非正交联合对角化盲源分离算法

提出一种表征联合对角化近似程度的代价函数,给出优化该代价函数的非正交联合对角化算法.该代价函数对经典的最小二乘代价函数进行了改进,使原算法中关于混迭矩阵的四次函数转化为3组待定参数的二次函数.因此,可通过基于梯度下降法的迭代算法交替估计3组待定参数,搜索代价函数最小点,从而得到混迭矩阵的估计,实现盲源分离.分析了算法的收敛性能,证明存在估计误差时,该算法依然全局渐进收敛.仿真结果表明,与经典的非正交联合对角化(ACDC)算法相比,该算法收敛所需计算时间仅为ACDC的一半,而全局拒噪水平改善了6dB,可有效地解决瞬时盲源分离问题.

Non-orthogonal joint diagonalization for blind source separation

A novel cost function and a corresponding iterative algorithm for the non-orthogonal joint diagonalization of a set of eigen-matrices are proposed. The proposed cost function, improved from the classical least squares cost function that is the fourth function associated with the mixture matrix, is quadratic if two of the three parameter sets are fixed. Therefore, a new iterative algorithm based on the gradient descend method contains three sub-steps. In each sub-step, the closed solution is found by minimizing the cost function associated with one parameter group while fixing the others. Furthermore, global convergence is analyzed even in the presence of the estimation error of the eigen-matrix group. Finally, the results of the simulations illustrate that the proposed algorithm has better convergence performance, lower computational complexity, and can accurately retrieve the source signals from a set of received signals.