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State and Parameter Estimation from Observed Signal Increments

Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam, Germany
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Entropy 2019, 21(5), 505; https://doi.org/10.3390/e21050505
Received: 26 March 2019 / Revised: 13 May 2019 / Accepted: 14 May 2019 / Published: 17 May 2019
(This article belongs to the Special Issue Information Theory and Stochastics for Multiscale Nonlinear Systems)
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Abstract

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. View Full-Text
Keywords: parameter estimation; continuous-time data assimilation; ensemble Kalman filter; correlated noise; multi-scale diffusion processes parameter estimation; continuous-time data assimilation; ensemble Kalman filter; correlated noise; multi-scale diffusion processes
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Nüsken, N.; Reich, S.; Rozdeba, P.J. State and Parameter Estimation from Observed Signal Increments. Entropy 2019, 21, 505.

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