涡旋电磁波雷达平动旋转目标三维微动参数提取方法

袁航; 何其芳; 罗迎; 王志浩; 张群

doi:10.12000/JR23065

涡旋电磁波雷达平动旋转目标三维微动参数提取方法

DOI: 10.12000/JR23065

袁航¹,
何其芳²,
罗迎^1, ,,
王志浩¹,
张群¹

1.
空军工程大学信息与导航学院西安 710077
2.
93114部队北京 100195

基金项目: 国家自然科学基金(61971434, 62131020)

详细信息

作者简介:
袁　航，博士生，主要研究方向为雷达成像及微多普勒效应

何其芳，助理工程师，主要研究方向为雷达目标识别、目标情报处理与应用

罗　迎，教授，博士生导师，主要研究方向为雷达成像、雷达目标识别

王志浩，博士生，主要研究方向为雷达目标微多普勒效应与目标识别

张　群，教授，博士生导师，主要研究方向为雷达成像、雷达目标识别

通讯作者:
罗迎 luoying2002521@163.com

责任主编：郭忠义 Corresponding Editor: GUO Zhongyi
中图分类号: TN957
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出版历程
- 收稿日期: 2023-04-28
- 修回日期: 2023-06-28
- 网络出版日期: 2023-07-17
- 刊出日期: 2023-08-28

Three-dimensional Micro-motion Parameters Extraction of Translational Rotating Targets Based on Vortex Electromagnetic Wave Radar

1.
College of Information and Navigation, Air Force Engineering University, Xi’an 710077, China
2.
Unit 93114 of PLA, Beijing 100195, China

Funds: The National Natural Science Foundation of China (61971434, 62131020)

More Information

Corresponding author: LUO Ying, luoying2002521@163.com

摘要

摘要: 与传统平面电磁波雷达相比，涡旋电磁波雷达能同时观测到目标投影到雷达径向和垂直于径向平面的微动分量，可为目标识别提供更多信息。当前关于涡旋电磁波雷达微多普勒效应的研究尚处于起步阶段，初步实现了对旋转目标的三维微动参数的提取，但均未考虑目标平动的影响。因此，该文研究了涡旋电磁波雷达中平动旋转目标的微多普勒效应，推导了平动旋转目标的角多普勒性质，提出了基于1/4微动周期多普勒频移曲线的三维微动参数提取方法，获得了目标旋转频率、旋转半径、旋转矢量和平动速度矢量等参数。仿真验证了角多普勒性质的正确性和参数提取方法的有效性。
- 涡旋电磁波雷达 /
- 微多普勒 /
- 旋转目标 /
- 三维微动 /
- 平动
Abstract: Compared with traditional Electromagnetic (EM) wave radars, vortex EM wave radars can simultaneously observe the micro-motion components projected onto the radar’s radial and perpendicular planes, providing more information for target recognition. The current research on the micro-Doppler effect of vortex EM wave radar is still in its infancy, and the extraction of three-dimensional micro-motion parameters of rotating targets has been preliminarily achieved. However, the impact of target translation was not considered. Therefore, the micro-Doppler effect of translational rotating targets in vortex EM wave radar is studied in this paper. The angular Doppler properties of translational rotating targets are derived, and a three-dimensional micro-motion parameter extraction method based on the 1/4 micro-motion period Doppler frequency shift curve is proposed. Estimation of parameters such as target rotation frequency, rotation radius, rotation vector and translational velocity vector is achieved. The correctness of angular Doppler properties and the effectiveness of parameter extraction method are verified by simulations.
- Vortex Electromagnetic Wave Radar (VEMWR) /
- Micro-Doppler /
- Rotating target /
- Three-dimensional micro-motion /
- Translational motion

HTML全文

图 1 平动旋转目标观测模型

Figure 1. Observation model of translational rotating targets

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图 2 三维旋转结果

Figure 2. The three-dimensional rotation result

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图 3 点q在平面${XOY}$上的轨迹

Figure 3. The trajectory of the point q on plane ${XOY}$

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图 4 角多普勒频移曲线

Figure 4. Angular Doppler frequency shift curve

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图 5 多数情况下的角多普勒频移曲线

Figure 5. Angle Doppler curve in most cases

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图 6 4种情况下的角多普勒频移曲线

Figure 6. Angle Doppler curve in four cases

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图 7 算法流程图

Figure 7. Algorithm flow chart

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图 8 多普勒曲线

Figure 8. The curve of Doppler

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图 9 俯仰角及贝塞尔函数值变化曲线

Figure 9. Pitch angle and Bessel function value change curve

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图 10 回波时频图(线多普勒＋角多普勒)

Figure 10. Echo time-frequency map (linear Doppler+ angular Doppler)

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图 11 不同微动参数倍数下的角多普勒曲线

Figure 11. Angular Doppler curves under different micro motion parameter multiples

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图 12 不同阶导数下的线多普勒曲线

Figure 12. Linear Doppler curve under different order derivatives

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图 13 1/4周期的多普勒频移曲线

Figure 13. Doppler frequency shift curve at quarter cycle

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图 14 添加误差后的角多普勒曲线

Figure 14. Angular Doppler curve after adding error

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表 1 雷达和目标参数

Table 1. Parameters of radar and target

参数	数值
载频(GHz)	10
阵列半径(m)	1
模态数	4
旋转半径(m)	0.4
旋转频率(Hz)	10
欧拉角(rad)	(1.0472,0.7854,0)
旋转矢量	(0.707,–0.612,0.353)
旋转中心(m)	(0.8,1,100)
速度矢量(m/s)	(–10, –5, 10)

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表 2 选取点的时刻和角多普勒值

Table 2. The time and angular Doppler value of the selected point

序号	时刻(s)	角多普勒(Hz)
1	0	4.8271
2	0.0133	6.1418
3	0.0267	8.5308
4	0.0400	12.2020
5	0.0534	9.2937
6	0.0667	–9.3425
7	0.0800	–5.6511
8	0.0934	4.6931

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表 3 求解过程的迭代误差

Table 3. Iterative error in the solving process

迭代次数	误差	学习率
1	2571.63	0.01
2	555.784	0.001
3	214.932	1
4	110.276	10
5	79.972	1
6	59.7386	0.1
7	15.365	0.01
8	9.63835	1
9	5.24274	0.1
10	0.994269	0.01
11	0.005036	0.001
12	5.25×10^–7	0.0001
13	5.26×10^–15	10^–5

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表 4 多元非线性方程组求解结果

Table 4. Solution results of multivariate nonlinear equations

参数	估计值	理想值
欧拉角(rad)	(1.047,0.785)	(1.0472,0.7854)
旋转半径相对大小(m)	0.631	0.4
旋转中心相对大小(m)	(1.26,1.57)	(0.8,1)
速度矢量相对大小(m/s)	(–15.79, –7.89)	(–10, –5)

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表 5 完整周期频移曲线下的微动参数估计结果

Table 5. Estimation results of micro-motion parameters under complete periodic frequency shift curve

参数	估计值	理想值	误差
旋转矢量	(0.707,–0.612,0.353)	(0.707,–0.612,0.353)	0.04%
旋转频率	9.944 Hz	10 Hz	0.56%
旋转半径	0.398 m	0.4 m	0.50%
旋转中心	(0.796,0.995) m	(0.8,1) m	2.75%
速度矢量	(–9.953, –4.976) m/s	(–10, –5) m/s	0.46%

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表 6 选取1/4周期内8个点的时刻和角多普勒值

Table 6. Select the time and angular Doppler Values of 8 points within a quarter cycle

序号	时刻(s)	角多普勒(Hz)
1	0.0010	4.9123
2	0.0043	5.2019
3	0.0076	5.5134
4	0.0110	5.8640
5	0.0143	6.2706
6	0.0176	6.7500
7	0.0210	7.3187
8	0.0243	7.9918

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表 7 1/4周期多元非线性方程组求解结果

Table 7. Solution results of multivariate nonlinear equations under 1/4 period

参数	估计值	理想值
欧拉角(rad)	(1.047,0.785)	(1.0472,0.7854)
旋转半径相对大小(m)	0.068	0.4
旋转中心相对大小(m)	(0.136,0.171)	(0.8,1)
速度矢量相对大小(m/s)	(–1.709, –0.854)	(–10, –5)

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表 8 1/4周期频移曲线下的微动参数估计结果

Table 8. Estimation results of micro-motion parameters at quarter periodic frequency shift curve

参数	估计值	理想值	误差
旋转矢量	(0.707,–0.612,0.353) m	(0.707,–0.612,0.353) m	0.04%
旋转频率	9.944 Hz	10 Hz	0.56%
旋转半径	0.398 m	0.4 m	0.50%
旋转中心	(0.796,0.995) m	(0.8,1) m	2.75%
速度矢量	(–9.953, –4.976) m/s	(–10, –5) m/s	0.46%

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表 9 添加误差后6个点的时刻和角多普勒值

Table 9. Time and angle Doppler values of 6 points after adding error

序号	时刻(s)	角多普勒(Hz)	误差(%)
1	0.0003	3.8878	19.93
2	0.0170	5.4510	18.01
3	0.0337	9.2341	11.79
4	0.0504	11.4651	1.48
5	0.0670	–8.7959	8.84
6	0.0837	–2.1743	11.49

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表 10 添加误差后的微动参数估计结果

Table 10. Estimation results of micro-motion parameters after adding errors

参数	估计值	理想值	误差
旋转矢量	(0.760, –0.583, 0.271) m	(0.707, –0.612, 0.353) m	12.36%
旋转频率	9.944 Hz	10 Hz	0.56%
旋转半径	0.389 m	0.4 m	2.62%
旋转中心	(0.71,1.02) m	(0.8,1) m	6.36%
速度矢量	(–9.00, –6.02) m/s	(–10, –5) m/s	15.18%

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