【作者】 孙永梅；

【导师】 邱天爽；

【作者基本信息】 大连理工大学 ， 信号与信息处理， 2006， 博士

【摘要】 随着科学技术的进展,非高斯随机信号处理理论与应用得到了广泛的重视与发展。在实际应用中所遇到的大量的非高斯信号或噪声具有显著的尖峰脉冲特性,由于这种脉冲特性,使得这类非高斯过程的统计特性显著偏离高斯分布,特别是其概率密度函数的衰减过程比高斯分布要慢,从而造成了显著的拖尾。如果采用高斯分布模型来描述这类过程,将会由于模型与信号噪声不能很好匹配而导致所设计的信号处理器性能退化,而α稳定分布则为这类过程提供了非常有用的理论工具。 α稳定分布是一种广义的高斯分布,它可以很好地描述现实生活中的许多高斯和非高斯α稳定分布信号和噪声,基于α稳定分布假定所设计的信号处理算法对信号噪声特性不确定情况具有较好的韧性。对α稳定分布信号处理理论的研究有助于信号处理理论从二阶统计量理论向高阶和分数低阶统计量理论的发展,从而形成一个完整的理论体系。为了丰富和发展α稳定分布和分数低阶统计量理论,本文对α稳定分布的参数估计问题和谱分析方法进行了深入的研究,并依据α稳定分布信号噪声特性,设计了具有韧性的时间延迟估计方法和EP潜伏期变化检测方法。论文的主要内容包括: (1) 为了保证信号噪声模型的准确性和算法的可靠性,由α稳定分布的一个样本实现得到信号噪声模型参数的精确估计显得十分重要。考虑到信号噪声模型的参数随时间变化的情况,本文设计了两种能够实现动态参数估计的递推参数估计方法,分别是基于负阶矩的递推参数估计方法和基于对数法的递推参数估计方法,新方法可以有效地跟踪信号噪声特征参数随时间的变化。在诱发电位(EP)潜伏期变化检测的问题中,考虑到EP信号背景噪声的时变特性,本文将上述动态参数估计方法与现有的EP潜伏期变化的检测方法相结合,提出了直接最小p范数(DLMP)算法和自适应分数低阶协方差(AFLC)算法的改进算法,新算法避免了原算法中参数选择对算法性能产生影响的问题,能够实时跟踪背景噪声的变化,进行系统参数调整,保证了算法的可靠性。此外,本文还提出一种基于神经网络预处理的EP潜伏期变化的动态韧性检测方法,理论分析和仿真实验表明,通过神经网络的预处理,可以有效地抑制带噪EP信号的脉冲噪声,实现潜伏期变化的可靠估计。 (2) 依据α稳定分布信号处理理论和分数低阶统计量理论,本文对α稳定分布的频域特性进行分析,定义了分数低阶协方差谱的概念,系统研究了分数低阶协方差谱的性质。同时,对分数低阶协方差谱的估计问题进行了深入研究,提出了直接法、间接法、加权交叠平均法和特征分解法等分数低阶协方差谱估计方法。理论分析和仿真实验表明,分更多还原

【Abstract】 With the development of science and technology, the theory and application of non-Gaussian stochastic signal processing gain widen regards and developments. In practice, various non-Gaussian signals and noises have distinct spiky and impulsive characteristics, leading them deviate from Gaussian distribution. If such processes are still modeled with Gaussian distribution, the designed signal processor will degenerate for the miss-match between the models and signals, while α-stable distribution is the useful tool for these processes.α-stable distribution is a kind of generalized Gaussian distribution. It can exactly describe the Gaussian and non-Gaussian α-stable distribution signals and noises in reality. The algorithms based on assumption of α-stable distribution is robust under uncertain characteristics of signals and noises. The study on the theory of a -stable distribution signal processing helps to the development of the theory of signal processing from second order statistics to both higher order and fractional lower order statistics, consequently form a integrated theory system. This dissertation focuses on the study of the parameter estimation and spectral analysis of α-stable distribution, and designs robust time delay estimation methods and evoked potential (EP) latency change estimation methods according to the characteristics of α -stable distribution. The main researches and conclusions are listed as follows:(1) In order to ensure the accuracy of models and the reliability of algorithms, it is important to obtain precise estimation of parameters from one sample realization of α-stable distribution. Considering of the condition of time variant parameters of the models, two dynamic parameter estimation methods based on the negative moment and the logarithm are proposed in order to realize dynamic estimation. The dynamic parameter estimation methods can track the changes of parameters effectively. On the latency change estimation of EP, this dissertation improves both Direct Least Mean p-norm (DLMP) algorithm and Adaptive Fractional Lower-order Covariance (AFLC) algorithms by combining the dynamic parameter estimation methods with the existing EP latency change estimation algorithms. The new algorithms overcome the drawbacks arosed by the parameter selection, and ensure the reliability of the algorithms. Further more, a new EP latency change estimation method based on neural network preprocessing is proposed. Theoretical analysis and simulation resultsshow that this method suppresses the impulsive noises in EP signals and realize reliable estimation of EP latency changes.(2) According to the theory of a -stable distribution signal processing and fractional lower order statistics, this dissertation analyze the frequency domain characteristics of a-stable distribution. A definition of fractional lower order covariance spectrum is proposed, and the properties and the corresponding proofs of fractional lower order covariance spectrum are given in the dissertation. A thorough study is conducted on the estimation of fractional lower order covariance spectrum. The direct method, indirect method, weighted overlap average method and character decompose method for the estimation of fractional lower order covariance spectrum is proposed. Theoretical analysis and simulation results show that the fractional lower order covariance spectrum is an effective tool of frequency domain analysis for a -stable distribution processes. Moreover, the output characteristic in time and frequency domains of linear time invariant system excited by a -stable distribution processes is discussed.(3) According to the degeneration of traditional second statistics based time delay estimation methods under a -stable distribution environments, this dissertation proposes weighted time delay estimation methods and adaptive weighted time delay estimation methods suitable for a -stable distribution environments. Moreover the new methods of multi-source time delay estimation are designed. The fractional lower order covariance spectrum based methods and the nonlinear transform based weighted time delay estimation methods perform robust under both Gaussian and non-Gaussian a -stable distribution environments because of the nonlinear preprocessing for noisy signals and the suppression of the spiky and impulsive noises. The adaptive weighted time delay estimation method based on minimum dispersion (MD) criterion and nonlinear transform is needless of priori-knowledge of signals and noises, and possesses the ability of dynamic tracking. The new methods perform robust under both Gaussian and non-Gaussian a -stable distribution environments because of the MD criterion in stead of the minimum mean square error (MMSE) criterion is adopted as well as the nonlinear transform method is adopted to suppress the spiky and impulsive noises.更多还原