Bistatic Radar Coincidence Imaging Based on Sparse Bayesian Learning
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摘要: 双基雷达具有隐蔽性高、抗干扰性能强等优点，在现代电子战中发挥重要作用。基于雷达关联成像原理，该文研究运动目标双基雷达关联成像问题。首先，针对采用均匀线性阵列作为收发天线的双基雷达系统，在发射随机频率调制信号条件下，分析运动目标雷达回波信号特点，建立双基雷达关联成像参数化稀疏表征模型；其次，针对建立的参数化稀疏表征模型，提出一种基于稀疏贝叶斯学习的迭代关联成像算法。该算法在建立贝叶斯模型基础上，通过贝叶斯推理，得到稀疏重构信号，从而实现对运动目标成像和运动参数的精确估计。最后，通过仿真实验验证所提方法的有效性。Abstract: Bistatic radar has the advantages of high concealment and strong anti-interference performance, and plays an important role in modern electronic warfare. Based on the principle of radar coincidence imaging, the problem of bistatic radar coincidence imaging of moving targets is studied. Firstly, based on the bistatic radar system that uses uniform linear array as the transmitting and receiving antenna, the characteristics of the moving target radar echo signal are analyzed under the condition of transmitting random frequency modulation signal, and a bistatic radar coincidence imaging parametric sparse representation model is established. Secondly, an iterative coincidence imaging algorithm based on sparse Bayesian learning is proposed for the parametric sparse representation model established. Based on the Bayesian model, the sparse reconstructed signal is obtained by Bayesian inference, so that the moving target imaging and accurate estimation of motion parameters can be achieved. Finally, the effectiveness of the proposed method is verified by simulation experiments.
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表 1 ICI-SBL算法步骤
ICI-SBL算法步骤 输入：输入${\text{y}}$, ${{\text{S}}_0}$, ${{\text{S}}_1}$和${{\text{S}}_2}$； (1) 迭代次数$k = 0$，初始化相关参数$\alpha _0^0$和${{\text{α}}^0}$，令$\rm{\rho } = 0.01$, $\rm{a} = \rm{b} = {10^{ - 4}}$, $v = {v_0}$, $\theta = {\theta _0}$，并设置终止迭代次数$K = 2000$，成像区域散射
强度矢量重构精度${\varepsilon _{{\text{σ}}}} = {10^{ - 2}}$，目标运动速度估计精度${\varepsilon _v} = {10^{ - 4}}$，目标运动方向估计精度${\varepsilon _\theta } = {10^{ - 6}}$；(2) 令$k = k + 1$； (3) 根据式(17)和式(18)，计算并更新第$k$次的成像区域散射强度矢量${{\text{σ}}^k}$后验分布的协方差${\text{Σ}}_{{\text{σ}}}^k$和均值${\text{μ}}_{{\text{σ}}}^k$； (4) 目标运动参数更新过程：根据式(22)和式(23)，计算并更新第$k$次的目标运动参数${v^k}$和${\theta ^k}$； (5) 判断是否满足终止条件：若$k > K$，或者$\left| {{\text{μ}}_{{\text{σ}}}^k - {\text{μ}}_{{\text{σ}}}^{k - 1}} \right| < {\varepsilon _{{\text{σ}}}}$，或者$\left| {{v^k} - {v^{k - 1}}} \right| < {\varepsilon _v}$且$\left| {{\theta ^k} - {\theta ^{k - 1}}} \right| < {\varepsilon _\theta }$，输出结果。否则，继续步骤(6)； (6) 环境参数即噪声功率更新过程：根据式(24)，计算并更新噪声功率的倒数$\alpha _0^k$； (7) 成像区域散射强度矢量${{{\text{σ}}}^k}$先验协方差矩阵更新过程：根据式(25)，计算并更新参数${{{\text{α}}}^k}$，跳转步骤(2)。 输出：输出成像区域散射强度矢量重构结果$\hat {{\text{σ}}} = {\text{μ}}_{{\text{σ}}}^k$，目标运动速度$\hat v = {v^k}$，目标运动方向$\hat \theta = {\theta ^k}$。 
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表 2 不同发射机天线阵元数目的条件数结果
发射机天线阵元数目${N_{\rm t}}$ 3 5 7 9 11 条件数($ \times {10^8}$) 2.1451 1.3506 0.8652 0.7393 0.5546
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表 3 不同接收机天线阵元数目的条件数结果
接收机天线阵元数目${N_{\rm r}}$ 1 2 4 8 16 条件数($ \times {10^{10}}$) 1.3644 0.0695 0.0057 0.0027 2.9464
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