宽带距离深度域最小二乘矩阵滤波器的设计

设计出基于拷贝向量处理的适用于宽带信号滤波的距离深度域矩阵滤波器。提出利用最小二乘原理将矩阵滤波器的设计问题转化为超定线性方程组求解问题，通过对线性方程组最小二乘解化简重构，得出最小二乘矩阵滤波器为期望拷贝向量矩阵与实际拷贝向量矩阵右伪逆的乘积。通过对宽带信号频谱中能量较高的频点进行采样处理，可以将矩阵滤波器应用于宽带信号处理。分别对垂直均匀线列阵接收到的窄带和宽带数据进行处理，发现宽带矩阵滤波器可以保证水听器阵在恶劣环境中更加有效地工作。相比于二阶锥规划矩阵滤波器，距离深度域最小二乘矩阵滤波器更快捷，滤波之后目标源与干扰源的相对幅度更大，有利于目标检测。

Design of least square broadband matrix filter in range-depth domain

This paper introduces the matrix filter based on replica vectors processing which can be used to filter the broadband signals in range-depth domain. The least square principle will simplify the design of the matrix filter as a pseudo inverse problem, and the filter will turn out to be the product of the expected replica vectors matrix and the right pseudo inverse of real replica vectors matrix. This filter can be applied to broadband signal processing by signal spectrum analysis, and filtering the signal frequencies with high energy. This paper can filter the narrowband and broadband signals received by the vertical linear array respectively. The results show that the broadband matrix filter in range-depth domain can guarantee the hydrophone array works efficiently in much worse conditions than the narrowband one. Compared with the matrix filter designed by second-order cone programming, the matrix filter designed by least square principle is more expedient, and the power ratio between target and interference is greater after filtering, which is helpful for target detection.