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  5. The new approach to nonparametric detection of chaotic signals against a white noise with use of "nonlinear dynamic statistics"

The new approach to nonparametric detection of chaotic signals against a white noise with use of "nonlinear dynamic statistics"

P.Y. Kostenko, K.S. Vasuta, O.M. Barsukov, S.N. Symonenko
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In paper reasons of insufficient efficiency of the energy approach to detection of signals of the unknown "shape", based on 2-statistics use are become clear. The concept "shape" of a signal about the help of correlative dimensions of a quantity and the BDS-statistics related to it is formalized. The approach to nonparametric detection of a random signal against a white noise with an unknown density function of its significances with use BDS-statistics is analyses. Algorithms of detection of a random signal, the skeleton diagrammed of its implementation, and also ATS-algorithm of shaping of substitute signals which are used for an empirical estimate of the ration of likelihood are offered.
Keywords: nonparametric detector, BDS - statistics, ATS – attractor trajectory surrogate, signal "form", correlative dimensions