基于格拉姆角场的空间锥体目标微动参数快速提取方法

doi:10.12305/j.issn.1001-506X.2026.10.08

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (10): 3351-3362.doi: 10.12305/j.issn.1001-506X.2026.10.08

• 传感器与信号处理 • 上一篇

基于格拉姆角场的空间锥体目标微动参数快速提取方法

王勇(), 刘明帆(), 张荣政(), 夏浩然()

哈尔滨工业大学电子与信息工程学院，黑龙江哈尔滨 150001

收稿日期:2025-07-21 接受日期:2025-11-28 出版日期:2026-10-25 发布日期:2026-09-30
通讯作者: 王勇 E-mail:wangyong6012@hit.edu.cn;850630263@qq.com;21b305001@stu.hit.edu.cn;13604186779@163.com
作者简介:王　勇（1979—），男，教授，博士，主要研究方向为雷达成像技术
刘明帆（2001—），男，博士研究生，主要研究方向为机器学习在雷达信号处理中的应用
张荣政（1995—），男，博士研究生，主要研究方向为雷达成像技术
夏浩然（2002—），男，硕士研究生，主要研究方向为基于深度学习的雷达成像技术
基金资助:
国家杰出青年科学基金（62325104）资助课题

Rapid extraction of micro-motion parameters for space cone-shaped targets based on Gramian angular field

Yong Wang(), Mingfan Liu(), Rongzheng Zhang(), Haoran Xia()

School of Electronics and Information Engineering，Harbin Institute of Technology，Harbin 150001，China

Received:2025-07-21 Accepted:2025-11-28 Online:2026-10-25 Published:2026-09-30
Contact: Yong Wang E-mail:wangyong6012@hit.edu.cn;850630263@qq.com;21b305001@stu.hit.edu.cn;13604186779@163.com

摘要/Abstract

摘要：

针对空间锥体目标外形相似、微动参数相差较大的特点，提出一种基于格拉姆角场的目标微动参数快速提取方法。首先利用改进可逆格拉姆角场对雷达回波进行预处理，进而采用卷积神经网络进行目标微动参数提取，最后通过计算目标的惯量比来体现目标的质量分布特征。所提方法利用可逆格拉姆角场代替时频分析技术，在显著降低计算量的同时可保持微动参数的估计精度，实现对空间锥体目标微动参数的快速提取。实验结果表明，所提方法能够有效地区分同一弹道中外形相同的弹头和诱饵等不同类型目标。

关键词: 卷积神经网络, 微动参数, 空间锥体目标, 格拉姆角场

Abstract:

Considering the similar appearance but significantly different micro-motion parameters among space cone-shaped targets, a rapid micro-motion parameter extraction method is proposed based on the Gramian angular field. First, the radar echo is preprocessed using an improved invertible Gramian angular field. Subsequently, a convolutional neural network is employed to extract micro-motion parameters. Finally, the mass distribution characteristics of the target are characterized by calculating its moment-of-inertia ratio. By replacing time-frequency analysis techniques with the reversible Gramian angular field, this method can significantly reduce computational complexity while maintaining the estimation accuracy of micro-motion parameters, achieving rapid extraction of micro-motion parameters for spatial conical targets. Experimental results demonstrate that the proposed method can effectively distinguish different types of targets such as warheads and decoys with identical appearance on the same trajectory.

Key words: convolutional neural network, micro-motion parameter, space cone-shaped target, Gramian angular field

中图分类号:

TN 957.51

王勇, 刘明帆, 张荣政, 夏浩然. 基于格拉姆角场的空间锥体目标微动参数快速提取方法[J]. 系统工程与电子技术, 2026, 48(10): 3351-3362.

Yong Wang, Mingfan Liu, Rongzheng Zhang, Haoran Xia. Rapid extraction of micro-motion parameters for space cone-shaped targets based on Gramian angular field[J]. Systems Engineering and Electronics, 2026, 48(10): 3351-3362.

图/表 18

图1

图2

图3

图4

图5

图6

图7

图8

表1

表2

图9

表3

图10

表4

图11

表5

表6

表7

参考文献 31

1	张群, 胡健, 罗迎, 等. 微动目标雷达特征提取、成像与识别研究进展[J]. 雷达学报, 2018, 7 (5): 531. doi: 10.12000/JR18049
2	Zhang R Z, Wang Y, Yeh C M, et al. Precession parameter estimation of warhead with fins based on micro-doppler effect and radar network[J]. IEEE Trans. on Aerospace and Electronic Systems, 2023, 59 (1): 443. doi: 10.1109/TAES.2022.3182635
3	李开明, 张袁鹏, 罗迎, 等. 弹道导弹雷达目标识别研究进展[J]. 系统工程与电子技术, 2025, 47(9) : 2870.
4	Chen V C. Analysis of radar micro-Doppler signature with time-frequency transform[C]//10th IEEE Workshop on Statistical Signal and Array Processing, 2000: 463466.
5	Liu L H, Wang Z, Hu W D. Precession period extraction of ballistic missile based on radar measurement[C]//CIE International Conference on Radar, 2006.
6	Yang X, Wu T, Wang N N, et al. HCNN-PSI: a hybrid CNN with partial semantic information for space target recognition[J]. Pattern Recognition, 2020, 108, 107531. doi: 10.1016/j.patcog.2020.107531
7	Liu L H, Ghogho M, Mclernon D, et al. Pseudo-maximum likelihood estimation of ballistic missile precession frequency[J]. Signal Processing, 2012, 92 (9): 2018. doi: 10.1016/j.sigpro.2012.01.011
8	Wang S R, Li M M, Hu Y, et al. Time-varying parametric scattering model guided network for multidimensional parameters estimation of dynamic group cone-shaped targets[J]. IEEE Trans. on Antennas and Propagation, 2025, 73 (8): 5839. doi: 10.1109/TAP.2025.3562925
9	Bai X R, Wang L, Zhou F, et al. Deep CNN for micromotion recognition of space targets[C]//CIE International Conference on Radar, 2016.
10	Yang L, Zhang W P, Jiang W D. Recognition of ballistic targets by fusing micro-motion features with networks[J]. Remote Sensing, 2022, 14 (22): 5678. doi: 10.3390/rs14225678
11	Wang Z H, Zhang Y P, Su L H, et al. Multidomain feature-level fusion for space micro-motion targets recognition based on networked radar systems[J]. IEEE Sensors Journal, 2025, 25 (12): 22250. doi: 10.1109/JSEN.2025.3565373
12	Bai X R, Mao X C, Tian X D, et al. Recognition of micro-motion space targets at low SNR based on complex-valued time convolutional attention denoising recognition network[J]. IEEE Trans. on Radar Systems, 2025, 3, 193. doi: 10.1109/TRS.2025.3527209
13	Wang Y B, Long B, Wang F. RCS statistical feature extraction for space target recognition based on bi-LSTM[C]//IGARSS IEEE International Geoscience and Remote Sensing Symposium, 2023: 6049.
14	Li S Y, Yang T, Li M M, et al. Inertia ratio parameter extraction of typical ballistic target based on deep learning[C]//International Applied Computational Electromagnetics Society Symposium, 2021.
15	Yang T R, Wang S, Li M M, et al. Electromagnetic analysis and micro-motion parameters extraction of moving targets[C]//Cross Strait Radio Science & Wireless Technology Conference, 2020.
16	向前, 王晓丹, 李睿, 等. 基于 DCNN 的弹道中段目标 HRRP 图像识别[J]. 系统工程与电子技术, 2020, 42 (11): 2426. doi: 10.3969/j.issn.1001-506X.2020.11.03
17	Zhu N N, Hu J, Xu S Y, et al. Micro-motion parameter extraction for ballistic missile with wideband radar using improved ensemble EMD method[J]. Remote Sensing, 2021, 13 (17): 3545. doi: 10.3390/rs13173545
18	Xu D, Zhao S Y, Li K M, et al. Micro-Doppler frequency extraction and scatterer classification for a smooth-surfaced cone-shaped precession target under narrowband radar[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2025, 18, 9368. doi: 10.1109/JSTARS.2025.3555068
19	Wang S R, Li M M, Yang T, et al. Cone-shaped space target inertia characteristics identification by deep learning with compressed dataset[J]. IEEE Trans. on Antennas and Propagation, 2022, 70 (7): 5217. doi: 10.1109/TAP.2022.3172759
20	Dai Y W, Zhang W P, Liu Y X. From global statistic to local statistic: micro-Doppler period estimation based on short-time similarity statistic[J]. IEEE Trans. on Signal Processing, 2024, 72, 1269. doi: 10.1109/TSP.2024.3369411
21	Dai Y W, Zhang W P, Liu Y X, et al. Irregular micromotion period measurement: reentry boosters as a case study[J]. IEEE Trans. on Instrumentation and Measurement, 2025, 74, 8503619.
22	Meng L H, Xie J Y, Zhou Z W, et al. A fault diagnosis method for power electronic circuits based on GADF coding and channel split residual network[C]//IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control, 2024: 360.
23	Wu Z F, Zhu Y B, Wang Y B, et al. Extracting static and dynamic features in joint GAF-MTF image for space target recognition[C]//IGARSS IEEE International Geoscience and Remote Sensing Symposium, 2024: 9840.
24	Zhu Y B, Wu Z F, Wang Y B, et al. Space target recognition based on RCS feature extraction using relative position matrix[C]//IEEE International Geoscience and Remote Sensing Symposium, 2024: 9596.
25	刘恒燕, 方君, 凌青, 等. 基于1D-2D-GRU-ResNet的辐射源个体识别方法[J]. 系统工程与电子技术, 2026, 48 (2): 727.
26	Zhang R Z, Wang Y, Mao J. Three-dimensional reconstruction of precession warhead based on multi-view micro-Doppler analysis[J]. Journal of Systems Engineering and Electronics, 2024, 35 (3): 541. doi: 10.23919/JSEE.2024.000030
27	Pan Z H, Li M M, Zhang Q, et al. Accurate modeling of target radar echoes based on dynamic RCS[C]//International Conference on Microwave and Millimeter Wave Technology, 2025.
28	李宏博, 吴文华, 张云. 基于准静态法的空间进动锥体HRRP序列快速生成[J]. 信号处理, 2023, 39 (12): 2205. doi: 10.16798/j.issn.1003-0530.2023.12.008
29	Wu J, Xu Z M, Ai X F, et al. Super-resolution micro-range curve extraction for precession cone-shaped targets based on multidimensional information[J]. IEEE Sensors Journal, 2024, 24 (22): 37544. doi: 10.1109/JSEN.2024.3471797
30	Wang Z G, Oates T. Encoding time series as images for visual inspection and classification using tiled convolutional neural networks[C]//Workshops at the 29th AAAI Conference on Artificial Intelligence, 2015: 40.
31	He K M, Zhang X Y, Ren S Q, et al. Deep residual learning for image recognition[C]//IEEE Conference on Computer Vision and Pattern Recognition, 2016: 770.

参数	参数值
中心频率/GHz	9.75
脉冲重复频率/Hz	512
带宽/MHz	1 500
距离向点数	256
方位向点数	256

参数	参数范围
自旋频率/Hz	[1,5]
锥旋频率/Hz	[1,5]
进动角/（°）	[1,10]
波束入射俯仰角/（°）	[30,60]
波束入射方位角/（°）	[0,360)
脉冲压缩前信噪比/dB	[−12,30]

估计参数算法	锥旋频率		自旋频率		进动角		惯量比
估计参数算法	低信噪比	高信噪比	低信噪比	高信噪比	低信噪比	高信噪比	低信噪比	高信噪比
inv-GAF	98.44	99.34	92.44	98.54	97.23	98.56	91.83	98.55
GAF	98.35	99.25	92.55	98.99	97.04	98.52	92.85	98.43
STSS	98.35	99.11	92.28	98.45	96.36	97.51	92.40	97.86
STFT	98.38	99.22	92.75	98.61	96.28	97.85	92.81	98.06
WVD	98.00	98.79	91.07	98.50	96.64	97.53	91.22	97.63
SPWVD	98.18	99.01	92.36	98.74	96.67	98.41	92.00	98.13

情况	弹道	目标	惯量比	微动类型
1	1	弹头	2	精控
2	1	诱饵	0.75	粗控
3	1	诱饵	0.75	无控
4	2	弹头	2	精控

情况	惯量比真实值	惯量比估计值
		0 dB		10 dB		20 dB
		均值	标准差	均值	标准差	均值	标准差
1	2	1.9984	0.0424	1.9953	0.0523	1.9907	0.0358
2	0.75	0.7478	0.0114	0.7472	0.0117	0.7510	0.0143
3	0.75	0.7289	0.0508	0.7571	0.0296	0.7545	0.0149
4	2	1.9278	0.1285	2.0005	0.0638	2.0134	0.0668

基于格拉姆角场的空间锥体目标微动参数快速提取方法

Rapid extraction of micro-motion parameters for space cone-shaped targets based on Gramian angular field

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 18

参考文献 31

相关文章 15

编辑推荐

Metrics

本文评价

硬件设备	规格或型号
中央处理器	Intel Core i7-13700F
显卡	NVIDIA RTX 4080
内存/GB	128

算法	序列长度为n的相对耗时
算法	n=128	n=256	n=512	$n$= 1 024
inv-GAF	2.00	5.73	33.07	103.94
GAF	1	2.83	31.60	104.79
STFT	15.38	41.52	167.97	518.67
WVD	15.89	52.33	266.30	713.37
SPWVD	201.62	888.40	5 866.35	22 241.28
STSS	360.67	1 493.34	6 447.51	30 661.85

[1]	魏帅, 谢荣, 杨洪飞, 许述文, 刘峥. 基于多尺度加权GCN的有源干扰识别方法[J]. 系统工程与电子技术, 2026, 48(9): 2958-2968.
[2]	王兆辰, 杨华东, 孙海文, 靳子荣. 基于霜冰优化算法的无人机路径优选CNN-LSTM-Attention模型[J]. 系统工程与电子技术, 2026, 48(9): 3104-3118.
[3]	王全全, 昝雨轩, 缪宜恒, 胡海峰, 吴城坤. 基于多维特征和TSOA-CNN的协作频谱感知方法[J]. 系统工程与电子技术, 2026, 48(9): 3260-3265.
[4]	刘畅, 王凌宇, 夏浪, 李岳峰, 林欣, 刘艳阳, 黄鹏辉. 基于小波散射激励与SimAM的轻量化抗噪卷积神经网络的目标识别[J]. 系统工程与电子技术, 2026, 48(7): 2184-2194.
[5]	黄琼丹, 刘露露, 韩洁婧, 王佳鹏, 康仕林. 基于差异特征反投影融合的图像超分辨重建[J]. 系统工程与电子技术, 2026, 48(6): 1809-1818.
[6]	罗雨泉, 何雨强, 李雅鑫, 梁松, 王俊. 基于CNN-BiLSTM-MHA时空融合框架的毫米波雷达人体姿态估计[J]. 系统工程与电子技术, 2026, 48(5): 1502-1514.
[7]	孙景荣, 张华, 陈哲哲, 赵方正. 基于卷积神经网络的雾天道路能见度测量方法[J]. 系统工程与电子技术, 2026, 48(4): 1112-1124.
[8]	蒋明煜, 张顺生, 肖思瑶. 面向轻量级交叉注意力卷积网络的SAR目标识别[J]. 系统工程与电子技术, 2025, 47(9): 2853-2861.
[9]	陈文洁, 张浦, 史高翔, 刘林, 刘烜. 基于余弦校验关系的卷积神经网络LDPC码盲识别[J]. 系统工程与电子技术, 2025, 47(9): 3117-3125.
[10]	段阿敏, 张朝辉. 基于二次分解的混合神经网络蜂窝流量预测[J]. 系统工程与电子技术, 2025, 47(5): 1687-1697.
[11]	付卫红, 张鑫钰, 刘乃安. 基于多尺度融合神经网络的同频同调制单通道盲源分离算法[J]. 系统工程与电子技术, 2025, 47(2): 641-649.
[12]	孔令宸, 刘桐辛, 周晨, 赵正予. 基于区域电离层高分辨率重构的到达时差定位分析[J]. 系统工程与电子技术, 2025, 47(11): 3521-3530.
[13]	师英杰, 周东东, 雷泰然, 黄三傲, 徐科. 纵波EMAT优化与非接触管道液位监测[J]. 系统工程与电子技术, 2025, 47(11): 3531-3542.
[14]	韦娟, 何德华, 宁方立. 基于自适应多分支卷积的声学场景分类[J]. 系统工程与电子技术, 2025, 47(10): 3148-3154.
[15]	邵永琪, 杨丽花, 常澳, 任露露. RIS辅助的OFDM系统中时变信道估计方法[J]. 系统工程与电子技术, 2025, 47(1): 324-331.