Detection of the chaotic process distorted by the white noise using BDS statistics

Abstract

A nonparametric criterion for the detection of a chaotic process observed against the background of white noise has been proposed with due regard for the dependence of the process values. BDS statistic is used for the numerical account of the degree of dependence of values of the process observed. It was shown that this criterion refined the conventional estimate of the chaotic process stealthiness that was obtained using the energy criterion for detecting deterministic signals of the unknown “waveform” and random processes. Characteristics of a nonparametric detector of chaotic processes with a different degree of the dependence of its values were obtained on the basis of computer simulation under condition of the exposure to additive white Gaussian noises of different intensity.