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 id...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2019-05, Vol.21 (5), p.505
Main Authors: Nüsken, Nikolas, Reich, Sebastian, Rozdeba, Paul J.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
continuous-time data assimilation
correlated noise
Data assimilation
ensemble Kalman filter
Kalman filters
Mathematical models
multi-scale diffusion processes
Parameter estimation
Parameter identification
Partial differential equations
Scale models
State estimation
Velocity
Velocity distribution
Vlasov equations
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e21050505