Geometric Analysis of Conditional Bias-Informed Kalman Filters
This paper presents a comparative geometric analysis of the conditional bias (CB)-informed Kalman filter (KF) with the Kalman filter (KF) in the Euclidean space. The CB-informed KFs considered include the CB-penalized KF (CBPKF) and its ensemble extension, the CB-penalized Ensemble KF (CBEnKF). The...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-05-01
|
| Series: | Hydrology |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2306-5338/9/5/84 |
| _version_ | 1797499385003638784 |
|---|---|
| author | Haksu Lee Haojing Shen Dong-Jun Seo |
| author_facet | Haksu Lee Haojing Shen Dong-Jun Seo |
| author_sort | Haksu Lee |
| collection | DOAJ |
| description | This paper presents a comparative geometric analysis of the conditional bias (CB)-informed Kalman filter (KF) with the Kalman filter (KF) in the Euclidean space. The CB-informed KFs considered include the CB-penalized KF (CBPKF) and its ensemble extension, the CB-penalized Ensemble KF (CBEnKF). The geometric illustration for the CBPKF is given for the bi-state model, composed of an observable state and an unobservable state. The CBPKF co-minimizes the error variance and the variance of the Type-II error. As such, CBPKF-updated state error vectors are larger than the KF-updated, the latter of which is based on minimizing the error variance only. Different error vectors in the Euclidean space imply different eigenvectors and covariance ellipses in the state space. To characterize the differences in geometric attributes between the two filters, numerical experiments were carried out using the Lorenz 63 model. The results show that the CBEnKF yields more accurate confidence regions for encompassing the truth, smaller errors in the ensemble mean, and larger norms for Kalman gain and error covariance matrices than the EnKF, particularly when assimilating highly uncertain observations. |
| first_indexed | 2024-03-10T03:46:34Z |
| format | Article |
| id | doaj.art-9ae0d1d621ae4e5a9ae9bab29c5b364f |
| institution | Directory Open Access Journal |
| issn | 2306-5338 |
| language | English |
| last_indexed | 2024-03-10T03:46:34Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Hydrology |
| spelling | doaj.art-9ae0d1d621ae4e5a9ae9bab29c5b364f2023-11-23T11:18:03ZengMDPI AGHydrology2306-53382022-05-01958410.3390/hydrology9050084Geometric Analysis of Conditional Bias-Informed Kalman FiltersHaksu Lee0Haojing Shen1Dong-Jun Seo2Len Technologies, Oak Hill, VA 20171, USADepartment of Civil Engineering, University of Texas at Arlington, Arlington, TX 76019, USADepartment of Civil Engineering, University of Texas at Arlington, Arlington, TX 76019, USAThis paper presents a comparative geometric analysis of the conditional bias (CB)-informed Kalman filter (KF) with the Kalman filter (KF) in the Euclidean space. The CB-informed KFs considered include the CB-penalized KF (CBPKF) and its ensemble extension, the CB-penalized Ensemble KF (CBEnKF). The geometric illustration for the CBPKF is given for the bi-state model, composed of an observable state and an unobservable state. The CBPKF co-minimizes the error variance and the variance of the Type-II error. As such, CBPKF-updated state error vectors are larger than the KF-updated, the latter of which is based on minimizing the error variance only. Different error vectors in the Euclidean space imply different eigenvectors and covariance ellipses in the state space. To characterize the differences in geometric attributes between the two filters, numerical experiments were carried out using the Lorenz 63 model. The results show that the CBEnKF yields more accurate confidence regions for encompassing the truth, smaller errors in the ensemble mean, and larger norms for Kalman gain and error covariance matrices than the EnKF, particularly when assimilating highly uncertain observations.https://www.mdpi.com/2306-5338/9/5/84geometric analysisconditional biasCBPKFCBEnKFcovariance ellipse |
| spellingShingle | Haksu Lee Haojing Shen Dong-Jun Seo Geometric Analysis of Conditional Bias-Informed Kalman Filters Hydrology geometric analysis conditional bias CBPKF CBEnKF covariance ellipse |
| title | Geometric Analysis of Conditional Bias-Informed Kalman Filters |
| title_full | Geometric Analysis of Conditional Bias-Informed Kalman Filters |
| title_fullStr | Geometric Analysis of Conditional Bias-Informed Kalman Filters |
| title_full_unstemmed | Geometric Analysis of Conditional Bias-Informed Kalman Filters |
| title_short | Geometric Analysis of Conditional Bias-Informed Kalman Filters |
| title_sort | geometric analysis of conditional bias informed kalman filters |
| topic | geometric analysis conditional bias CBPKF CBEnKF covariance ellipse |
| url | https://www.mdpi.com/2306-5338/9/5/84 |
| work_keys_str_mv | AT haksulee geometricanalysisofconditionalbiasinformedkalmanfilters AT haojingshen geometricanalysisofconditionalbiasinformedkalmanfilters AT dongjunseo geometricanalysisofconditionalbiasinformedkalmanfilters |