Spatial aliasing-free broadband direction of arrival estimation under strong interference
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摘要:
提出了基于改进频率差分(FD)技术的空间抗混叠波达方位(DOA)估计方法, 实现了阵元稀疏排布, 即在阵元间距远大于入射信号波长时, 存在栅瓣模糊情况下多水下声学目标的方位估计。首先, 确定目标方位角度搜索范围, 建立阵列信号处理模型, 对宽带信号不同频率成分之间进行频率差分处理, 从而降低信号频率以满足阵元稀疏排布阵列的空间奈奎斯特采样要求。然后, 基于投影子空间正交性检验(TOPS)算法构建一个对角变换矩阵, 利用对角酉变换矩阵正交性直接对阵列流形进行频率差分处理, 使其频率差分处理输出的信号个数与输入信号个数相等。最后, 进一步推导频率差分域等效目标方位与真实入射信号角度等价的条件, 并基于该等价条件进行频率筛选, 最终获得无模糊的空间方位谱结果。经仿真实验验证, 所提算法在信噪比为−10~20 dB范围内, 估计结果均方根误差低于0.1°, 有效抑制了栅瓣且受干扰强度影响较小。经海试数据验证, 所提算法可以有效估计出目标方位, 并避免空间混叠项干扰。所提空间抗混叠波达方位估计方法能够有效抑制栅瓣模糊, 提高目标方位估计精度, 且在强干扰条件下仍具有较好的角度估计性能。
Abstract:A spatial aliasing-free direction of arrival (DOA) estimation method based on improved frequency difference (FD) technology has been proposed, which achieves sparse array element arrangement, that is, when the array element spacing is much longer than the incident signal wavelength, the DOA estimation of multiple underwater acoustic targets in the presence of gate lobe ambiguity is achieved. Firstly, the target azimuth angle search range is determined, the array signal processing model is established, and the frequency difference processing is performed between the different frequency components of the wideband signal, so as to reduce the signal frequency to meet the spatial Nyquist sampling requirements of the array with sparse array elements. Then, based on the test of orthogonality of projected subspaces, a diagonal transformation matrix is constructed, and the orthogonality of the diagonal unitary transformation matrix is used to directly perform frequency difference processing on the array manifold, so that the number of signals output by the frequency difference processing is equal to the number of input signals. Finally, the condition for the equivalence between the equivalent target orientation and the true incident signal angle in the frequency difference domain is further derived, and frequency screening is performed based on this equivalence condition, ultimately obtaining a spatial orientation spectrum result without ambiguity. The simulation results show that the root-mean-square deviation of the proposed algorithm is less than 0.1° in the signal to noise ratio range of −10−20 dB, which effectively suppresses the gate lobe and is less affected by the interference intensity. Verified by sea experiment data, the proposed algorithm can effectively estimate the target orientation and avoid spatial aliasing interference. The proposed spatial aliasing-free DOA estimation method can effectively suppress gate lobe ambiguity, improve target direction estimation accuracy, and still have good angle estimation performance under strong interference conditions.
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Key words:
- Direction of arrival /
- Aliasing-free /
- Frequency-difference technique /
- Subspace
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表 1 本文所提方法的算法流程
输入: 阵列接收信号$ {{\boldsymbol{x}}_l}({f_q}) $, 阵元个数M, 阵元间距$ d $, 声波在水中的传播速度$ c $, FFT点数$ Q $, 时间间隔段数L 1. 设置搜索范围
定义测试角度方位扫描网格为$\varTheta $; 设置$i = 1$, 且${\vartheta _i} \in \varTheta $;
2. 设计对角变换矩阵
将接收信号转化为式(3)中的频域阵列输出矩阵$ {{\boldsymbol{x}}_l}({f_q}) $;
设计对角变换矩阵$ {\boldsymbol{\varPhi }}({f_q} - \Delta f,\vartheta ) $;
根据$ {{\boldsymbol{x}}_l}({f_q}) $和$ {\boldsymbol{\varPhi }}({f_q} - \Delta f,\vartheta ) $, 利用式(11)计算频率差值$ \Delta f $的阵列输出矩阵$ {{\boldsymbol{\widetilde x}}_l}({f_q}) $;
3. 计算等效协方差矩阵
利用式(5)计算接收信号的采样协方差矩阵$ {{\boldsymbol{\widehat R}}_{{f_q}}} $;
利用式(12)计算差分频率$ \Delta f $上的等效协方差矩阵$\overline {\boldsymbol R}_{\Delta f}^{}$;
4. 估计方位谱
① 令$ {f_q}{\text{ = }}{f_{{q_L}}} + \Delta f $, 利用式(17)计算方位谱$ P\left( {{f_q},{\vartheta _i},\theta } \right) $, 并搜索峰值;
② 判断峰值角度与测试角度${\vartheta _i}$的差值是否小于设定的阈值$h$;
③ 如果小于阈值$h$, 存储方位谱值$ P\left( {{f_q},{\vartheta _i},\theta } \right) $;
④ 令$q = q + 1$, 重复步骤②和③, 直至$ {f_q}{\text{ = }}{f_{{q_H}}} $, 计算满足条件的频率个数$ D = \dim \left\{ {{f_q}\left| {\left| {{{\overline \theta }_k} - {\vartheta _i}} \right| < h,{f_{{q_L}}} + \Delta f \leqslant {f_q} \leqslant {f_{{q_H}}}} \right.} \right\} $;
⑤ 利用式(14)计算抗混叠方位谱${\boldsymbol{P}}\left( {{\vartheta _i}} \right)$;
5. 遍历搜索范围
令$i = i + 1$, 重复步骤2 ~ 4, 计算每个${\vartheta _i}$下的${\boldsymbol{P}}\left( {{\vartheta _i}} \right)$, 直到$i$大于等于扫描网格${{\varTheta}} $的最大维度;输出: 目标估计方位谱${\boldsymbol{P}}$, $\vartheta \in {{\varTheta}} $ 
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