最小范数法的新解释及其谱的分析

New Explanation of Minimum-Norm Method and Its Spectral Analysis

本文从一个新的角度对著名的超分辨阵处理法一最小范数(M N)法从数学上进行了重新的考虑,并指出M N法就是总的最小均方(TLS)问题的最小范数解,从而给出了一个其他文献中没有指出的数学事实.这种解释加深了我们对MN法的物理意义的理解,同时也为MN法与多信号分类(MUSIC)法及线性方程(L E)法的比较提供了方便.文中还推导了M N法、MUSIC法的渐近谱.模拟结果证明了文中理论的正确。

In this paper, the well-known superresolution array processing method- Minimum -Norm(MN)method is reconsidered at a now mathematical angle. It is shown thaat the MN method is essentially a minimumnorm solution for the total least squares (TLS) problem-Hence a mathematical fact which has been presentedin other papers is given. The new explanation prorides clearer physical meaning and is easy to show the relationof the MN method to the MUSIC method and the linear equation (LE) method. The asymptotically statisticalspectrum of the MN method and the MUSIC method. Computer simulations validate the theory.