In tensor theory, the parallel factorization （PARAFAC）decomposition expresses a tensor as the sum of a set of rank-1tensors. By carrying out this numerical decomposition, mixedsources can be separated or unknown sys...In tensor theory, the parallel factorization （PARAFAC）decomposition expresses a tensor as the sum of a set of rank-1tensors. By carrying out this numerical decomposition, mixedsources can be separated or unknown system parameters can beidentified, which is the so-called blind source separation or blindidentification. In this paper we propose a numerical PARAFACdecomposition algorithm. Compared to traditional algorithms, wespeed up the decomposition in several aspects, i.e., search di-rection by extrapolation, suboptimal step size by Gauss-Newtonapproximation, and linear search by n steps. The algorithm is ap-plied to polarization sensitive array parameter estimation to showits usefulness. Simulations verify the correctness and performanceof the proposed numerical techniques.展开更多
文摘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.
基金supported by the National Natural Science Foundation of China(61571131)the Technology Innovation Fund of the 10th Research Institute of China Electronics Technology Group Corporation(H17038.1)
文摘In tensor theory, the parallel factorization （PARAFAC）decomposition expresses a tensor as the sum of a set of rank-1tensors. By carrying out this numerical decomposition, mixedsources can be separated or unknown system parameters can beidentified, which is the so-called blind source separation or blindidentification. In this paper we propose a numerical PARAFACdecomposition algorithm. Compared to traditional algorithms, wespeed up the decomposition in several aspects, i.e., search di-rection by extrapolation, suboptimal step size by Gauss-Newtonapproximation, and linear search by n steps. The algorithm is ap-plied to polarization sensitive array parameter estimation to showits usefulness. Simulations verify the correctness and performanceof the proposed numerical techniques.
