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Subband Information Geometry Detection Method Based on Orthogonal Projection for Weak Radar Targets
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摘要: 基于信息几何理论的雷达目标检测是一种新兴的技术，它将目标检测问题转化为流形上目标与杂波的区分问题，在低信杂比检测中具有优势。对于复杂背景下的弱小目标检测，目标与杂波难以区分，限制着检测性能。因此，该文基于矩阵信息几何检测器，提出一种基于正交投影的子带信息几何目标检测方法。该文利用滤波器组对雷达回波信号进行子带分解，并在矩阵流形上稳健估计子带内强杂波信号子空间，提出基于流形的正交投影方法以抑制强杂波，增强目标与杂波的区分性。最后，采用仿真数据和实测海杂波数据验证所提方法的有效性。结果表明，所提方法能够有效抑制强杂波，具有较好的检测性能。Abstract: Herein, a novel and effective method for detecting radar targets with a low signal-to-clutter ratio is proposed based on the information geometry theory. In the proposed method, the target detection problem is converted to distinguishing the target from a clutter background on a manifold. However, this is challenging when dealing with small and weak targets embedded in a complex and strong clutter background, which limits the detection performance. Therefore, to address this issue, an orthogonal projection based subband information geometry detection method is proposed. In this method, the received radar signal undergoes subband decomposition by a designed filter bank, and the robust estimation of clutter signal subspace in each subband is implemented on the matrix manifold. Subsequently, the suppression of the strong clutter is achieved through orthogonal projection based on the manifold, thereby improving the discrimination between the target and the clutter. Finally, the effectiveness of the proposed method is evaluated using simulated and real sea clutter data. The experimental results confirm that the proposed method effectively suppresses strong clutter and exhibits excellent detection performance.
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图 5 基于正交投影的子带信息几何检测流程图
Figure 5. Flowchart of subband geometric detection based on orthogonal projection
图 6 加入干扰信号后不同方法的平均影响函数值
Figure 6. Mean value of the influence function for different methods after adding interferences
图 7 K分布杂波下的检测概率(
$K = n$ )Figure 7. Probabilities of detection for K distribution clutter (
$K = n$ )
图 8 K分布杂波下的检测性能曲线(
$K = 2n$ )Figure 8. Probabilities of detection for K distribution clutter (
$K = 2n$ )
图 10 IPIX雷达数据的归一化检测统计量(
${f_{\rm{d}}} = 160$ Hz)Figure 10. Normalized detection statistics of the IPIX radar data (
${f_{\rm{d}}} = 160$ Hz)
图 11 基于IPIX雷达数据的检测概率(
${f_{\rm{d}}} = 160$ Hz)Figure 11. Probabilities of detection for the IPIX radar data (
${f_{\rm{d}}} = 160$ Hz)
图 12 基于IPIX雷达数据的检测概率(
${f_{\rm{d}}} = 350$ Hz)Figure 12. Probabilities of detection for the IPIX radar data (
${f_{\rm{d}}} = 350$ Hz)
图 13 海杂波与目标探测数据采集的试验场景
Figure 13. Sea clutter and target detection experimental scenario
图 14 数据集20210106150614_02_staring的归一化距离-脉冲图
Figure 14. Normalized range-pulse of data set 20210106150614_02_staring
图 15 NAU实验数据(目标位于4.84 km处)
Figure 15. Experimental data of NAU (the target is located at 4.84 km)
1 基于正交投影的子带信息几何检测方法
1. Subband MIG detection method based on orthogonal projection
输入：雷达待检测单元回波信号$ {{\boldsymbol{z}}_D} $和杂波参考单元回波信号$ {\left\{ {{{\boldsymbol{z}}_k}} \right\}_{k \in \left[ K \right]}} $。 输出：检测决策：${\mathcal{D}^{(l)} }\left( {\Re \left( { { {\boldsymbol{z} }_D} } \right),\bar \Re \left( { { {\left\{ { { {\boldsymbol{z} }_k} } \right\} }_{k \in \left[ K \right]} } } \right)} \right)\mathop \gtrless \limits_{ {\mathcal{H}_0} }^{ {\mathcal{H}_1} } {\eta ^{(l)} }, \;\;{l = - L,-(L-1), \cdots ,0, \cdots ,L}$。 For $l = - L,-(L-1), \cdots ,0, \cdots ,L$: 1：首先基于子带滤波器，对雷达回波信号进行子带滤波，获得子带滤波信号$ {\boldsymbol{z}}_D^{(l)} = \mathfrak{L}\left( {{{\boldsymbol{z}}_D}} \right) $和$ {\left\{ {{\boldsymbol{z}}_k^{(l)} = \mathfrak{L}\left( {{{\boldsymbol{z}}_k}} \right)} \right\}_{k \in \left[ K \right]}} $； 2：基于流形估计子带内的杂波信号子空间，并进行稳健的正交投影，得到目标增强信号$ {\boldsymbol{\tilde z}}_D^{(l)} = \mathfrak{P}\left( {{\boldsymbol{z}}_D^{(l)}} \right) $和$ {\left\{ {{\boldsymbol{\tilde z}}_k^{(l)} = \mathfrak{P}\left( {{\boldsymbol{z}}_k^{(l)}} \right)} \right\}_{k \in \left[ K \right]}} $； 3：将基于流形正交投影后的信号表征为HPD矩阵，计算待检测单元HPD矩阵$ \Re \left( {{{\boldsymbol{z}}_D}} \right) $和杂波参考单元HPD矩阵$ {\left\{ {\Re \left( {{{\boldsymbol{z}}_k}} \right)} \right\}_{k \in \left[ K \right]}} $，并计算
几何均值$ \bar \Re \left( {{{\left\{ {{{\boldsymbol{z}}_k}} \right\}}_{k \in \left[ K \right]}}} \right) $；4：计算几何检测统计量$ {\mathcal{D}^{(l)}}\left( {\Re \left( {{{\boldsymbol{z}}_D}} \right),\bar \Re \left( {{{\left\{ {{{\boldsymbol{z}}_k}} \right\}}_{k \in \left[ K \right]}}} \right)} \right) $，并与门限$ {\eta ^{(l)}} $进行比较，完成检测判决
$ {\mathcal{D}^{(l)}}\left( {\Re \left( {{{\boldsymbol{z}}_D}} \right),\bar \Re \left( {{{\left\{ {{{\boldsymbol{z}}_k}} \right\}}_{k \in \left[ K \right]}}} \right)} \right)\mathop \gtrless \limits_{{\mathcal{H}_0}}^{{\mathcal{H}_1}} {\eta ^{(l)}} $。End 
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表 1 不同方法的计算复杂度
Table 1. The computation complexity of different methods
方法 计算复杂度 本文方法 $ \mathcal{O}\left( {M\left( {K{n^3} + {n^3} + \left( {n + Q} \right)\log \left( {n + Q} \right)} \right)} \right) $ RD $ \mathcal{O}\left( {\nu K{n^3}} \right) $ LE $ \mathcal{O}\left( {K{n^3}} \right) $ KLD $ \mathcal{O}\left( {K{n^3}} \right) $ LD $ \mathcal{O}\left( {\varepsilon K{n^3}} \right) $ FFT $ \mathcal{O}\left( {n\log n + Kn} \right) $ ANMF $ \mathcal{O}\left( {{n^3} + K{n^2}} \right) $ SANMF $ \mathcal{O}\left( {M\left( {{n^3} + K{n^2}} \right)} \right) $ ME $ \mathcal{O}\left( {K\left( {{n^3} + n} \right)} \right) $ PS-GLRT $ \mathcal{O}\left( {{n^3} + K{n^2}} \right) $ 2S-Rao $ \mathcal{O}\left( {{n^3} + K{n^2}} \right) $
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表 2 数据文件19980204_155537_ANTSTEP参数
Table 2. Parameters of data file 19980204_155537_ANTSTEP
参数 数值 载频(GHz) 9.39 脉冲重复频率(Hz) 1000 距离单元数 28 脉冲数 60000 距离分辨率(m) 30
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表 3 数据文件20210106150614_02_staring参数
Table 3. Parameters of data file 20210106150614_02_staring
参数 数值 载频(GHz) 9.3~9.5 脉冲重复频率(Hz) 1704 距离单元数 4346 脉冲数 6000 采样频率(MHz) 60 目标位置(km) 4.84
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