Study On The Frequency Estimation Approaches Of Periodical Signal From Chaotic Noise Background

In recent years, the study on chaos signal theory have been paid attention by a large number of scholars. In many occasions this situation may happen that the target signal is submerged by the noise signal which has chaos behavior. If we don't know the noise is the chaos signal beforehand, because of the complex noise signal wave, the statistic methods will be used to detect the signals, thus the noise which has limited variable can be regarded as stochastic noise to be dealt with. But sometimes the modeling of noise signal is not well and the detecting capability is bad. If we use the transcendent knowledge that the noise is chaos signal and use the characters of chaos to deal with the signals, the signals submerged in the chaos noise can be detected. Therefore, the signal estimation under chaos noise background has important meanings in theory study and practice applications, this method may be widely used in all kinds of fields such as photics, electricity, magnetism, acoustics, calorifics, biology, mechanics, geology, entironment, medicine, laser, material and so on.In many signal estimations which are under chaos noise, the most important one is to estimate periodical signals. Because of the structural particularity of periodical signals, the estimation theories and study methods have great meanings not only in theory aspects, but also have broad applicatiibs in practice project fields such as radar, communication, biomedicine and so on.There are plenty of methods to estimate the parameters of periodical signals under chaos noise background. Usually the chaos characters are used. According to the received signals to reconstruct the phase space of the background signal, the chaos forecasting mode can be acquired. Then using the received signal to subtract the forecasted chaos noise, the periodical signal submerged in chaos noise background can be estimated. The existing methods are MPSV method, false neural network method, short time forecasting method, nonlinear filter and phase space reconstruction method, local cutting space projection method and so on. But these methods are all based on the phase space reconstruction of chaos system, this may brings many errors, increases the calculation and the resisting noise capability is bad.In view of this, the paper starts from another point of view, using the correlation method and wavelet transform method to estimate the frequencies of periodical signals submerged in chaos noise background. These two methods can effectively estimate the frequencies of the periodical signals submerged in chaos noise background when the SNR is lower. The paper lucubrates on these two methods and takes the harmonic signals as examples. The work and main conclusion of the paper are as follows:1. Analyse the major characteristics of chaos movement. Chaos has the specialties such as long time inscrutability, poor correlation, inner randomicity etc. In the existing chaos systems, one kind of them has the frequency spectrum specialty of limited bandwidth and its energy mainly focus on the low frequency segment, such as Duffing system, Lorenz system and Rossler system etc. For the chaos system of this kind, if the chaos noise overlapped with the frequencies of the periodical signals which are submerged in the chaos noise, the estimation of the frequencies of the periodical signals may become difficult. So the estimation of the periodical signals from the chaos noise background has practice meanings. The paper takes the three chaos system as noise, analyses their dynamics mode and specialties. At the same time, the time response pictures and the phase slot curves are given.2. Use the correlation theory to estimate the frequencies of the harmonic signals from chaos noise background. The paper introduces the basis theory using the correlation to estimate the frequencies of the harmonic signals which is under the chaos high frequency segment. First, the characteristics of the noise are given and are used to analyse chaos noise. Then the correlation method is used to estimate the harmonic signals under chaos noise. The paper takes Duffing system, Lorenz system and Rossler system for example respectively and process with simulating experiments. The experiment results prove that the correlation method can detect the frequencies of the harmonic signals under chaos noise effectively and the method has good resisting noise quality. When the frequencies of the harmonic signals focus on the high energy segment of the chaos noise, the double frequency method is used to move the frequencies of the harmonic signals to the higher frequency segment of the mixed signals. This can disjoin the frequency of the harmonic signals from chaos noise. Then the correlation method is used to estimate the frequencies of the harmonic signals effectively.3.Use the combination of wavelet transform method and correlation method to estimate the frequencies of the harmonic signal under chaos noise background. The Daubechies vertical wavelets are used to decompose the harmonic signal under the chaos noise background, then the low frequency coefficients acquired from the decomposed result are used to reconstruct the signal. The signal is the estimate signal of the chaos noise. The estimate signal subtractes from the measured signal and the residual signal is gained in which there are a lot of components of the harmonic signal. Then the correlation method is used to calculate the gained signal, the frequencies of the harmonic signal can be estimated effectively.4. Estimate the frequencies of the harmonic signals submerged in the mixed noise background. The mixed noise are composed by the white noise and the chaos noise, the color noise and the chaos noise respectively. Then the correlation method and the wavelet transform method are used to detect and pick up the harmonic signals submerged in the mixed noise. Meanwhile, the simulating experiments are given. The experiment results show that the methods are not only adapt to the chaos noise but also adapt to the mixed noise which are composed by the white noise and the chaos noise, the color noise and the chaos noise respectively. The methods can estimate the frequencies of the harmonic signals in a low SNR situation.In a word, through the study work of the paper, the conclusion is that the correlation method and the wavelet method can be used to estimate the frequencies of the periodical signals under chaos noise background. Especially for estimation of the frequencies of the harmonic signals, the methods have obvious superiority. Using the methods can estimate the frequencies of the weak harmonic signals under the chaos noise successfully and reach upper precision in a low SNR situation. The large number of simulating experiments shows that the methods used in the paper are feasible and effective. Besides this, the methods can detect the frequencies of the harmonic signals under the mixed noise which are composed by the white noise and the chaos noise, the color noise and the chaos noise respectively. The methods used in the paper compensate the deficiencies of the existing methods of estimating the frequencies of the periodical signals under the chaos noise background. It has very high practical value in the actual project application, specially in the heart electrical signal, theradar signal, seismic signal processing,etc.