确定盲分离中未知信号源个数的奇异值分解法

在信号源少于传感器观测到的混合信号时，未知信号源数目的估计一直是已有盲分离算法中一个未解决的问题，通过理论分析，提高并证明了在信号源盲分离问题中，可以通过计算混合信号数据矩阵的秩数来确定信号源的个数，存在观测噪声时，可以通过计算混合信号数据矩阵的奇异值分解进行估计未知信号源数目，给出了实际的计算方法，并通过计算实例证明了该方法的正确性和有效性，从而解决了盲分离中信号源个数的估计问题，为盲分离技术的应用进一步奠定了基础。

Determination of the Number of Source Signals in Blind Source Separation by Singular Value Decomposition

The determination of the number of unknown source signals when there are fewer sources than the mixtures in blind source separation (BSS) has always been an unsolved problem. It is demonstrated that the source number can be estimated by computing the rank of the data matrix of the mixed signals. However, in the presence of noise, this simple conclusion will no longer hold. It is further proved that the number of sources can also be estimated reliably by computing the singular value decomposition of the data matrix of the signal mixture. A solution to the problem of source number estimation is thus found. It paves the way to wider applications of BSS methods to real world signal processing. The computer simulation shows the efficacy of the proposed method.