| The frequency estimation in noise background is one of the key problems of spectral estimation areas. It has widely applications in radar, sonar, oscillation measurement, biomedicine, seismic signal processing and etc. Traditional methods of spectral estimation were based on the assumption that the background noise is white noise. But in practical conditions, the assumption of white noise is not always true. When the noise model is not white, the traditional high resolution methods will be deteriorative and even invalid. So, it causes the development of frequency estimation in colored background noise. Recent years, study of high order statistics has been developing quickly, and become a new powerful tool in signal processing. Its application in frequency estimation of colored noise background has achieved good effect. In this dissertation, we put the emphasis on the study of frequency estimation in colored noise background using high order cumulants. Simultaneously, an important problem, the number of signals, which is must to be determined before estimating the frequency, is also discussed here. Firstly, the basic concept and properties of high order cumulants is presented, which is the theoretic base through this dissertation. Then the cumulant-based approaches to the frequency estimation in Gaussian and non-Gaussian colored noise are discussed respectively. And numeric simulations are used to verify the performance of these approaches. Next, we discuss the effect about number estimation of signals to frequency estimation and present some ordinary approaches of determining the number of signals. Then, a novel method, MD (Mean of Difference), is proposed to determining the number of signals. The MD method can work well either in white noise or colored noise environment. The computer simulations verify that its performance is superior to the AIC and MDL criteria based on information theoretic criteria and also superior to the method based on Gerschgorin Disk Criterion. |
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