The Phase-space Projection Method Of The Signal Extraction From Chaotic Background

The chaos theory is one of the most important achievements in the field of the non-linear science. Along with the theory of relativity, quantum mechanics, the chaos theory is one of the three major twentieth century revolution in physics. The emergence of chaos theory provides new challenges and opportunities to signal processing. The chaos is a complex behavior showned by nonlinear deterministic dynamical systems. It provides a powerful concept, so that people can use the easy power system to explain the very irregular exercises caused by the nature of the performance of certain physical phenomena. One direction of Chaos engineering research is based on chaos theory. Chaotic signal processing is to solve the problem of the separation of the chaotic signal (noise) and useful signal. In accordance with the different purpose of the separation, it can be divided into two situations. A situation wish to get more pure chaotic signal, which is the issue of noise reduction. Another situation is extract useful signal from the chaos' background, which is the signal extraction problem. When infront of with different situations, these two issues are different.This article focuses on the signal extraction from the chaotic background, especially in the direction of weak signal extraction. Meanwhile, there is no priori knowledge beside the observations time series. This is a typical problem blind source separation. Researching on blind source separation problem has two main purpuses. First blind source separation problem is one important theoretical issues of chaotic signal processing. It has not only the important theoretical significance, but also great actually 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.Chaotic phenomena is prevailing in various research fields, and gradually get used in engineering applications, such as chaotic encryption technology, the heart signal processing computer, chaotic secure communication and so on. Therefore, the chaotic signal processing has developed into a new area of signal processing research. the signal detection and extraction from the chaos and noise has great significance. Raised against the methods outlined above, raised the point that when the signal to noise ratio is very low, how to extract usefle signal from the chaotic background is of a great worthy issue. We note that in the last 20 years, the chaotic signal processing techniques have been developed greatly. One of the important branch of the study is that Chaotic dynamical systems equation is in unknown circumstances, assuming that the noise statistics are independent of the additive noise, eliminating noise chaos approach. These methods include wavelet methods, singular spectrum analysis and projection algorithm, and so on. Phase space projection technology has been studied deeply. All methods assummed that: Chaos is Certainly, predictable in short-term. It also appears a specific geometry performance in the reconstructed phase space. In this paper, drawing on these theories and methods, time-frequency analysis to phase space reconstruction theory and technology, the development of some new phase-space projection method, extraction of chaotic signal interference.The creativity task of this paper focuses on three aspects:1.The research of chaotic signal processing technology for extracting signal from chaos is still in its early development.In this paper,the methods in this field are summarized,especially,minimizing phase space volume method,local projection of attractor method,Stark prediction method,the nonlinear inverse of linear filter method and neural network method are discussed.The point of view for each method is analyzed,and a new technology for chaotic signal processing is put forward.2. In this paper, deeply research the chaotic characteristics of the geometric structure. Using the phase-space projection method based on the discrete cosine transform to achive the purpuse, which is used to extract the harmonic singal from the chaos background. Moreover, the results in the simulation using Lorenz chaotic system as background noise are analyzed to prove the performance in the system. At the basis of previous work on,using the method of optimizing neighboring points. Compared with the method of Conventional methods of the smallest Euclidean distance, the frequency of the harmonic signals can be extracted even when the SNR is extremely low. 3. In order to enhance the ability of signal processing in the lower SNR, the Local Space Projection Method based on PCA is given to separate the chaotic and harmonic signals. Moreover, the results in the simulation using Lorenz chaotic system as background noise are analyzed to prove the performance in the system. The frequency of the harmonic signals can be extracted even when the SNR is extremely low, which has been verified through the experiments.In this paper, the main organization of the work and its contents are summarized as follows:First of all, the background and significance of the study are introduced briefly in the first chapter, and the principle of blind signal separation in chaotic surrounding, the problems existed in the research and the development at home and abroad are also introduced in detail.The basic theory about the conception, characteristics and statistical description of chaos are given in the second chapter. Then several models for chaotic attractors and the Local Space Projection Method are introduced as well, which are the basis of following chapters.he third chapter introduced several algorithms for extracting signal in chaotic background. All sorts of technologies used for chaotic signal detection and extraction , the separation technology from chaos and useful signal based on the prediction,RBFneuralnetwork at first. The advantages and problems of signal separation technique based on geometric projection are pointed out at the end of chapter.According to the in-depth analysis of the geometric characteristics of chaos, in combination with DCT, the projection rule is established, and the phase-space projection method based on DCT is also proposed which is used to masking the harmonic signal in Lorenz chaotic interference. The results in the simulation, using Lorenz chaotic system as background noise and sinusoidal signal as the target signal, are analyzed, in order to prove the performance and figure out the disvantages of the method in the system.In chapter V, the approaches of PCA based on the geometric properties of chaos are studied. the projection rule is established when these methods are combined with the Local Space Projection Method, and the phase-space projection method based on PCA is also proposed which is used to masking the harmonic signal in Lorenz chaotic interference. In this section, the results in the simulation using Lorenz chaotic system as background noise and sinusoidal signal as the target signal, are analyzed, in order to prove the performance and figure out the disvantages of the method.A summary of the text, the study also pointed out that there are a number of issues to be resolved that the next step would be to look forward.