﻿ 具有多频极点特征的高频雷达目标识别算法研究
 舰船科学技术  2024, Vol. 46 Issue (10): 178-181    DOI: 10.3404/j.issn.1672-7649.2024.10.032 PDF

Research on high frequency radar target recognition algorithm with multi frequency pole features
ZHANG Xin-chao
College of Big Data and Artificial Intelligence, Zhengzhou University of Science and Technology, Zhengzhou 450064, China
Abstract: This article provides the amplitude variation curves of the radar scattering cross-sectional area under different electrical sizes. Analyzed the calculation method of target scattering characteristics. Explored the target recognition method for multi frequency poles, provided the target impact response curve, and determined the number of target poles using the minimum description length method. At the same time, solved the target poles using the Prony method. Finally, simulation was conducted on high-frequency radar target recognition, and the variation curves of correct recognition rate and rejection with signal-to-noise ratio were provided.
Key words: multi frequency pole     high frequency radar     target recognition
0 引　言

1 雷达目标识别技术 1.1 雷达散射截面积

 ${w_i} = \frac{1}{2}{E^i}{H^{{i^*}}} = \frac{1}{{2{Z_0}}}{\left| {{E^i}} \right|^2}\text{。}\\$ (1)

 $P = \frac{1}{{2{Z_0}}}\sigma {\left| {{E^i}} \right|^2}\text{。}$ (2)

 ${w_s} = \frac{{\sigma {{\left| {{E^i}} \right|}^2}}}{{8{\text{π}} {Z_0}{R^2}}}\text{。}$ (3)

 $\sigma = 4{\text{π}} {R^2}{\left| {\frac{{{E^s}}}{{{E^i}}}} \right|^2}\text{，}$ (4)
 $\sigma ' = \mathop {\lim }\limits_{R \to \infty } 4{\text{π}} {R^2}\frac{{{{\left| {{H^s}} \right|}^2}}}{{{{\left| {{H^i}} \right|}^2}}}\text{。}$ (5)

 ${P_r} = \frac{{{P_t}{G_t}}}{{{L_t}}}\frac{1}{{4{\text{π}} r_t^2{L_{mt}}}}\sigma \frac{1}{{4{\text{π}} r_r^2{L_{mr}}}}\frac{{{G_r}\lambda _0^2}}{{4{\text{π}} {L_r}}}\text{，}$ (6)
 ${P_r}^\prime = \frac{{{P_t}{G_t}}}{{4{\text{π}} r_t^2}}\frac{\sigma }{{4{\text{π}} }}\frac{{{A_r}}}{{r_r^2}}\text{。}$ (7)

 ${c_{dBsm}} = 10\lg c\text{。}$ (8)

 图 1 反射强度随电尺寸长度的变化曲线 Fig. 1 The curve of reflection intensity changing with the length of electrical size
1.2 目标散射特性的计算

 $\left\{ {\begin{array}{*{20}{l}} {{E^s} = \int_S {\left( {j\omega \mu J\phi + \dfrac{1}{\varepsilon }\rho \nabla \phi } \right){\rm{d}}S} }，\\ {{H^s} = \int_S {\left( {\hat n \times H \times \nabla \phi } \right){\rm{d}}S}。} \end{array}} \right.$ (9)

 $g\left( z \right) = \int_b^a {G\left( {z,z'} \right)f\left( {z'} \right){\rm{d}}z'} 。$ (10)

 $f\left( {z'} \right) \approx \sum\limits_{n = 1}^N {{a_n}{f_n}\left( {z'} \right)} \text{。}$ (11)

 $g'\left( z \right) \approx \sum\limits_{n = 1}^N {{a_n}L\left[ {{f_n}\left( {z'} \right)} \right]} \text{。}$ (12)

 $\varepsilon \left( z \right) = \sum\limits_{n = 1}^N {{a_n}L\left[ {{f_n}\left( {z'} \right)} \right] - g\left( z \right)} \text{。} \\$ (13)

 $\left\langle {{w_m},\varepsilon } \right\rangle = \sum\limits_{n = 1}^N {{a_n}\left\langle {{w_m},L\left[ {{f_n}\left( z \right)} \right]} \right\rangle } - \left\langle {{w_m},g\left( z \right)} \right\rangle \text{。}$ (14)

wmε之间是正交的时候，那么残数矢量εφ(wm)空间上的投影等于0，并且随着N数值的增加，残数ε也会不断变小。式（14）中使用的基函数为：

 $f\left( z \right) = \sum\limits_{n = 1}^\infty {{a_n}{f_n}\left( z \right)} \text{。}$ (15)

 图 2 不同频率下雷达散射截面积变化情况 Fig. 2 Changes in radar scattering cross-sectional area at different frequencies
2 基于多频极点的目标识别方法

 $MDL\left( m \right) = - 2L\left( {{\theta _m}} \right) + m\ln N\text{。}$ (16)

 $L\left( {{\theta _m}} \right) = \max \sum\limits_{i = 1}^N {\ln f\left( {{x_i}|{\theta _m}} \right)} \text{。}$ (17)

 $MDL\left( k \right) = \left( {k - 1} \right)\left[ {1 + \ln 2{\text{π}} + \ln \frac{{\left\| {Y - {A^{\left( k \right)}}Y} \right\|}}{{N - L}}} \right]\text{，}$ (18)
 $MDL\left( {\hat M} \right) = \min \left\{ {MDL\left( 0 \right),L,MDL\left( {L - 1} \right)} \right\}\text{。}\\$ (19)

 图 3 目标冲击响应 Fig. 3 Target shock response
 $\left\{ {\begin{array}{*{20}{l}} {{s_{1,2}} = - 0.1 \pm j0.5} ，\\ {{s_{3,4}} = - 0.2 \pm j4} 。\end{array}} \right.$ (20)
 ${r_{1,2}} = {r_{3,4}} = 1 \pm j\text{，}$ (21)
 ${y_n} = \sum\limits_{k = 1}^M {{r_k}{e^{{s_k}n\Delta t}} + {w_n}} \text{。} \\$ (22)

 图 4 最小描述长度随极点数的变化曲线 Fig. 4 The curve of minimum description length with the number of poles

 $\sum\limits_{k = 0}^M {{\alpha _k}{h_{j + k}} = 0} \text{，}$ (23)
 $\sum\limits_{k = 0}^M {{\alpha _k}z_i^k} = 0\text{，}$ (24)
 ${S_i} = \frac{1}{T}\ln {z_i}\text{。}$ (25)
3 高频雷达目标识别仿真分析

 ${d_m} = {\left[ {\sum\limits_{j = 1}^k {{{\left( {{D_j} - {D_{mj}}} \right)}^2}} } \right]^{\frac{1}{2}}}\text{。}$ (26)

 ${d_m} \lt {d_n}，\begin{array}{{c}} {}{m,n = 1,2,...,M;n \ne m} \end{array}。$ (27)
 ${P_B} \leqslant {P_{NN}} \leqslant 2{P_B}\text{。}$ (28)

 $SNR = \frac{1}{k}\sum\limits_{j = 1}^k {\frac{{{D_{mj}}}}{{{\sigma ^2}}}} \text{，}$ (29)

 $平均正确识别率=\frac{正确识别次数}{总的试验次数} \text{。}$ (30)

 图 5 基于近邻分类器的正确识别率曲线 Fig. 5 Correct recognition rate curve based on nearest neighbor classifier
 $x = 10\lg \left( {\frac{{\Delta {D_{mj}}}}{{{D_{mj}}}}} \right)\text{。}$ (31)

 图 6 基于扩展近邻分类器的正确识别率曲线 Fig. 6 Correct recognition rate curve based on extended nearest neighbor classifier

 图 7 拒判率随信噪比的变化曲线 Fig. 7 The variation curve of rejection rate with signal-to-noise ratio
4 结　语

 [1] 赵尤信, 姚海飞, 李佳慧, 等. 超宽带雷达生命探测技术研究[J]. 工矿自动化, 2023(49): 178-186. ZHAO You-xin, YAO Hai-fei, LI Jia-hui, et al. Research on ultra wideband radar life detection technolog[J]. Journal of Mine Automation, 2023(49): 178-186. [2] 万显荣, 易建新, 占伟杰, 等. 基于多照射源的被动雷达研究进展与发展趋势[J]. 雷达学报, 2020(9): 939-958. WAN Xian-rong, YI Jian-xin, ZHAN Wei-jie, et al. Research progress and development trend of the multi-illuminator-based passive radar[J]. Journal of Radar, 2020(9): 939-958. [3] 马超, 李中林, 吴道庆, 等. 基于改进最大熵谱估计的弹道目标超分辨成像[J]. 现代雷达, 2021(43): 46-53. MA Chao, LI Zhong-lin, WU Dao-qing, et al. Hyper-resolution imaging of ballistic targets based on improved maximum entropy spectral estimation[J]. Modern Radar, 2021(43): 46-53. [4] 于家傲, 韩鹏, 周儒勋. 基于海杂波修正的OTHR空中目标RCS估计[J]. 现代雷达, 2023(45): 30-36. YU Jia-ao, HAN Peng, ZHOU Ru-xun. RCS estimation of OTHR air target based on sea cultter correction[J]. Modern Radar, 2023(45): 30-36. [5] 原培新, 蔡炟, 曹文伟, 等. 基于双目立体视觉的列车目标识别和测距技术[J]. 东北大学学报, 2022(43): 335-343. YUAN Pei-xin, CAI Da, CAO Wen-wei, et al. Train target recongintion and ranging technology based on binocular stereoscopic vision[J]. Journal of Northeastern University, 2022(43): 335-343. [6] 彭韶文, 李商远, 薛晓晓, 等. 基于微波光子学的超分辨率双波段雷达[J]. 雷达科学与技术, 2021(19): 172-177+182. PENG Shao-wen, LI Shang-yuan, XUE Xiao-xiao, et al. Super-resolution dual-band radar based on photonics technology[J]. Radar Science and Technology, 2021(19): 172-177+182. [7] 周丽军. 极点特征聚类的公路隐藏裂缝自动识别算法[J]. 太原科技大学学报, 2020(41): 390-395. ZHOU Li-jun. Automatic recognition algorithm for hidden cracks in highway based on pole feature clustering[J]. Journal of Taiyuan University of Science and Technology, 2020(41): 390-395.