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
Parent title (English):Entropy : an international and interdisciplinary journal of entropy and information studies
Place of publishing:Basel
Publication type:Article
Year of first publication:2019
Year of completion:2019
Release date:2021/02/22
Tag:continuous-time data assimilation; correlated noise; ensemble Kalman filter; multi-scale diffusion processes; parameter estimation
Page number:23
Funding institution:Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [CRC 1294, CRC 1114]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Publishing method:Open Access / Gold Open-Access
License (German):License LogoCreative Commons - Namensnennung, 4.0 International