一种多级维纳滤波器的快速实现算法——迭代相关相减算法

Fast algorithm for implementing multistage wiener filter:iterative correlation subtraction algorithm

证明了由相关相减算法实现的多级维纳滤波器是一种酉多级维纳滤波器,并且其各级的匹配滤波器与对应的降秩子空间的基向量相等。在证明结论的基础上,将后向迭代算法应用于相关相减算法多级维纳滤波器,提出了多级维纳滤波器的迭代相关相减实现算法。迭代相关相减算法具有前向递推计算量低、后向滤波实时性好、采样均方误差和自适应权矢量计算简单、秩选计算量低等优点,降秩性能与相关相减算法完全相同。

Firstly, it was proved that the multistage wiener filter （MWF） implemented by the correlation subtraction algorithm （CSA） was a unitary MWF and that the matched filters were equal to the corresponding basis vectors of the rank reducing subspace in the CSA-MWF. Based on the results about CSA proven, the iterative CSA for implementing the MWF was proposed by applying the backward iteration to the CSA-MWF. The iterative CSA has the advantages such as a lower complexity of forward recursion, real-time backward filtering, computing the SMSE and the adaptive weight vector more simply, and the low overall computation burden for rank selection. Furthermore, the reduced rank performance of the iterative CSA is the same as the CSA.