Some quantitative characteristics of error covariance for Kalman filters
Some quantitative characteristics of error covariance are studied for linear Kalman filters. These quantitative characteristics include the peak value and location in the matrix, the decay rate from peak to bottom, and some algebraic constraints of the elements in the covariance matrix. We mathemati...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Stockholm University Press
2021-01-01
|
| Series: | Tellus: Series A, Dynamic Meteorology and Oceanography |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16000870.2020.1852834 |
| _version_ | 1818538199196106752 |
|---|---|
| author | Wei Kang Liang Xu |
| author_facet | Wei Kang Liang Xu |
| author_sort | Wei Kang |
| collection | DOAJ |
| description | Some quantitative characteristics of error covariance are studied for linear Kalman filters. These quantitative characteristics include the peak value and location in the matrix, the decay rate from peak to bottom, and some algebraic constraints of the elements in the covariance matrix. We mathematically prove a matrix upper bound and its quantitative characteristics for the error covariance of Kalman filters. Computational methods are developed to numerically estimate the elements in a matrix upper bound and its decay rate. The quantitative characteristics and the computational methods are illustrated using three examples, two linear systems and one nonlinear system of shallow water equations. |
| first_indexed | 2024-12-11T21:25:54Z |
| format | Article |
| id | doaj.art-9095d398bdad4f4684613cfa8a061bdd |
| institution | Directory Open Access Journal |
| issn | 1600-0870 |
| language | English |
| last_indexed | 2024-12-11T21:25:54Z |
| publishDate | 2021-01-01 |
| publisher | Stockholm University Press |
| record_format | Article |
| series | Tellus: Series A, Dynamic Meteorology and Oceanography |
| spelling | doaj.art-9095d398bdad4f4684613cfa8a061bdd2022-12-22T00:50:20ZengStockholm University PressTellus: Series A, Dynamic Meteorology and Oceanography1600-08702021-01-0173111910.1080/16000870.2020.18528341852834Some quantitative characteristics of error covariance for Kalman filtersWei Kang0Liang Xu1Department of Applied Mathematics, Naval Postgraduate SchoolNaval Research LaboratorySome quantitative characteristics of error covariance are studied for linear Kalman filters. These quantitative characteristics include the peak value and location in the matrix, the decay rate from peak to bottom, and some algebraic constraints of the elements in the covariance matrix. We mathematically prove a matrix upper bound and its quantitative characteristics for the error covariance of Kalman filters. Computational methods are developed to numerically estimate the elements in a matrix upper bound and its decay rate. The quantitative characteristics and the computational methods are illustrated using three examples, two linear systems and one nonlinear system of shallow water equations.http://dx.doi.org/10.1080/16000870.2020.1852834error covariancekalman filterquantitative characteristicslocalisation |
| spellingShingle | Wei Kang Liang Xu Some quantitative characteristics of error covariance for Kalman filters Tellus: Series A, Dynamic Meteorology and Oceanography error covariance kalman filter quantitative characteristics localisation |
| title | Some quantitative characteristics of error covariance for Kalman filters |
| title_full | Some quantitative characteristics of error covariance for Kalman filters |
| title_fullStr | Some quantitative characteristics of error covariance for Kalman filters |
| title_full_unstemmed | Some quantitative characteristics of error covariance for Kalman filters |
| title_short | Some quantitative characteristics of error covariance for Kalman filters |
| title_sort | some quantitative characteristics of error covariance for kalman filters |
| topic | error covariance kalman filter quantitative characteristics localisation |
| url | http://dx.doi.org/10.1080/16000870.2020.1852834 |
| work_keys_str_mv | AT weikang somequantitativecharacteristicsoferrorcovarianceforkalmanfilters AT liangxu somequantitativecharacteristicsoferrorcovarianceforkalmanfilters |