﻿ 一种级联型自适应滤波器的混响抑制技术
 舰船科学技术  2021, Vol. 43 Issue (3): 130-133    DOI: 10.3404/j.issn.1672-7649.2021.03.025 PDF

LAN Tong-yu, ZHOU Sheng-zeng
Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
Abstract: The performance of active sonar often degrades dramatically because of reverberation in shallow water. Reverberation is caused by the transmitted signal. In the frequency domain, its coverage area basically coincides with the transmitted signal, and in the time domain, it has strong correlation with the transmitted signal and target echo signals. This make it difficult to separate the reverberation from the target echo signals. This paper draws on a mature method of moving target detection in PD radar, and proposes an algorithm of filter design for underwater situation. The algorithm uses the differences between target echo signals and reverberation in the time and frequency domains, and designs two cascaded adaptive filters. The two filters accomplish the aim of reverberation suppression and target echo signals enhancement. On this basis, matched filters or other processing method will achieve optimal performance. This algorithm can increase the signal-to-reverberation ratio and effectively improve the detection ability of moving targets.
Key words: active sonar     reverberation suppression     doppler shift     adaptive filter     eigenvector method
0 引　言

1 AMTI滤波器的构造 1.1 特征矢量法

AMTI的设计思想是找出一组滤波权系数最大程度抑制混响并使得目标的能量损失最小化。基于最大改善因子的特征矢量法是目前雷达中主要的杂波抑制方法[9]

 $S(f)=\left\{ \begin{array}{l} {1},\qquad -\dfrac{B}{2}\leqslant f\leqslant \frac{B}{2},\\ {0},\qquad{\rm{others}}\text{。}\end{array} \right.$ (1)

 ${{R_S}}(m) = \frac{1}{B}\int_{ - B/2}^{B/2} {{e^{j2\text{π} fm}}{\rm d}f},$ (2)

 ${{R_S}}(m) = \frac{{\sin (\text{π} mB)}}{{\text{π} mB}},$ (3)

 ${{{R_S}}}(m) = \left\{ \begin{array}{l} 1,\qquad m = 0 ,\\ 0,\qquad m \ne 0 ,\end{array} \right.$ (4)

RS为单位矩阵。

 $I = ({P_{SO}}/{P_{RO}})/({P_{Si}}/{P_{Ri}})\text{。}$ (5)

 $\begin{array}{l} {P_{SO}} = E[|{W^H}S{|^2}] = E[{W^H}S{S^H}W] = \\ {W^H}{M_S}W = {S_i}{W^H}{{R_S}}W ,\end{array}$ (6)

 ${P_{RO}} = {C_i}{W^H}{{{R_r}}}W\text{。}$ (7)

 $I = \frac{{{W^H}{{R_S}}W}}{{{W^H}{{{R_R}}}W}},$ (8)

 $I = \frac{{{W^H}W}}{{{W^H}{R_R}W}},$ (9)

RR的特征向量张成的向量空间可分为2个子空间。大特征值张成信号子空间，杂波的主要分量位于这个子空间；小特征值张成噪声子空间。因为噪声子空间和信号子空间正交，因此上式的最大值存在，即当WRR的最小特征值所对应的特征向量时，改善因子达到最大值，即解如下方程：

 ${{R_R}}{W_i} = {\lambda _i}{W_i}{\text{。}}$ (10)

1.2 AMTI滤波器的设计

 ${S_c}(f) = \frac{1}{{{{(2\text{π} \sigma _c^2)}^{1/2}}}}\exp \left( - \frac{{{{(f - {f_c})}^2}}}{{2\sigma _c^2}}\right)\text{。}$ (11)

 ${R_z}(i,j) = \frac{1}{{2\text{π} }}\int_{ - \infty }^{ + \infty } {{S_c}(f){e^{j2\text{π} f({t_i} - {t_j})}}{\rm d}f} ,$ (12)

 ${R_z}(i,j) = \exp \left\{ \frac{{{{({f_0} + j2\text{π} \sigma _f^2{\tau _{ij}})}^2} - {f_0}}}{{2\sigma _f^2}}\right\} ,$ (13)

f0=0时，即混响谱中心频率为0时：

 ${R_z}(i,j) = \exp ( - 2{\text{π} ^2}\sigma _f^2{\tau _{ij}}^2),$ (14)

 $H = {\rm{diag}}\{ 1\;{e^{ - j2\text{π} {f_c}{T_s}}}\quad\;{e^{ - j2\text{π} {f_c}(N - 1){T_s}}}\},$ (15)
 ${W_c} = H*{W_0}{\text{。}}$ (16)

2 自适应目标增强器的设计

 图 1 自适应目标增强器原理框图 Fig. 1 The principle diagram of adaptive target enhancer

 $d(n) = {x_1}(n) = {s_1}(n) + {r_1}(n),$ (17)
 ${x_2}(n) = {s_2}(n) + {r_2}(n),$ (18)
 $y(n) = {W^H}(n)*{x_2}(n),$ (19)
 $e(n) = d(n) - y(n),$ (20)
 $W(n + 1) = W(n) + 2\mu e(n){X_2}(n){\text{。}}$ (21)
3 数据处理流程

CW脉冲信号的滤波处理过程：

1）预处理

2）参数估计

3）AMTI滤波

4）自适应目标增强滤波

AMTI滤波结果作为滤波器输入，初始信号作为期望信号进行自适应滤波。

5）FFT处理

6）显示

 图 2 常规FFT处理结果 Fig. 2 Result of conventional FFT processor

 图 3 目标所在时间段滤波器频率响应 Fig. 3 The filter frequency response in target echo period

 图 4 目标所在时间段信号处理结果 Fig. 4 Results of target echo signals passing through filters

 图 5 滤波后FFT处理结果 Fig. 5 Result of FFT processor after filter processing
4 结　语

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