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Antijamming Target Detection Method Based on Expectation-Maximization Classification
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摘要: 在存在有源人工干扰的复杂环境中，雷达信号参数估计精度往往显著下降，目标检测性能相应发生退化。为有效解决这一问题，该文提出了一种基于期望最大化分类辅助的抗干扰检测框架。具体而言，在雷达被动工作模式下，提出被动探测模式下的抗噪声覆盖脉冲(NCP)检测方法，建立被动干扰预警机制：构建表征NCP类别的潜在变量模型，结合期望最大化算法与特征值分解实现NCP样本分类与角度/能量参数估计，实现稳健NCP自适应检测。在雷达主动工作模式下，提出主动探测模式下的抗相干干扰(CJ)目标检测方法：构建目标回波与CJ存在性假设的分类模型，利用网格搜索与期望最大化算法完成样本分类与角度估计，实现CJ识别与目标自适应检测。仿真结果表明，所提方法能够有效识别目标或干扰存在的样本单元，准确估计目标与干扰的入射角度，提升恒虚警目标检测的抗干扰性能。Abstract: In complex environments with active artificial jammers, the accuracy of signal parameter estimation often deteriorates substantially, thereby degrading target-detection performance. To address this challenge, this paper proposes an anti-jamming detection framework based on Expectation-Maximization (EM) classification. For passive detection, a Noise Covered Pulse (NCP) detection method is developed, together with a passive jamming early-warning mechanism. A latent variable model representing NCP categories is constructed, and by integrating the EM algorithm with matrix decomposition, NCP sample classification and angle/energy parameter estimation are jointly achieved, enabling robust adaptive NCP detection. For active radar operation, a Coherent Jamming (CJ) target-detection method is proposed. A classification model based on the presence hypotheses of target echoes and CJ is formulated, and grid search combined with the EM algorithm is employed to perform sample classification and angle estimation, thereby enabling CJ identification and adaptive target detection. Simulation results demonstrate that the proposed framework effectively identifies range bins containing targets or jammers, accurately estimates their angles of incidence, and significantly enhances the anti-jamming performance of constant false-alarm-rate target detection.
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图 2 CJ与目标存在下的雷达主动探测模型
Figure 2. Radar active detection model with CJ and target presence
图 3 $\Delta L(m)$随EM迭代次数$(m)$的平均收敛曲线
Figure 3. Average convergence curve of $\Delta L(m)$ over $(m)$ EM iterations
图 7 不同$h_{\mathrm{max}}$下$\Delta L(m)$随EM迭代次数$(m)$的平均收敛曲线
Figure 7. Average convergence curves of $\Delta L(m)$ over $(m)$ EM iterations under different $h_{\mathrm{max}}$
图 8 4种假设下的分类正确率
Figure 8. Probability of correct classification under four assumptions
1 NCP样本分类与参数估计流程
1. Estimation procedure of NCP classification and parameters
输入：$ {{\boldsymbol p}_l},l = 1,2,\cdots,L $ 初始化：${\left( {{\sigma ^2}} \right)^{(0)}}$, $ {\boldsymbol{M}}_{{\rm{NCP}},t}^{(0)} $, $ \mu _r^{(0)} $ for：$m = 1:\bar m $ E步优化：计算$ {{\boldsymbol p}_l} $的条件期望，得到
$ {q_l}(r),l = 1,2,\cdots,L,r = 0,1,\cdots,T $的更新规则式(9)；M步优化： (1) 通过最大化对数似然函数更新$ {\mu _r} $，如式(11)所示； (2) 利用式(17)更新${\sigma ^2}$； (3) 利用式(18)更新$ {{\boldsymbol{M}}_{{\rm{NCP}},t}} $； end 输出：$ {\hat \sigma ^2} $, $ {\hat {\boldsymbol{M}}_{{\rm{NCP}},t}} $, ${\hat {\boldsymbol{\varOmega}} _{1,t}}$, ${\hat {\boldsymbol{\varOmega}} _{1,0}}$ 
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2 目标干扰场景分类与参数估计流程
2. Estimation procedure of scenario classification and parameters
输入：z, ${{\boldsymbol{z}}_x},x \in 1,2,\cdots,X$, ${\theta _1}$, ${\theta _2}$ 初始化：$ {\alpha ^{(0)}} $, $ {w^{(0)}} $, $ \chi _e^{(0)} $ for：${\theta _1} \in \varTheta ,{\theta _2} \in \varTheta $ for：$m = 1:\bar m $ E步优化：利用式(22)计算$ q(e),e = 0,1,2 $的优化结果； M步优化： (1) 结合辅助样本，利用式(24)计算M的估计值； (2) 利用式(25)对$ {\chi _e} $进行优化； for $h = 1:\bar h $ (3) 利用式(27)更新w； (4) 利用式(28)更新$ \alpha $； end end end 利用式(29)、式(30)估计目标与干扰的入射角度$ {\theta _t} $, $ {\theta _{\rm{cj}}} $； 输出：$ \hat \alpha $, $ \hat w $, $ {\hat \theta _t} $, $ {\hat \theta _{\rm{cj}}} $, $\hat e$
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表 1 NCP参数设置
Table 1. Parameter settings of NCP
场景 类别 信号成分 JNR 入射角度 所在样本单元 场景1 1 无 \ \ 1～4, 9～19, 25～34, 41～59, 64～74, 80～89, 96～100 2 NCP1 15.0 dB –2° 5～8, 60～63 3 NCP2 15.0 dB 0° 20～24, 75～79 4 NCP3 15.0 dB 2° 35～40, 90～95 场景2 1 无 \ \ 1～4, 9～19, 25～34, 41～59, 64～74, 80～89, 96～100 2 NCP1 15.0 dB 0° 5～8, 60～63 3 NCP2 17.5 dB 0° 20～24, 75～79 4 NCP3 20.0 dB 0° 35～40, 90～95
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表 2 CJ与目标参数设置
Table 2. Parameter settings of CJ and targets
场景 类别 目标数量 SINR 入射角度 CJ数量 JNR 入射角度 $ {{\rm H}_0} $ 1 0 \ \ 0 \ \ $ {{\mathrm{H}}_{1,1}} $ 2 0 \ \ 1 10 dB 20° $ {{\mathrm{H}}_{1,2}} $ 3 1 10 dB 0° 0 \ \ $ {{\mathrm{H}}_{1,3}} $ 4 1 10 dB 0° 1 10 dB 20°
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