基于共轭梯度法的盲分离在线算法

Online Algorithm of Blind Source Separation Based on Conjugate Gradient Method

在严格论证盲分离问题与数学上的最优化问题等价的基础上,把问题的重点集中在对该最优化问题的寻优上。由于盲分离最优化问题的目标函数的特点,在欧氏空间中对决策变量(分离矩阵W)进行寻优求解带来诸多复杂因素,寻优算法在弯曲的黎曼空间中动态运行是解决这些问题的一条可行途径。为此,本文在改进NGA和PDFA算法的基础上,结合在线算法PDEA在估计信号的得分函数的较好效果,和求解最优化问题的共轭梯度法较快收敛性能,提出了具有自学习能力,并继承共轭梯度法特点的盲分离在线算法PDEA-CONJ。此算法应用到盲分离问题中,在混合矩阵严重病态情况下能取得了较好分离效果。实际算例验证了其收敛性和有效性。

Firstly what the Blind Signal Separation Problem （P1） in engineering is equivalent to an optimization problem （P2） is described,which is presented as the necessary and sufficient condition that makes the components of Y （t） statistically independent of each other. In the following investigation,we focus on searching methods of the optimization problem. As for the feature of the object function in （P2） , the decision variable （ separation matrix W） searched in traditional Euclidean space raise up with some difficulty computations and optimization methods are pro- mote to running in curve Riemannian space to get optimal solution. On the basis of NGA and PDFA algorithms, combining the better performance of the score function estimation in online algorithm PDEA and faster convergence property of conjugate gradient method in solving BSS optimization problem, the Online Algorithm PEDA - CONJ is proposed, which has both virtues of adaptive learning and conjugate gradient convergence. The convergence rate of PEDA -CONJ is sped up,and there is a good performance in ill conditioned mixture when applying PEDA -CONJ in BSS. The convergence and efficiency of the algorithm are showed in the numerical simulations.