Noise Robust Method for Analytically Solvable Chaotic Signal Reconstruction

A new chaotic signal reconstruction method for analytically solvable chaotic systems (ASCS) under strong noise condition is proposed in this paper, which solves the problem of unsatisfactory reconstruction performance under strong noise condition. In the proposed method, firstly, binary symbols of ASCS are obtained under strong noise condition by integrating the observed signal over a specific interval of every binary symbol period and comparing integration results with a zero value threshold. Then, the relationship between the original signal and another ASCS is derived analytically based on the obtained binary symbol sequence. According to the derived relationship, the original signal can be reconstructed by the output of another ASCS which is driven by the obtained binary symbol sequence reversed in time. Theoretically, the proposed method can reconstruct signals under strong noise condition with small error since the integration result of additive white Gaussian noise in every integration interval approaches zero. Finally, the proposed method is demonstrated with numerical simulations which show the original chaotic signal can be reconstructed with small error even when the signal-to-noise ratio is -30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-30$$\end{document} dB, and thus the proposed method outperforms conventional methods.