Abstract: Based on the character of the rank，a kind of criterion about the probability of Blind Signal Extraction（BSE） is put forward when the mixing matrix is ill-conditioned（singular or underdetermined）.A kind of fast extraction algorithm is put forward.The fourth-order cumulants about the extraction signals and the signals observed are only used so that the complication of the calculations is reduced.The precision is improved because the error of the extraction signals forward is not cumulated for the extraction signals backward.The algorithm is simple.Simulation results illustrate the efficiency and the good performance of the algorithm.

Key words: mixing matrix, ill-conditioned case, Blind Signal Extraction（BSE）, probability of extraction, non-Gauss

摘要： 在盲信号提取技术中，当混合矩阵是病态情况（混合矩阵奇异或欠定）时，根据混合矩阵秩的性质，提出了在该情况下的盲信号可提取性判据，并给出了一种可提取信号的快速提取算法。该算法中只使用了待提取信号与其他观测量之间的四阶累积量，而不需要计算各个观测量之间的四阶累积量，因此大大减少了算法的复杂度。先提取信号的误差没有对后提取的信号产生累积，因此提高了提取信号的精确度。该算法简单。仿真结果表明该算法有效，并且有很好的性能。

关键词: 混合矩阵, 病态, 盲信号提取, 可提取性, 非高斯性