多维广义次成分提取准则及自适应算法

针对广义次成分在信号处理中没有与之相对应的信息准则,而且只能提取单维广义次成分,提出一种多维广义次成分提取准则,并通过矩阵微分法证明了所提出信息准则只有唯一的全局极大值.基于该信息准则,采用梯度上升法导出一种多维广义次成分提取算法,并采用李雅普诺夫函数法对所提出算法的全局收敛性进行证明.与其他现有算法不同,所提出算法可以并行提取多维次成分,而并不需要模值归一化.仿真实验表明,所提出算法相比一些现有算法具有收敛速度快和估计精度高的优点.

Multiple minor generalized eigenvectors extraction information and its adaptive algorithm

Up to now, it is a hard work to find the corresponding information criterions for minor generalized components in many signal processing fields, and only one dimension minor generalized component can be extralted. In order to solve this problem, this paper proposes a multiple minor generalized components extraction information criterion, which is proved to have only one global maximum. A novel algorithm is also derived by using gradient ascent method to this information criterion. The global convergence of the proposed algorithm is analyzed by using the Lyapunov function method. Compared with existing algorithms, the proposed algorithm does not need normalization operation and can extract multiple minor generalized components in parallel. Simulation results show the accuracy and the speed advantages of the proposed algorithm.