State and parameter estimation from observed signal increments
- The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.
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| Author details: | Nikolas NüskenORCiD, Sebastian ReichORCiDGND, Paul J. RozdebaORCiD |
|---|---|
| URN: | urn:nbn:de:kobv:517-opus4-442609 |
| DOI: | https://doi.org/10.25932/publishup-44260 |
| ISSN: | 1866-8372 |
| Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
| Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (916) |
| Publication type: | Postprint |
| Language: | English |
| Date of first publication: | 2020/05/27 |
| Publication year: | 2019 |
| Publishing institution: | Universität Potsdam |
| Release date: | 2020/05/27 |
| Tag: | continuous-time data assimilation; correlated noise; ensemble Kalman filter; multi-scale diffusion processes; parameter estimation |
| Issue: | 916 |
| Number of pages: | 25 |
| Source: | Entropy 21 (2019) 5, 505 DOI: 10.3390/e21050505 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
