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Identification of models for chaotic systems from noisy data: implications for performance and nonlinear filtering. (English) Zbl 0888.93015
Summary: This paper investigates the identification of global models from chaotic data corrupted by additive noise. It is verified that noise has a strong influence on the identification of chaotic systems. In particular, there seems to be a critical noise level beyond which the accurate estimation of polynomial models from chaotic data becomes very difficult. Similarities with the estimation of the largest Lyapunov exponent from noisy data suggest that part of the problem might be related to the limited ability of predicting the data records when these are chaotic. A nonlinear filtering scheme is suggested in order to reduce the noise in the data and thereby enable the estimation of good models. This prediction-based filtering incorporates a resetting mechanism which enables the filtering of chaotic data and which is also applicable to non-chaotic data.

MSC:
93B30 System identification
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
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