Research On Methods Of Extracting Signals From Chaos

A wide variety of natural phenomena exhibit complicated, unpredictable and seemingly stochastic behavior. Chaotic dynamics appears to provide a relatively simple and possibly more satisfactory explanation to a lot of complicated phenomena among them. Chaos theory shows that simple deterministic systems with only a few variables can generate seemingly stochastic behavior. The purpose of chaotic theory is discovering possible simple rules which hide in the seemingly random phenomena and obtaining common rules which a kind of complex phenomena keep to. Chaos is an outer complex behavior of nonlinear definite system, produced by the system's internal stochastic property, a non- stochastic movement while looks like stochastic. One of the basic characteristics is that the system is highly sensitive to original condition, that is to say, the little difference of original condition assumes exponential increase until it is unacceptable. Chaotic signal differs from traditional periodic signal and pseudo- periodic signal, it also differs from purely stochastic signal. Chaos is essentially deterministic, but the long-playing trend cannot be forecasted. The deterministic, pseudo-stochastic and short-time divinable characteristics of chaos make it have application value in some applying field, such as chaotic secure communications, electron counterwork.Chaotic signal processing is a fire-new branch of non-linear signal processing. It has abundant research tasks in natural and engineering field, such as ocean, geology, biology and chemistry et al. Nowadays, Chaotic signal processing becomes a pop science research field. As an important branch of chaotic signal processing, signal extraction from chaotic background has important theory and application value. For example, target signal extracted from sea clutter(which has been proved to be chaotic), fetal electrocardiogram extracted from matrix in biomedicine, weak signal extracted from visual evoked potential and resisting chaotic interference all belong to signal extraction from chaotic background. On the other hand, signal extraction blindly from chaotic background is the most important and effective means to attack chaotic secure communication. Doing research on signal separation blindly supply use for reference to chaotic secure communication. In this thesis, many new theoretical methods ,which are used to extract signals from chaos backgroungs under different conditions such as signal to noise ratio ,frequence ranges, have been put forward application of natures of chaos (time-frequence nature, geometrical nature, statistical nature) and modern signals processing theories (Fourier transform, wavelet transform, harmonic wavelet transform, empirical mode decomposition, cosine transform, principal component analysis, independent component analysis, power spectrum dense analysis, phase space reconstruction technique). Imitations by computer have proved effectiveness, robustness and usefulness of these methods.The creative works of this thesis include three aspects:1. Time-frequency characteristics of two kinds of typical chaos (Lorenz attractor and Henon attractor) have been analyzed. Energy distributions of chaos, harmonics and noise in wavelet domain was resrarched .Based on the results, the method of wavelet multi-scale decomposition was proposed to extract harmonics from chaos interference. The method is simple, has faster calculation speed, and gives satisfactory results for extraction of harmonics in Lorenz chaos under condition that signal to noise ratio is not lower.In the presence of white Gaussian noise in chaos, a new method was put forward based on combining wavelet threshold denoising and wavelet multi-scale decomposition. Two new threshold denoising algorithms were derived. Through analyzing the experiment result, the two threshold methods are valid, especially station wavelet soft-threshold algorithm with variable universal threshold. The methods that combine wavelet multi-scale decomposition and threshold denoising are antinoise.Aimed at energy leakage that come from wavelet decomposition and in-band noise, a synthesis approach based on harmonic wavelet transform and empirical mode decomposition was proposed for resolving them through making use of box-like spectrum specific property of harmonic wavelet and data-adaptive property of empirical mode decomposition. The technique has better quality of extraction.2. The geometrical structure property of chaos was systematically analyzed, and three phase space projection methods are provided that are method based on wavelet, method based on cosine transformation and orthogonal projection method.The first two methods can be used to extract harmonics from Lorenz chaos, and acquire high-quality estimation of harmonics, provided that signal to noise ratio is higher than -55dB.The orthogonal projection method, because of using new algorithms of selection of neighborhoods, can be used to extract harmonics and other signals, provided that signal to noise ratio is higher than -80dB.3. This thesis also studied the statistical property of chaos, comes up with the concept that signals can be extracted by non-gauss property using independent component analysis. It has been tested in experiments that various signals can be obtained with this method provided that signal to noise ratio is not lower than -100dB. What is more important, the extraction dosen't suffer frequency restriction, which is an advantage over other methods.The dissertation consists of seven chapters.Chapter 1 explains the dissertation research contents and principal work. At the same time, the chapter briefly introduces the history and present situation information of signal extraction blindly from chaotic background, points out the existing problems.In Chapter 2, some basic theories on chaos are described. It introduces the basic knowledge of chaotic signal processing, including the concept of dynamic system and chaos, the fundamental characteristic, statistical description of chaotic strange attractors and state space reconstruction. The above contents are the base of later research.Chapter 3 introduces several algorithms of predecessors: algorithm of minimizing the phase space volume, separation algorithm of chaos and signals based on prediction, separation algorithm of chaos and signals based on projection and algorithm based on neural network. At the same time, this section analyzes the algorithms above and points out disadvantage, then proposes new thinking of signals retrieval from chaotic background.In Chapter 4, analyzing time-frequency properties and energy distribution characteristics in wavelet domain of Lorenz chaos whose mathematic model is differential equation and Henon chaos whose mathematic model is difference equation, wavelet multi-scale decomposion based method was put forward, and mostly is used to extract signals from Lorenz chaos. Through a series of simulations, its effectiveness is verified. At the same time, some disadvantages are discussed. When there is noise in the chaos background, two new algorithms of wavelet threshold filtering were presented as post-processing way to eliminate white gauss noise and residul from chaos in harmonics, thus lower influence of noise. Because of multi-scale decomposition bringing about in-band noide and energy leakage, this causes extraction quality to drop. To rsolve the problems, a new method based on harmonic wavelet transform and empirical mode decomposition is adopted to extract harmonics from Lorenz chaos. The simulations show that the method receives good results.In Chapter 5, continue to study how to extract signals in chaos when signal to noise ratio is lower than -32 dB. The geometrical property of chaos was investigated, and principal component analysis was applied to analyze the singular value distribution of chaos. Then phase space projection method based on wavelet transform and cosine transform were used to extract harmonics from Lorenz chaos. The experiment results show that the methods make level of extracting harmonics to increase 20dB. But in the case of very low signal to noise ratio or extracting signals from Henon chaos, the above methods failed. Thus orthogonal local projection with new algorithms of selection of neighbourhoods was applied to extract signals from two standard chaoses. The experiment results verify that the approach is effective, provided signal to noise ratio is higher than -80dB.Chapter 6 Time-frequency methods and phase space projection methods are limited to two aspects: one is chaotic model, associated with continuous chaos system and discrete chaos system; the other is frequency of signals. For the sake of solving the probems, according to the statistical property of chaos, a new thinking was presented to separate signals from chaos by using independent component analysis with non-gauss property criterion. A series of experiments were conducted, and the results are quite satisfactory, provided signal to noise ratio is not lower than -100dB. What is more important, the method overcomes frequency restriction.Chapter 7 a brief summary of the thesis was given. Some problems and further research aspects have been presented.