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Accurate state and parameter estimation in nonlinear systems with sparse observations

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Schumann-Bischoff,  Jan
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Parlitz,  Ulrich
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Rey, D., Eldridge, M., Kostuk, M., Abarbanel, H. D. I., Schumann-Bischoff, J., & Parlitz, U. (2014). Accurate state and parameter estimation in nonlinear systems with sparse observations. Physics Letters A, 378, 869-873. doi:10.1016/j.physleta.2014.01.027.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-0F6F-D
Abstract
Transferring information from observations to models of complex systems may meet impediments when the number of observations at any observation time is not sufficient. This is especially so when chaotic behavior is expressed. We show how to use time-delay embedding, familiar from nonlinear dynamics, to provide the information required to obtain accurate state and parameter estimates. Good estimates of parameters and unobserved states are necessary for good predictions of the future state of a model system. This method may be critical in allowing the understanding of prediction in complex systems as varied as nervous systems and weather prediction where insufficient measurements are typical.