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Monopulse Forward-looking Imaging Based on Doppler Estimation Using Fast Iterative Interpolated Beamforming Algorithm
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摘要: 在单脉冲前视成像技术中，同分辨单元内多目标的辨识一直是单脉冲雷达的研究热点。尽管多普勒处理可以提高对前斜视多目标的分辨能力，但在真实目标数量未知、强点目标能量泄露的情况下，多普勒频率的精确估计面临巨大挑战。针对以上问题，该文在单脉冲前视成像中引入具有目标个数估计和单快拍处理能力的快速迭代插值波束形成(FIIB)算法，结合信息论准则估计目标个数，实现对多普勒频率的无偏估计。点目标仿真数值分析结果显示，FIIB对于同分辨单元内的目标数估计和参数估计性能优于调频Z变换(CZT)算法，能实现对±5°外点目标的准确估计。场景仿真和实测数据成像结果表明基于FIIB的单脉冲前视成像算法聚焦能力强，图像对比度更高，并能有效抑制背景杂波。
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关键词:
- 单脉冲雷达 /
- 前视成像 /
- 多普勒频率估计 /
- 快速迭代插值波束形成算法
Abstract: Distinguishing multiple targets in the same resolution cell is an important and challenging task in the forward-looking imaging process of monopulse radar. Although Doppler processing can improve the recognition performance for multiple targets at high squint angles, the precise estimation of Doppler frequency remains challenging under conditions with unknown target numbers and energy leakage from strong point targets. To address these issues, this paper proposes a Fast Iterative Interpolated Beamforming (FIIB) algorithm with model order estimation and single snapshot processing for monopulse forward-looking imaging, which combines information theory to unbiasedly estimate the number of targets and Doppler frequencies. The simulation results show the superiority of the proposed FIIB algorithm over the Chirp-Z Transform (CZT) algorithm for estimating target numbers and Doppler frequencies within the same resolution cell in the presence of multiple point targets. In addition, the proposed FIIB algorithm can accurately estimate point targets beyond a ±5° azimuth angle in monopulse angle measurement tasks. Real-data experiments also reveal that FIIB-based monopulse forward-looking imaging has high focusing capability and imaging contrast and can effectively suppress background clutter. -
图 2 强点目标仿真结果(
${W_1}/{W_2} = 20\;{\text{dB}}$ )Figure 2. Simulation result of strong point targets (
${W_1}/{W_2} = 20\;{\text{dB}}$ )
图 3 相邻点目标仿真结果 (
$\Delta f = 1/N$ )Figure 3. Simulation result of neighboring point targets (
$\Delta f = 1/N$ )
图 4 多点目标仿真结果(
$L = 10$ )Figure 4. Simulation result of multiple point targets (
$L = 10$ )
图 5 不同迭代次数下同多普勒单元内两个目标的FIIB仿真结果
Figure 5. Simulation results of FIIB for two targets situated in a Doppler bin by different iterations
图 7 距离向1700 m处目标方位向剖面图
Figure 7. Azimuthal contour plots for point targets at the range cell 1700 m
图 8 仿真场景前视成像效果对比
Figure 8. Comparison of simulation results in forward-looking imaging
图 9 实测数据前视成像效果对比
Figure 9. Comparison of experimental results in forward-looking imaging
初始化： 令 ${\hat f_l} = 0$, ${\hat A_l} = 0$, $l = 1,2, \cdots ,L$ 设 $q = 0$ ${\boldsymbol{X}} = {\text{FFT}}({\boldsymbol{x}},N)$ 迭代(Q次)： 对于 $l = 1,2, \cdots ,L$ IF $q = 1$(粗估计)： $\tilde X(k) = X(k) - \displaystyle\sum \limits_{i = 1,i \ne l}^L {\hat A_i}{\hat S_i}(k),k = 0,1, \cdots ,N - 1$ (i) $ {\hat m_l} =\arg \mathop{\max}\limits_{0 \le k \le N - 1 } {\left| {\tilde X(k)} \right|^2} $ (ii) ${\hat f_l} = \dfrac{1}{N}{\hat m_l}$ (iii) END IF (精估计):
$ {\tilde X_p}({\hat f_l}) = {X_p}({\hat f_l}) - \displaystyle\sum \limits_{i = 1,i \ne l}^L {\hat A_i}{\hat S_i} \left( {{{\hat f}_l} + \dfrac{p}{N}} \right),p = \pm \dfrac{1}{2} $ (iv)其中， ${X_p}({\hat f_l}) = X\left( {{{\hat f}_l} + \dfrac{p}{N}} \right)$ (v) $ \delta = \dfrac{1}{2}{{\mathrm{Re}}} \left[ {\dfrac{{{{\tilde X}_{0.5}}({{\hat f}_l}) + {{\tilde X}_{ - 0.5}}({{\hat f}_l})}}{{{{\tilde X}_{0.5}}({{\hat f}_l}) - {{\tilde X}_{ - 0.5}}({{\hat f}_l})}}} \right] $ (vi) ${\hat f_l} \leftarrow {\hat f_l} + \dfrac{\delta }{N}$ (vii) $ {\hat A_l} = \dfrac{1}{N} \left\{ {\displaystyle\sum \limits_{k = 0}^{N - 1} x(k){{\text{e}}^{ - {\text{j}}{\textstyle\frac{{2\pi }}{N}}k{{\hat f}_l}}} - \displaystyle\sum \limits_{i = 1,i \ne l}^L {{\hat A}_i}{{\hat S}_i}({{\hat f}_l})} \right\} $ (viii) $q \leftarrow q + 1$ 输出: $\left\{ {{{\hat f}_l},{{\hat A}_l}} \right\},l = 1,2, \cdots ,L$ 
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2 具有目标个数估计功能的FIIB算法
2. The FIIB algorithm with model order estimation
初始化： 设 ${L_{\max }}$, Q 循环: 对于 $L = 1,2, \cdots ,{L_{\max }}$ $\left\{ {{{\hat f}_l},{A_l}} \right\}_{l = 1}^L = {\text{FIIB(}}{\boldsymbol{x}},L,Q)$ 计算 ${C_{{\text{ITC}}}}(L)$ 结束 取: $ \hat{L}=\mathrm{arg}\mathop{ \mathrm{max}}\limits_{L=1,2,\cdots, {L}_{\mathrm{max}} }\{{C}_{\text{ITC}}(L)\} $ 输出: $\hat L,\{ {\hat f_l},{\hat A_l}\} ,l = 1,2, \cdots ,\hat L$
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表 1 点目标仿真参数
Table 1. Simulation parameters of point targets
参数 数值 参数 数值 频率值${f_1}$ 0.2687 信号长度N 64 复振幅${A_1}$ 5.0000+3.0000j 迭代次数Q 10 频率值${f_2}$ 0.3000 设定最大目标数${L_{\max}}$ 5 复振幅${A_2}$ 0.5000–0.3000j 信噪比$\rho $ (dB) 20
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表 2 强点目标参数估计结果(
${\boldsymbol{W}}_{\bf{1}}/{\boldsymbol{W}}_{\bf{2}} $ =20 dB)Table 2. Estimation result of strong point targets (W1/W2=20 dB)
参数 方法 目标1 目标2 假目标 假目标 假目标 假目标 频率 True 0.2687 0.3000 / / / / FIIB 0.2687 0.3000 / / / / CZT 0.2689 0.2737 0.2578 0.2912 0.3063 0.3232 FFT 0.2656 / / / / / 复振幅 True 5.0000+3.0000j 0.5000–0.3000j / / / / FIIB 4.9906+3.0169j 0.4905–0.3066j / / / / CZT 4.9230+3.1262j 4.6314–1.8004j –1.8767+0.8188j 1.0581–0.5353 0.5413–0.8405j 0.3429–0.4851j FFT 2.2325+5.0000j / / / / /
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表 3 相邻点目标参数估计结果(
${\boldsymbol{\Delta}} {\boldsymbol{f}} = {\bf{1}}/{\boldsymbol{N}}$ )Table 3. Estimation result of neighboring point targets (
${\boldsymbol{\Delta}} {\boldsymbol{f}} = {\bf{1}}/{\boldsymbol{N}}$ )参数 方法 目标1 目标2 假目标 假目标 假目标 假目标 频率 True 0.2844 0.3000 / / / / FIIB 0.2844 0.3000 / / / / CZT 0.2828 0.3021 0.3049 0.2734 0.3227 0.2550 FFT 0.2813 0.2969 / / / / 复振幅 True 5.0000+3.0000j 5.0000–3.0000j / / / / FIIB 4.9852+3.0081j 4.9980–3.0238j / / / / CZT 4.1085+4.3364j 4.1257–4.3441j 1.5993–5.3751j –1.9113+1.6013j 0.2152–1.7055j –0.5516+0.9638j FFT 3.0812+5.0246j 4.9664–0.8527j / / / /
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表 4 不同迭代次数下同多普勒单元内两个目标的FIIB参数估计结果
Table 4. Estimation result of FIIB for two targets situated in a Doppler bin by different iterations
迭代次数Q ${f_1}$ ${f_2}$ ${A_1}$ ${A_2}$ 50 0.2899 0.2980 2.4221+2.4827j 7.3413–2.0001j 100 0.2915 0.2994 4.0880+2.9784j 5.9220–2.9249j 200 0.2920 0.2999 4.7896+2.9998j 5.2107–2.9917j 300 0.2922 0.3000 4.9617+2.9887j 5.0442–2.9834j (真实值) 0.2922 0.3000 5.0000+3.0000j 5.0000–3.0000j
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表 5 前视扫描成像实验仿真参数
Table 5. Simulation parameters of a forward-looking scanning radar
参数 数值 参数 数值 平台飞行速度(m/s) 100 场景中心地距(m) 1700 雷达中心频率(GHz) 18 距离×方位分辨单元 (m×m) 3×3 信号带宽(MHz) 50 和通道3 dB波束宽度(°) 5 信号脉宽(μs) 1 波束扫描范围(°) –15～15 脉冲重复频率PRF (Hz) 2000 天线扫描速度(°/s) 30
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表 6 场景仿真不同方法的定量评价
Table 6. Quantitative evaluation of different methods of scenario simulation
方法 MSE C 传统单脉冲前视成像 $0.00663$ $51.4994$ 基于CZT重建多普勒估计的单脉冲成像 $0.00394$ $52.3441$ 基于FIIB重建多普勒估计的单脉冲成像 $0.00387$ $ 59.7068 $
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表 7 实测数据不同方法的定量评价
Table 7. Quantitative evaluation of different methods of real data
方法 $ {\text{ENT}} $ C 实孔径图像 $4.2660$ $411.9599$ 传统单脉冲前视成像 ${\text{3}}{\text{.6825}}$ $213.4888$ 基于CZT重建多普勒估计的单脉冲成像 $3.5228$ $233.1903$ 基于FIIB重建多普勒估计的单脉冲成像 $2.9651$ $292.8872$
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