Study On The Weak Signal Detection Approaches Based On The Specific Chaotic System

The WSD(weak signal detection)is a new technology, which studies the principle and the method of detecting the weak signal under the strong noise background. Using this kind of technology can detect the weak signal (for example weak light, small displacement, micro vibration and so on), which the traditional method cannot solve. Therefore, this method may be widely used in optics,material and so on. Finding the new method of detecting the weak signal and developing new equipment has been the hot topic in the weak signal detecting area.The multitudinous methods of detecting the weak sine signal are mostly based on study the noise's rule (for example the noise's scope, frequency, phase and so on) and analysis the signal's characteristic (for example signal's frequency spectrum, coherence and so on). The work of restrain noise is the main aspect in signal processing research field, using the traditional high step statistical methods, people have given some satisfied results, but there exist low SNR ubiquity. The traditional methods have not well satisfied results for these aspect problems, in the complex noise (the correlation and un-correlation multiply or plus noise) or very low SNR background, are not well-solved focus problems.As the core of nonlinear scientific research, chaotic theory has important the academic and practical meanings. People have made great progresses in the discussion of chaotic theory and application of chaotic project in recent 20 years. With using the chaos theory to the field of WSD , the measurement by applying original parameter sensitive of chaotic theory is a newer way of weak signal measuring, has expanded the chaos theory application domain and promoted the WSD to be a major step.This dissertation makes a deeply research on WSD, using different chaos oscillators such as Duffing systems and Lorenz systems, getting hold of the effective detection methods in low SNR. The contents of this dissertation are summarized as following:1. Introduce some basic concepts of chaos theory and dynamic systems, including some important characters such as the sensitivity on initial condition and parameters value. In fact, there are many non-linear dynamics models, which can produce the chaos phenomenon. Analyze Duffing systems and Lorenz systems in detail, make a deeply research on dynamic behavior of chaos theory to weak signal detection systems and the time-frequency distribution characteristics of Duffing systems, plot the phase orbit by the different initial condition and parameters value. 2. Analyze several common methods to judge the chaotic system's state. At present, in the aspect of the application on how to use the chaotic measure methods for weak signal parameters estimate, people always select the waiting-measured-weak-signal to disturb the chaotic system, then observe the photograph change situation, this methods will easily bring into very great observation error, there least a efficient mathematic tool to measure the chaotic criterion. Therefore, the article discussed two mathematic chaotic criterion : The Information entropy method and the Chaotic measurement method, which advance two quantificational standard to judge whether the chaos system enters to the chaotic state, these methods are accuracy, moreover they need not to observe the entire moving process of the chaos system.. Use the basic theory of information, calculate the information Shannon value of chaotic system, find out that the chaotic system has very big information Shannon value, enhance the accuracy of the judgment. About the chaotic measurement method, analyze the construction of the measurement function and the special-parameters-mapped-muster. Actually, we usually use these two kinds of quantificational criterions to judge the chaos system's condition, which enhances the judgment's accuracy.3. Analyze the amplitude measurement methods of the known frequency signal. Based on the important character of the sensitivity on initial condition and parameters value, on the one hand, the article associates the correlation theory with the chaos method to detect the weak sine signal. First, make the mutual correlation operation with the noise and the weak signal, then sent the signal into the chaos system to detect the weak signal's amplitude by the chaotic measurement method. On the other hand, the article brings another method, associate the ANC (adaptive noise canceller) theory with the chaos method to detect the weak sine signal. The experiment result has proved that use the two methods can lower the SNR. The article has carried on enough simulations to confirm the method is good and effective to detect the weak signal's amplitude.4. Discuss the dynamics characteristic of Lorenz systems. The three step non-linear systems have many perfect quantities. It may become to be a chaotic system under some conditions. The detection method uses every step equation to estimate parameters of a series signal. We analyze three step Lorenz system, and then bring forward the methods to estimate parameters of faint periodic signal with the use of some step equation of Lorenz system, and even we can realize unite estimation for parameters of a series faint signal. Every step equation of Lorenz system has high sensitivity to the parameters of the input signal, which can bring the great change of the motioning state of the chaos system. We bring out the methods to estimate frequency of the single input signal with use of this sensitivity. Then, we pay more attention on the estimation for parameters of multi-input signals. The simulation experiments show that Lorenz systems can effectively detect the frequency of the unknown sinusoidal signal under the noise background.The method about WSD based on chaos theory is a kind of novel, completely different signal processing method compared with the traditional time domain signal detecting method,specially to detect the weak sine signal. Through enough simulations, it confirmed that the method is feasible and effective in detecting the weak signal,provided new methods for the signal processing. We believe that the outstanding features such as high linearity and high sensitive fit for the WSD are attracting more and more people plunge into.