The Use of BDS Statistics for Estimating the Parameters of Chaotic Mappings and Regular Signals in the Presence of Noise

摘要

A new method has been proposed in this paper for estimating the parameters of chaotic and regular signals by their observation against the background of white noise under conditions of the a priori uncertainty about the distribution of its values. The method is based on using the nonparametric BDS statistic revealing the sensitivity toward topological properties of the attractors of chaotic, regular and random processes that are characterized by the correlation dimension. The results of numerical simulation of the method proposed for the estimation of parameters of one-dimensional and two-dimensional chaotic mappings and also the harmonic oscillation frequency for the noise with uniform and Gaussian distribution at different levels of its intensity have been presented. This study also includes the analysis of accuracy of estimating the harmonic oscillation frequency by the proposed method and its comparison with potentially attainable values.