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Nonlinear dynamical system identification from uncertain and indirect measurements. (English) Zbl 1129.93545

Summary: 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.

MSC:

93E12 Identification in stochastic control theory
37M10 Time series analysis of dynamical systems
62F10 Point estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93E10 Estimation and detection in stochastic control theory
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