一种等效快速非正交联合对角化算法

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。

An Equivalent Algorithm for Fast Nonorthogonal Joint Diagonalization

In view of the instantaneity requirement of parameter estimation of spatial source, an algorithm, named Equivalent Fast Joint Diagonalization (EFJD), is proposed in this paper. The EFJD algorithm, owns lower computational complexity and faster convergence and available for the parameter estimation of dynamic source. It reduces the computational complexity and accelerates the convergence of joint diagonalization by using two ways. Firstly, according to the situation that the number of matrices belonged to target matrix set is normally bigger than the rank of matrix, the number of matrices is reduced to the rank of matrix by using equivalent transformation, and the computational complexity in every iteration is decreased. Secondly, EFJD accelerates convergence by seeking a good initial value for iterative optimization algorithm. Mathematical derivation shows that EFJD can greatly reduce computational complexity , especially when the number of matrices belonged to the target set is much bigger than the rank of target matrices. Numerical simulations have shown that EFJD can not only reduce computational complexity of joint diagonalization but also improve the accuracy of joint diagonalization, compared with FFDiag.