Abstract: Aimad at the blind separation problem with time structure, this paper proposes a joint diagonalization algorithm based on two positive definite matrices. Firstly, two positive definite matrices are constructed by using several different time delay statistics. Next, a new algorithm is proposed to realize the joint diagonalization of the two positive definite matrices. Then separation matrix can be obtained. Finally, the source signals can be estimated. The proposed algorithm overcomes the shortcomings of the existing algorithms： the heavy computation load caused by the joint diagonalization of multiple matrices and the low separation accuracy caused by the single matrix. Simulation results show that the proposed algorithm is superior to other comparison algorithms in the presence or absence of noise.

Key words: blind source separation, joint diagonalization, singular value decomposition

摘要： 针对具有时间结构的盲分离问题，提出了一种基于两正定矩阵精确联合对角化的盲分离算法。利用多个不同时延统计量构造了两个正定矩阵，以提取出数据的时间结构；再利用所提算法联合对角化构造的两个正定矩阵，得到分离矩阵，进而估计出源信号。所提算法克服了已有算法因采用多个矩阵联合对角化导致的计算量大和采用单个矩阵导致的分离精度低的缺点。计算机仿真结果表明了在有或无噪声情况下，所提算法性能均优于其他对比算法。

关键词: 盲源分离, 联合对角化, 奇异值分解