不需要特征值分解的几种幂迭代算法研究

针对MUSIC算法中协方差矩阵特征值分解运算量大,难以在嵌入式系统中实现的问题,分析了普通幂迭代算法、逆幂迭代算法和特征值平移幂迭代算法3种幂迭代算法,比较了它们的优缺点。并且考虑到麦克风阵列采集到的声信号为宽带信号,分析了阵元间距选择的影响。并用计算机仿真来验证,在选择合适阵元间距的基础上选取特征值平移幂迭代算法可以代替特征值分解,降低了运算的复杂度。

Research on MUSIC Algorithms without Eigenvalue Decomposition

Because the eigenvalue decomposition of covariance matrix has a large computing amount in MUSIC algorithm,and it is difficult to be implemented in the embedded system,In this paper,common power iteration algorithm,inverse power iteration algorithm,eigenvalue shift power iteration algorithm are analyzed and compared.Considering the sound signals have very wide bandwidth,influence of array element spacing choice is analyzed.Simulation experiment according to several different array element spacing value.Simulation analysis shows that eigenvalue shift power iteration algorithm can replace the eigenvalue decomposition by selecting proper element spacing,which reduces the computing complexity.