一种利用结构特点实现复数域联合对角化解盲源分离新算法研究及应用

发布时间：2018-11-15 14:40

【摘要】：联合对角化方法是求解盲源分离问题的有力工具.但是现存的联合对角化算法大都只能求解实数域盲源分离问题,且对目标矩阵有诸多限制.为了求解更具一般性的复数域盲源分离问题,提出了一种基于结构特点的联合对角化(Structural Traits Based Joint Diagonalization,STBJD)算法,既取消了预白化操作解除了对目标矩阵的正定性限制,又允许目标矩阵组为复值,具有极广的适用性.首先,引入矩阵变换,将待联合对角化的复数域目标矩阵组转化为新的具有鲜明结构特点的实对称目标矩阵组.随后,构建联合对角化最小二乘代价函数,引入交替最小二乘迭代算法求解代价函数,并在优化过程中充分挖掘所涉参量的结构特点加以利用.最终,求得混迭矩阵的估计并据此恢复源信号.仿真实验证明与现存的有代表性的对目标矩阵无特殊限制的复数域联合对角化算法FAJD算法及CVFFDIAG算法相比,STBJD算法具有更高的收敛精度,能有效地解决盲源分离问题.
[Abstract]:Joint diagonalization is a powerful tool for blind source separation. However, most of the existing joint diagonalization algorithms can only solve the blind source separation problem in real number domain, and have many limitations on the target matrix. In order to solve the more general problem of blind source separation in complex domain, a joint diagonalization (Structural Traits Based Joint Diagonalization,STBJD) algorithm based on structural characteristics is proposed, which eliminates the whitening operation and removes the positive definiteness restriction on the target matrix. The target matrix group is also allowed to be complex value, which has wide applicability. Firstly, the matrix transformation is introduced to transform the target matrix set of complex field to a new set of real symmetric objective matrices with distinct structure. Then the diagonalized least squares cost function is constructed and the alternating least squares iterative algorithm is introduced to solve the cost function. The structural characteristics of the parameters involved are fully exploited in the optimization process. Finally, the estimation of the aliasing matrix is obtained and the source signal is recovered accordingly. The simulation results show that the STBJD algorithm has higher convergence accuracy and can effectively solve the blind source separation problem than the existing representative complex domain joint diagonalization algorithm FAJD algorithm and CVFFDIAG algorithm which has no special restrictions on the target matrix.
【作者单位】：长安大学电子与控制工程学院;长安大学公路学院;长安大学信息工程学院;
【基金】：国家自然科学基金(No.61201407,No.61473047) 中国博士后科学基金面上资助(No.2013M542309) 陕西省自然科学基础研究计划(No.2016JQ5103) 长安大学中央高校基本科研业务费(No.0009-2014G1321038)
【分类号】：TN911.7

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