一种等效快速非正交联合对角化算法

发布时间：2018-04-12 10:58

本文选题：盲源分离 + 快速联合对角化　；参考：《宇航学报》2014年03期

【摘要】：针对空间源信号参数估计实时性的需求,提出一种等效快速非正交联合对角化(EFJD)算法。该算法具有计算复杂度低和收敛速度快的特点,可有效提高空间源信号参数估计的实时性。该算法从两个方面减少运算量,从而加快联合对角化的收敛速度。一方面根据欲联合对角化的目标矩阵组中矩阵的个数通常大于矩阵秩的实际情形,对目标矩阵组进行预处理,将其中的矩阵个数降为矩阵的秩,减少了每次迭代的运算量;另一方面对初始值进行优化,减少了迭代次数。数学推导证明,当目标矩阵组中矩阵的个数相对于矩阵秩取较大值时,EFJD算法就可降低运算量,而且运算量随二者差值的增加显著降低。仿真结果不但验证了这一结论,还表明其联合对角化精度较快速Frobenius范数对角化(FFDiag)算法有所提高。
[Abstract]:An equivalent fast non-orthogonal joint diagonalization (EFJDD) algorithm is proposed for real-time estimation of spatial source signal parameters.The algorithm has the advantages of low computational complexity and fast convergence speed, which can effectively improve the real-time performance of spatial source signal parameter estimation.The algorithm reduces the computational complexity from two aspects, thus accelerates the convergence speed of joint diagonalization.On the one hand, according to the actual situation that the number of matrices in the diagonalized target matrix group is usually larger than the rank of the matrix, the number of matrices in the target matrix group is reduced to the rank of the matrix, which reduces the computation amount of each iteration.On the other hand, the initial value is optimized to reduce the number of iterations.It is proved by mathematical derivation that when the number of matrices in the target matrix group is relatively large relative to the rank of the matrix, the computational complexity can be reduced, and the computation amount decreases significantly with the increase of the difference between the two.The simulation results not only verify this conclusion, but also show that the precision of joint diagonalization is higher than that of fast Frobenius norm diagonalization algorithm.
【作者单位】：中国人民解放军理工大学通信工程学院;
【基金】：国家自然科学基金(61001106) 国家973项目(2009CB320400)
【分类号】：TN911.7

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