The Application Of Local Polynomial Estimation In Weak Signal Detection

Signal-detection is an important means of capturing the information for people. It hasbeen widely used in many fields in recent years. However, it often occurs that the usefulsignal is weak while the noise is strong in actual application. Weak signal detection is adifficult and hot spot of research for the domestic and foreign scholars. With thedevelopment of science and technology, we make still great demands on the detection ofweak signal. Weak signal detection is a vital means in developing new and high technologyand in discovering new physical laws. It is also important for promoting the developmentin relevant fields.At the same time we find that Chaotic Phenomena is common in nature and in variouskinds of engineering. It is a very complicated phenomenon and some useful signals areoften contaminated in the form of chaotic noise. For example, chaotic noise exists in thefields of biomedicine radar and sonar. At first of this thesis, we build a model of theproblem as follows：y(t)=s(t)+I(t)+n(t),t∈R, where s(t) is the useful cosinesignal and is very weak; I(t) is strong chaotic noise, n(t) is white noise. We wish toremove the strong chaotic noise from the mixture signals. A new method for combiningphase space reconstruction of chaotic time series and multivariate local polynomialestimation is proposed for the problem of the strong chaotic noise suppression. Wereconstruct the strong chaotic noise according to the theory of phase space reconstructionof chaotic time series. Then we fit it applying local polynomial theory and estimate it witha more accurate method in order that the chaotic noise can be suppressed. We detect theexistence of the Periodic Signals according to the immunity of the Duffing oscillator tonoise. This paper is composed by five chapters, which read as follows：The fist part: the proposition of the problem. We discuss the research background thestudying situation and purpose, train of thought, structure and the main innovations.The second part: we discuss the model of the phase space reconstruction of chaotictime series and local polynomial theory. The theory of phase space reconstruction ofchaotic time series, local polynomial fitting，optimization of parameters are included in thepart.The third part: the suppression of chaotic noise. We reconstruct the strong chaoticnoise according to the theory of phase space reconstruction of chaotic time series. Then we fit it applying local polynomial theory and estimate it with a more accurate method in orderthat the chaotic noise can be suppressed. At last we simulate experiments with Matlab.The fourth part: applying Duffing oscillator to detect weak signals. Weak signaldetection by Duffing oscillator. We prove that Duffing chaotic oscillator is immunologic tonoise both in theory and in experiments by analyzing the trajectory quality of the chaoticsystem. Then we gave the simulative result of the weak signal detection by chaoticoscillator.A summation is made to generalize the work in this paper. Suggestions are proposedfor further research and improvement.