独立分量分析及其在阵列信号处理中的应用
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摘要
独立分量分析是一种从多维统计数据中寻找独立分量的方法，这种方法与其它方法相比较，其特点是所寻找的分量间满足独立非高斯性。独立分量分析只利用观测数据，在源信号和混合信道未知的情况下来提取独立分量。本文将从独立分量分析的学习算法和应用两方面进行研究，主要工作概括如下：
1．本文从独立分量分析的定义和假设条件出发，分析了独立分量分析的一些基本准则和常用方法；白化处理以及独立分量分析中信号的分类方法：利用非线性函数完成独立性分析的条件；给出了独立分量分析算法性能评价指标方法：将独立分量分析与主分量分析进行了比较。
2．在独立分量分析的理论研究框架下，研究了最优估计函数形式，获得了一种对得分函数进行估计的独立分量分析研究方法；本文通过利用混合高斯模型，给出了估计概率密度函数的EM算法，在此基础上利用高斯混合模型法获得了对分离矩阵的梯度学习算法。为了提高算法的稳定度和精确度，给出了一种迭代概率密度估计的独立分量分析学习算法。这种块处理方法可实现超、亚高斯混合信源的情况，同时在仿真实验过程中，研究了学习速率对学习算法的影响。
3．对于复值信号基于频率域的分析优于时域分析法，因为频率域分析能够提供更准确的信息。针对复值信号的独立分量分析问题，本文通过广义EHA准则和快速复值定点算法的研究，给出了一种改进的广义EHA准则算法，分析结果表明，这种算法可以实现对独立复值信号的分离。
4．研究了独立矢量基特性在阵列信号处理中的应用。独立分量分析方法针对统计独立信源的混合情况，在学习过程中所获得的分离矩阵提供了一组投影基矢量，具有相应的投影独立性。在此基础上，本文定义了独立矢量基，并利用独立矢量基的投影关系，对阵列中常见的DOA问题进行了研究，获得了对阵列信号的方位角估计。同时研究了白化过程所具有的自适应波束形成器特性。
Independent component analysis(ICA) is a method for finding underlying components from multivariate (multidimensional) statistical data. What distinguishes ICA from other methods is that it looks for components that are both statistically independent and non-Gaussian. The aim of ICA is to extract independent components given only observed data that are mixtures of the unknown sources without any knowledge of the mixed channel. This dissertation aims at the study of the theories and applications ICA. The main work can be summarized as follows:1. This dissertation reviews briefly the principles and the methods in the ICA. The prewhitening and the classify of signals is presented. The conditions of nonlinear function in ICA are discussed, and the ICA is compared with PCA.2. Based on the optimal estimation function, a method for estimation of the score function is developed. By using the Gaussian mixture model, an EM algorithm for approximating the probability density of the data is presented, and a stochastic gradient method is given to separate the independent components. To improved the accuracy and stability of the algorithm, an iterative method for estimating the pdf of data is presented, which can perform the separation of mixed sub-Gaussian and super-Gaussian sources. The optimal learning rate problem is studied, and the performance of the method is shown by computer simulations.3. For separation of complex valued signals, frequency domain implementations is better than time domain implementations. By studying the Hebbian learning and the fast fixed-point algorithm, a improved EHA is obtained. The simulations show the effectiveness of this method.4. The application of the independent bases in array signal processing is studied. The independent bases are denned for ICA. Using the independent
bases in ICA, the DOA of signals can be estimated. Then the property of the prewhitening as a self-organizing beamformer is discussed.
1．本文从独立分量分析的定义和假设条件出发，分析了独立分量分析的一些基本准则和常用方法；白化处理以及独立分量分析中信号的分类方法：利用非线性函数完成独立性分析的条件；给出了独立分量分析算法性能评价指标方法：将独立分量分析与主分量分析进行了比较。
2．在独立分量分析的理论研究框架下，研究了最优估计函数形式，获得了一种对得分函数进行估计的独立分量分析研究方法；本文通过利用混合高斯模型，给出了估计概率密度函数的EM算法，在此基础上利用高斯混合模型法获得了对分离矩阵的梯度学习算法。为了提高算法的稳定度和精确度，给出了一种迭代概率密度估计的独立分量分析学习算法。这种块处理方法可实现超、亚高斯混合信源的情况，同时在仿真实验过程中，研究了学习速率对学习算法的影响。
3．对于复值信号基于频率域的分析优于时域分析法，因为频率域分析能够提供更准确的信息。针对复值信号的独立分量分析问题，本文通过广义EHA准则和快速复值定点算法的研究，给出了一种改进的广义EHA准则算法，分析结果表明，这种算法可以实现对独立复值信号的分离。
4．研究了独立矢量基特性在阵列信号处理中的应用。独立分量分析方法针对统计独立信源的混合情况，在学习过程中所获得的分离矩阵提供了一组投影基矢量，具有相应的投影独立性。在此基础上，本文定义了独立矢量基，并利用独立矢量基的投影关系，对阵列中常见的DOA问题进行了研究，获得了对阵列信号的方位角估计。同时研究了白化过程所具有的自适应波束形成器特性。
Independent component analysis(ICA) is a method for finding underlying components from multivariate (multidimensional) statistical data. What distinguishes ICA from other methods is that it looks for components that are both statistically independent and non-Gaussian. The aim of ICA is to extract independent components given only observed data that are mixtures of the unknown sources without any knowledge of the mixed channel. This dissertation aims at the study of the theories and applications ICA. The main work can be summarized as follows:1. This dissertation reviews briefly the principles and the methods in the ICA. The prewhitening and the classify of signals is presented. The conditions of nonlinear function in ICA are discussed, and the ICA is compared with PCA.2. Based on the optimal estimation function, a method for estimation of the score function is developed. By using the Gaussian mixture model, an EM algorithm for approximating the probability density of the data is presented, and a stochastic gradient method is given to separate the independent components. To improved the accuracy and stability of the algorithm, an iterative method for estimating the pdf of data is presented, which can perform the separation of mixed sub-Gaussian and super-Gaussian sources. The optimal learning rate problem is studied, and the performance of the method is shown by computer simulations.3. For separation of complex valued signals, frequency domain implementations is better than time domain implementations. By studying the Hebbian learning and the fast fixed-point algorithm, a improved EHA is obtained. The simulations show the effectiveness of this method.4. The application of the independent bases in array signal processing is studied. The independent bases are denned for ICA. Using the independent
bases in ICA, the DOA of signals can be estimated. Then the property of the prewhitening as a self-organizing beamformer is discussed.
引文
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