【作者】 郝菊屏；

【导师】 王先来；

【作者基本信息】 天津大学 ， 控制理论与控制工程， 2006， 硕士

【摘要】 盲信号分离是最近兴起的一个新的研究领域,它在实际中有着非常广泛的应用。在不知道源信号和混合矩阵的情况下,只需假设源信号是独立的,独立分量分析算法能够很好的解决盲分离问题。本文的主要工作围绕着独立分量分析算法展开,对它进行了研究。本文介绍了盲信号的背景和发展的历史,给出了独立分量分析的概念和理论,讨论了几种独立分量分析算法及其特点,对先验知识在独立分量分析中的应用进行了总结。在独立分量分析算法的预处理中,白化是相当重要的。对于白化过程,研究了它方差。对算法中得到的矩阵进行正交化,这对某些独立分量分析算法是必不可少的。在对已有的正交算法分析的基础上本文进行了推广,提出了更高收敛速度的新算法。本文对现有的相对梯度进行了推广,提出了广义梯度的概念并将它应用于独立分量分析算法中。对于任何算法稳定性是必须的要保证的,本文对独立分量分析算法中的稳定性的推导将现有的几个稳定性的结论进行了统一。在独立分量分析中,如何确定源信号的概率密度函数是相当关键的。本文讨论了三个方法:使用固定的概率密度函数,自适应的调节概率密度函数和逼近品质函数。最后本文研究了在何种线性变换下概率密度函数是不变的。更多还原

【Abstract】 Blind signal separation is a new research field recently rising and it has a widely application in practice. Under the condition without knowing the source and mixing matrix, independent component analysis can solve the problem of blind signal separation soundly with the assumption that the sources are mutual independent. The work of this paper is extended from independent component analysis algorithm. In this thesis the background and the history of blind signal is introduced and the theory as well as concepts of independent component analysis are given. Some independent component analysis algorithms and their traits are discussed and the priors used in independent component analysis are summarized in this thesis.Among the prime process of independent component analysis, whitening is rather important. For the whitening process, its variance is studied. At the same time, for some independent component analysis algorithms it is dispensable to orthogonalize their output matrix. The existing orthogonalization algorithm is generalized based on its analysis and the new algorithm with higher convergence speed is proposed.In this thesis the existing relative gradient is generalized and the new concept of generalized gradient and its application in the independent component analysis algorithms are proposed. For any algorithm its stability must be guaranteed, the deduction of the stability of independent component analysis algorithm in this thesis unified some results on stability.In independent component analysis, how to decide the probability density functions of the sources is very critical. Three methods are discussed: using fixed probability density function, adaptive probability density function and approximating the score function. At last under which linear transform the probability density function is invariable is studied.更多还原