Study On Time Delay Estimation And Filtering Methods In α-stable Noise

Non-Gaussian signal processing is a new signal processing field in recent years. The traditional signal processing is based on Gaussian distribution and second-order statistics in theory and technology. Because the Gaussian model is easier and reasonable in many instances, it often leads to analytically tractable solutions for signal processing problems.Though in many instances the Gaussian assumption is reasonable, there are many non-Gaussian signals and noises in the actual applications, the remarkable characteristic of the sort of stochastic signals or noises is that the tails of the stable density are heavier and results in the remarkable impulsive nature in waveform. In nature, this impulsive and heavy tailed nature are remarkable characteristics of the fractional lower orderα-stable distribution(FLOA). Theα-stable distribution, which is one kind of mathematical model of non-Gaussian noises, is an important issue in signal processing field.Firstly, this paper introduces the parameter estimation methods ofαandγin the symmetricα-stable distribution(SαS), then places extra emphasis on the algorithms of time delay estimation under the SαS distributed noise condition, in the end, introduces adaptive filter algorithms under the SαSG distributed noise condition, The main content includes the followings:1. Review the research background ofα-stable distribution, expound research status, fundamental conceptions, features, principle and application prospects.2. Introduce the parameter estimation methods of symmetricα-stable distribution. The computer simulations based on quantiles of samples method and log SαS method indicate that the two methods both can give better estimated results and the results can satisfy the needs of the study, and log SαS method has smaller computation and the closed-form formula for calculating, so it has a more superior performance.3. Under the condition of symmetricα-stable distributed and spatial and temporal independent noises, the thesis analyzes the shortcoming of time delay estimation algorithm based on fractional lower order covariance (FLOC) which requests the previous estimation of characteristic exponentαin order to choose an appropriate value of fractional lower order exponents of input signals A and B, and combines time delay estimation algorithm based on FLOC and anti-hyperbolic sine transform to introduce time delay estimation algorithm based on anti-hyperbolic sine transform. The new algorithm overcomes the shortcoming of depending on the previous estimation of the characteristic exponentα. It is easy to real-time signal processing, and has got a high estimated precision through computer simulations. But it exits the shortcoming of significant degradation when the independence of the symmetricα-stable distributed noise can not be satisfied.4. On the foundation of log SαS process, cost function is defined based on third-order moment of the log SαS process. A new time delay estimation method is introduced by minimizing the cost function. The parameterαcan be estimated by the new method introduced in the thesis. The experimental results indicate that robustness of this method is stronger and can give better test results regardless of SαS niose whether or not to meet the independence, and well resolves the problem of notably degeneration when the independence of SαS distributed noise can not be satisfied.5. When the system noise satisfies SαSG distribution, the thesis adopts sigmoid function transform on instantaneous error based on RMN filter algorithm in order to transform the instantaneous error to two-order process. In this way the processing of SαSG distribution noise is converted into the processing of two-order process. The optimizing simulation results of normalizd weight error vector indicate that performance of this algorithm has been improved.In the end, the work is summarized and the further research direction is pointed out.