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Estimability and dependency analysis of model parameters based on delay coordinates.

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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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Luther,  Stefan
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

Schumann-Bischoff, J., Luther, S., & Parlitz, U. (2016). Estimability and dependency analysis of model parameters based on delay coordinates. Physical Review E, 94(3): 032221. doi:10.1103/PhysRevE.94.032221.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-A30B-3
Abstract
In data-driven system identification, values of parameters and not observed variables of a given model of a dynamical system are estimated from measured time series. We address the question of estimability and redundancy of parameters and variables, that is, whether unique results can be expected for the estimates or whether, for example, different combinations of parameter values would provide the same measured output. This question is answered by analyzing the null space of the linearized delay coordinates map. Examples with zero-dimensional, one-dimensional, and two-dimensional null spaces are presented employing the Hindmarsh-Rose model, the Colpitts oscillator, and the Rossler system.