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Nonlinear dynamical system identification from uncertain and indirect measurements

  • We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples

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Metadaten
Author:Henning U. Voss, Jens Timmer, Jürgen KurthsORCiDGND
ISSN:0218-1274
Document Type:Article
Language:English
Year of first Publication:2004
Year of Completion:2004
Release Date:2017/03/24
Source:International Journal of Bifurcation and Chaos. - ISSN 0218-1274. - 14 (2004), 6, S. 1905 - 1933
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik