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Sparse Array ISAR 3-D Imaging Method for Ship Targets via Joint Error Calibration and Super-resolution DOA Estimation
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摘要: 岸基雷达因固定阵位限制探测能力受限，无人机集群利用其灵活部署特性构成空时混合孔径可实现舰船目标高分辨阵列逆合成孔径雷达(ISAR)三维成像。受海风等海洋环境影响，无人机集群非理想初始状态和速度同步误差会造成阵列构型畸变与ISAR复图像相位错位，降低目标测角与三维重构质量。针对上述问题，该文提出一种稀疏阵列ISAR联合误差校正与角度超分辨的舰船目标三维成像方法。该方法利用多脉冲与ISAR波达方向(DOA)估计的相关性构建关联匹配机制，抑制时变波程差造成的相位误差累积；将两维精细化速度误差模型和多准则融合指标嵌入DOA超分辨估计，实现多维误差补偿与超分辨测角一体化；依据单、多特显点的空间谱差异，结合误差时间分布特性与信噪比加权，提出距离维和方位维联合优化策略，提高测角精度和运算效率。点目标与电磁仿真结果表明，所提方法可在非理想稀疏无人机集群条件下实现舰船目标稳健三维成像，重构误差小于10%，可为舰船目标预警探测与引导打击提供技术支撑。Abstract: Shore-based radar systems are constrained by fixed deployment locations, which limits their detection capability. Owing to their flexible deployment, Unmanned Aerial Vehicles (UAVs) can form a space–time hybrid aperture to enable high-resolution array Inverse Synthetic Aperture Radar (ISAR) three-Dimensional (3-D) imaging of ship targets. However, marine environmental disturbances, such as sea winds, together with nonideal initial states and velocity synchronization errors within the UAV cluster, can distort the array geometry and cause phase misalignment among complex-valued ISAR images, thereby degrading target angle estimation and 3-D reconstruction quality. To address these issues, this paper proposes a sparse-array ISAR 3-D imaging method for ship targets via joint error calibration and super-resolution Direction-of-Arrival (DOA) estimation. The proposed method exploits the correlation between multipulse and ISAR DOA estimates to establish an association-matching mechanism that suppresses phase-error accumulation induced by time-varying differential ranges. A refined two-Dimensional (2-D) velocity-error model and a multicriteria fusion metric are incorporated into super-resolution DOA estimation, enabling the integrated estimation of multidimensional errors and angles. In addition, a joint Range-Azimuth Optimization Strategy (RAOS) is developed by exploiting differences in the spatial spectra of range cells containing either a single prominent scatterer or multiple prominent scatterers, together with the temporal distribution of errors and signal-to-noise ratio weighting, thereby improving both angle-estimation accuracy and computational efficiency. Point-target and electromagnetic simulations demonstrate that the proposed method achieves robust 3-D imaging of ship targets under nonideal sparse UAV-cluster conditions, with reconstruction errors below 10%, providing technical support for early-warning detection and strike guidance.
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Key words:
- Array ISAR /
- UAV cluster radars /
- 3-D imaging /
- Ship targets /
- Error calibration
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图 1 DOA估计和ISAR三维成像结果对比
Figure 1. Comparison of DOA estimation and ISAR 3-D imaging results
图 5 误差存在下使用SBL完成DOA估计结果
Figure 5. DOA Estimation in one range cell with SBL with errors considered.
图 9 所提阵列ISAR三维成像方法流程图
Figure 9. Flowchart of the proposed array ISAR 3-D imaging method
图 10 对比实验模型及ISAR二维成像结果
Figure 10. Comparison experiment model and ISAR 2-D imaging results
图 13 不同误差场景下对比算法1和所提算法ISAR三维成像结果对比
Figure 13. Comparison of 3-D ISAR imaging results between Compared Algorithm 1 and the proposed algorithm under varying error scenarios
图 16 3种信噪比下所提算法三维成像结果
Figure 16. 3-D Imaging results under different SNRs with proposed algorithm
图 17 CAD舰船姿态一所提算法ISAR三维成像结果
Figure 17. Experimental results in the real-world scenario 1
图 18 CAD舰船姿态二所提算法ISAR三维成像结果
Figure 18. Experimental results in the real-world scenario 2
图 19 引入不同海杂波时ISAR二维成像结果
Figure 19. ISAR 2-D imaging results under different sea clutter conditions
图 20 不同信杂比下对比算法1和所提算法三维成像结果图
Figure 20. Comparison of 3-D imaging results between Comparison Algorithm 1 and the proposed algorithm under different SCRs
图 21 不同信杂比下所提算法ISAR三维成像结果图
Figure 21. ISAR 3-D imaging results of the proposed algorithm under different SCRs
1 超分辨DOA估计与多维误差补偿一体化处理
1. Integrated processing of super-resolution DOA estimation and multidimensional error compensation
输入：$ \boldsymbol{x} $, $ {\boldsymbol{\varSigma }} $，.$ \boldsymbol{Q} $, $ {\boldsymbol{\varLambda }} $，stopping rule，M，N，limits 初始化：$ i=0 $，$ j=0 $, ${\boldsymbol{p}}^{\boldsymbol{i}}=\left({p}^{i,1},{p}^{i,2},\cdots ,{p}^{i,M}\right)= $
$ \mathrm{rand}\left\{\mathrm{limits}\right\} $, $ \mathrm{gbest} $直到 $ i=N $ 1. $ i=i+1 $ 直到 $ j=M $ 1) $ j=j+1 $ 2) $ \mathcal{F}^{\mathrm{i},j}=f\left({p}^{i,j}\right) $ 3) $ {\mathcal{L}}^{i,j}={\boldsymbol{\varPhi }}\mathcal{F}^{\boldsymbol{i},j} $ 初始化：$ k=0 $，$ \varepsilon ={10}^{-2} $ 直到满足停止条件 a) $ k=k+1 $ b) $ {\gamma }_{k}=1-{\alpha }_{k}{{\varSigma }}_{k} $ c) $ {\alpha }_{k}=\dfrac{{\gamma }_{k}+c}{{\overset{\frown }{x}}_{k}{}^{2}+d} $ d) $ {\boldsymbol{\varLambda }}\mathbf{=}\mathrm{diag}\left\{{\alpha }_{1}{}^{-1},{\alpha }_{2}{}^{-1}\cdots ,{\alpha }_{N}{}^{-1}\right\} $ e) $ \sigma =\dfrac{{\left|\left|\boldsymbol{y}-{\mathcal{L}}_{i,j}\boldsymbol{X}\right|\right|}_{2}{}^{2}+b}{M-\displaystyle\sum \limits_{i=1}^{M}{\gamma }_{i}+a} $ f) $ {\boldsymbol{\varSigma }}\mathbf{=}{\boldsymbol{\varLambda }}-\sigma {\boldsymbol{\varLambda }}{\mathcal{L}}_{i,j}{}^{\mathrm{H}}{\boldsymbol{Q}}^{-1}{\mathcal{L}}_{i,j}{\boldsymbol{\varLambda }} $ g) $ \overset{\frown }{\boldsymbol{x}}\mathbf{=}\sigma {\boldsymbol{\varLambda }}{\mathcal{L}}_{i,j}{}^{\mathrm{H}}{\boldsymbol{Q}}^{-1}\boldsymbol{y} $ h) $ {\mathcal{C}}_{m}{}^{i,j}={h}_{1}{A}_{s}{}^{i,j}+{h}_{2}\Delta {\theta }^{i,j}+{h}_{3}PC{R}^{i,j}+{h}_{4}{\sigma }^{i,j} $ 输出：$ \overset{\frown }{\boldsymbol{x}}=\arg \min {\left|\left|\boldsymbol{y}-{\mathcal{L}}_{i,j}\boldsymbol{x}\right|\right|}_{2} $, $ {\mathcal{C}}_{m}{}^{i,j} $ 4) $ \mathrm{pbest}=\max \left\langle \mathrm{pbest},{\mathcal{C}}_{m}{}^{i,j}\right\rangle $ 2. $ \mathrm{bestpos}=\arg \underset{{\boldsymbol{p}}^{{{}_{\boldsymbol{i}}}}}{\max }\left\langle \mathrm{gbest},\mathrm{pbest}\right\rangle $ 3. $ {\boldsymbol{p}}^{\boldsymbol{i}\mathbf{+1}}={c}_{1}\times \left[{\boldsymbol{p}}^{\boldsymbol{i}}-\mathrm{pbest}\right]+{c}_{2}\times \left[{\boldsymbol{p}}^{\boldsymbol{i}}-\mathrm{bestpos}\right]+{\boldsymbol{p}}^{\boldsymbol{i}} $ 输出：$ \mathrm{bestpos} $, $ \overset{\frown }{\boldsymbol{x}} $ 
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表 1 实验所用三维成像算法
Table 1. 3-D Imaging algorithms used in experiments
算法名称 算法细节 单脉冲ISAR RDA+和差法测角 InISAR RDA+干涉处理 对比算法1 RDA+SBL 对比算法2 RDA+SRDOA-AM+SRDOA-EC+SPSR 对比算法3 RDA+SRDOA-AM+SRDOA-EC+AOS 对比算法4 RDA+SRDOA-AM+SRDOA-EC+ROS 所提算法 RDA+SRDOA-AM+SRDOA-EC+RAOS
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表 2 阵列ISAR三维成像系统主要仿真参数
Table 2. Main parameters of the electromagnetic simulation scene
参数 数值 参数 数值 中心频率 10 GHz 脉冲宽度 1 μs 带宽 300 MHz 采样频率 400 MHz PRF 300 Hz 中心斜距 4 km 距离单元 1300 脉冲数 300 阵元间距 1 m 阵元个数 8
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表 3 4种策略下阵列误差估计结果
Table 3. Array errors estimation results with four strategies
算法 指标 真实值 估计值 相对误差(%) 平均误差(%) 对比算法2 阵元3阵列向位置误差 0.2 m 0.193486 m 3.26 7.61 阵元3阵列向速度误差 1 m/s 1.166218 m/s 16.6 阵元3航向速度误差 3 m/s 3.168175 m/s 5.61 阵元5航向速度误差 4 m/s 3.801440 m/s 4.96 对比算法3 阵元3阵列向位置误差 0.2 m 0.197384 m 1.31 3.45 阵元3阵列向速度误差 1 m/s 1.082571 m/s 8.26 阵元3航向速度误差 3 m/s 3.086318 m/s 2.88 阵元5航向速度误差 4 m/s 4.054391 m/s 1.36 对比算法4 阵元3阵列向位置误差 0.2 m 0.206382 m 3.19 4.13 阵元3阵列向速度误差 1 m/s 1.096488 m/s 9.65 阵元3航向速度误差 3 m/s 2.958247 m/s 1.39 阵元5航向速度误差 4 m/s 3.908311 m/s 2.29 所提算法 阵元3阵列向位置误差 0.2 m 0.201541 m 0.77 1.67 阵元3阵列向速度误差 1 m/s 0.967528 m/s 3.25 阵元3航向速度误差 3 m/s 3.047742 m/s 1.59 阵元5航向速度误差 4 m/s 3.957633 m/s 1.06
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表 4 算法运行时间及RMSE对比
Table 4. Algorithm Runtime and RMSE Comparison
算法 运行时间(min) RMSE 对比算法1 0.26 3.4752 对比算法2 0.33 1.5736 对比算法3 7.61 1.0317 对比算法4 15.85 1.1793 对比算法5 1.22 0.8866
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表 5 电磁仿真参数
Table 5. Main parameters of the electromagnetic simulation scene
参数 数值 参数 数值 中心频率 10 GHz 脉冲宽度 1 μs 带宽 300 MHz 采样频率 400 MHz PRF 300 Hz 中心斜距 4 km 距离单元 1024 脉冲数 1024 阵元间距 1 m 阵元个数 8
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表 6 不同信杂比下平均相对误差
Table 6. Average relative errors under different SCRs
信杂比(dB) 平均相对误差(%) 10 7.63 15 7.0 20 6.05
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表 7 不同信杂比下误差估计结果
Table 7. Array errors estimation results under different SCRs
信杂比(dB) 指标 真实值 估计值 相对误差(%) 平均误差(%) 10 阵元3阵列向位置误差 0.2 m 0.1852 m 7.4 7.39 阵元3阵列向速度误差 1 m/s 1.0812 m/s 8.12 阵元3航向速度误差 3 m/s 3.3233 m/s 10.78 阵元5航向速度误差 4 m/s 3.8702 m/s 3.24 15 阵元3阵列向位置误差 0.2 m 0.2179 m 8.95 6.04 阵元3阵列向速度误差 1 m/s 1.0754 m/s 7.54 阵元3航向速度误差 3 m/s 2.8861 m/s 3.80 阵元5航向速度误差 4 m/s 4.1549 m/s 3.87 20 阵元3阵列向位置误差 0.2 m 0.2182 m 9.1 5.86 阵元3阵列向速度误差 1 m/s 1.0685 m/s 6.85 阵元3航向速度误差 3 m/s 3.1258 m/s 4.19 阵元5航向速度误差 4 m/s 3.8687 m/s 3.28
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