Long-Time stability and accuracy of the ensemble Kalman-Bucy Filter for fully observed processes and small measurement noise
- The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman-Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman-Bucy filter is consistent with the classic Kalman-Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system.
| Author details: | Jana de WiljesORCiDGND, Sebastian ReichORCiDGND, Wilhelm StannatORCiD |
|---|---|
| DOI: | https://doi.org/10.1137/17M1119056 |
| ISSN: | 1536-0040 |
| Title of parent work (English): | SIAM Journal on Applied Dynamical Systems |
| Publisher: | Society for Industrial and Applied Mathematics |
| Place of publishing: | Philadelphia |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2018/04/17 |
| Publication year: | 2018 |
| Release date: | 2022/03/25 |
| Tag: | Kalman Bucy filter; accuracy; asymptotic behavior; data assimilation; ensemble Kalman filter; stability |
| Volume: | 17 |
| Issue: | 2 |
| Number of pages: | 30 |
| First page: | 1152 |
| Last Page: | 1181 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [CRC 1294] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Hybrid Open-Access |
| License (German): |  CC-BY-NC - Namensnennung, nicht kommerziell 4.0 International |
