble kalman filtering of non linear systems |
| topic | ensemble Kalman filter data assimilation non-linear dynamics covariance inflation adaptive filtering |
| url | http://www.tellusa.net/index.php/tellusa/article/download/20331/pdf_1 |
| work_keys_str_mv | AT tyrusberry adaptiveensemblekalmanfilteringofnonlinearsystems AT timothysauer adaptiveensemblekalmanfilteringofnonlinearsystems |