Nonparametric BDS detector of chaotic signals against the background of white noise




nonparametric detector, BDS-statistics, ATS-attractor trajectory surrogate, signal form, correlative dimension


This paper includes an algorithm proposed for detecting a chaotic signal, the functional block diagram for implementing the algorithm proposed, and also the ATS algorithm for generation of surrogate signals that are used in a detector for empirical estimation of the likelihood ratio. A comparative analysis of the detection characteristics obtained by using a conventional (energy) approach and the proposed approach based on using topological properties of signals and noises.


P. Yu. Kostenko, A. N. Barsukov, K. S. Vasiuta, and S. N. Symonenko, “Detection of the Chaotic Process Distorted by the White Noise Using BDS Statistics,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 52(11), 41 (2009) [Radioelectron. Commun. Syst. 52(11), 599 (2009)].

G. I. Tuzov, V. A. Sivov, V. I. Prytkov, et al., Noise Immunity of Radio Systems with Compound Signals (Radio i Svyaz’, Moscow, 1985) [in Russian].

W. A. Brock, W. D. Dechert, and J. A. Scheinkman, “A Test for Independence Based on the Correlation Dimension,” in Working Paper No. 8702, Department of Economics, University of Wisconsin, 1987.

H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, 2nd ed. (Cambridge University Press, Cambridge, 2004).

S. E. Fal’kovich and P. Yu. Kostenko, Fundamental Statistical Theory of Radio Engineering Systems. Tutorial (NAU KhAI, Kharkov, 2005) [in Russian].

J. P. Eckmann and D. Ruelle, “Fundamental Limitations for Estimating Dimensions and Lyapunov Exponents in Dynamical Systems,” Physica 56, 185 (1992).

J. Theiler, S. Eubank, A. Longtin, et al., Testing for Nonlinearity in Time Series: The Method of Surrogate Data,” Physica 58, 77–94 (1992).

M. Small, Applied Nonlinear Time Series Analysis Applications in Physics, Physiology and Finance (World Scientific Publishing Co. Pte. Ltd., Singapore, 2005).

L. Kanzler, Very Fast and Correctly Sized Estimation of the BDS Statistic (Christ Church and Department of Economics, University of Oxford, 1999).

G. G. Malinetskii and A. B. Potapov, Modern Problems of Nonlinear Dynamics (Editorial UkrRSS, Moscow, 2000) [in Russian].





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