多维盲信源分离的联合块对角化方法

根据多维盲信源分离中源信号组内相关、组间独立的特点，提出一种利用联合块对角化解决该问题的方法，并用经过改造的雅克比算法实现。源信号自相关矩阵具有块对角结构，使得白化后观测数据的时延相关矩阵具有可联合块对角化的结构，因此可以通过联合块对角化来辨识分离矩阵中的正交部分以恢复源信号。针对联合块对角化的特点，对传统的雅克比方法加以改造，将GIVENS旋转矩阵中参数的选择问题转化为一元四次三角函数多项式的优化问题，同时调整旋转的循环顺序。这样，通过连续的GIVENS旋转即可实现联合块对角化。实验仿真和分析表明了算法的有效性。 

Multidimensional blind source separation using joint block-diagonalization

In multidimensional blind source separation(MBSS)， sources belonging to the same tuples are correlated whereas sources belonging to different tuples are independent. We propose a method of MBSS using approximate joint block diagonalization and implement it with the improved Jacobi algorithm. The correlation matrix of sources is block-diagonal. This makes the whitened signal’s time delay correlation matrices containing? joint block-diagonalizable structure. So， separating matrix can be identified by joint block-diagonalization and sources can be recovered. Then， based on the property of joint block diagonalization，we improve the Jacobi method in two aspect: one is transforming the parameter selection of rotation matrix to the optimization problem of a trigonometric function polynomial of degree 4，the other is adjusting the sequences of loops. So joint block-diagonalization can be implemented with successive GIVENS rotation. Numerical experiments with analysis demonstrate the effectiveness of the algorithm.