雷达风场反演下的空飘球轨迹预测与载荷判断

doi:10.12305/j.issn.1001-506X.2025.09.07

摘要/Abstract

摘要：

为了更好探测识别与跟踪空飘球，考虑到空飘球运动与环境风的高度相关性，综合应用雷达探测定位、风场反演技术提出一种预测空飘球轨迹并判断其载荷的方法。基于当下主流的速度平面处理方法提出双体积单元风场反演方案。方案中，通过建立空飘球流体力学分析下的动力学模型实现空飘球在空轨迹的预测；引入轨迹惯性度（degree of inertia，DOI）和质阻比计算空飘球空载状态下理论轨迹与实际轨迹的差异，分析其自身空飘属性与携带载荷状况。通过仿真实验验证所提方法，结果表明所提风场反演方法各方向风场反演平均绝对误差在0.1以下，轨迹预测误差小于0.162，且在随机观测误差下展现了较好的鲁棒性；通过DOI值能有效判断空飘球带载有无的情况且判断结果受风场观测误差影响较小，相较于空载状态，载荷质量增加1%时DOI值增加16倍，并能较好表现空飘球与载荷之间的质量分布关系，且当载荷质量占比7%以上时DOI判据更为有效；同时通过DOI值能用于判断空飘球是否具备自主动力，根据仿真结果可以认为DOI值大于202，表明空飘球可能具备自主动力。

关键词: 空飘球, 轨迹预测, 载荷识别, 风场反演, 轨迹惯性度

Abstract:

To better detect, identify, and track air floating ball, considering the high correlation between the movement of air floating ball and environmental winds, a method that integrates radar detection and positioning, wind field inversion technology to predict the trajectory of air floating ball and determine their payloads is proposed. Based on the current mainstream velocity plane processing method, a dual-volume unit wind field inversion scheme is introduced. In the scheme, a dynamic model with the analysis of aerodynamics for air floating ball is established to predict their trajectories in the air. Additionally, the trajectory degree of inertia （DOI） and mass resistance ratio are introduced to calculate the difference between the theoretical and actual trajectories of air floating ball in an unloaded state, thereby analyzing their inherent aerial attributes and payload conditions. The proposed method is verified by simulation experiments. The results show that the mean absolute error of wind field inversion is below 0.1. The trajectory prediction error is less than 0.162 and it also shows a good robustness with the random observation error. The DOI value can effectively judge the existence of the payload of air floating ball, and the judgment result is less affected by the wind field observation error. Compared to the unloaded state, a 16-fold increase in DOI values with a 1% increase in payload mass. DOI can better display the mass distribution relationship between the air floating ball and the load, when the payload mass accounts for more than 7%, the DOI criterion is more effective. At the same time, the DOI value can be used to judge whether the air floating ball has independent power. From the simulation results, it can be considered that the DOI values greater than 202 indicates that the air floating ball may have autonomous power.

Key words: air floating ball, trajectory prediction, payload recognition, wind field inversion, trajectory degree of inertia (DOI)

中图分类号:

V 19

王雪松, 殷加鹏, 黄建开, 李健兵, 李永祯. 雷达风场反演下的空飘球轨迹预测与载荷判断[J]. 系统工程与电子技术, 2025, 47(9): 2839-2852.

Xuesong WANG, Jiapeng YIN, Jiankai HUANG, Jianbing LI, Yongzhen LI. Air floating ball trajectory prediction and payload judgment with radar wind field inversion[J]. Systems Engineering and Electronics, 2025, 47(9): 2839-2852.

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参考文献 35

1	杨建军, 廖秋燕, 王卫星, 等. 空飘气球在军事对抗中的运用[J]. 舰船电子对抗, 2022, 45 (2): 28- 31.
	YANG J J, LIAO Q Y, WANG W X, et al. The application of airborne balloons in military confrontation[J]. Ship Electronic Countermeasures, 2022, 45 (2): 28- 31.
2	SIMON H. Qatar B773 at Sao Paulo on July 3rd 2022, hot air ball on final approach[EB/OL]. [2024-07-04]. https://www.aeroinside.com/airline/qatar-airways.
3	黄宛宁, 栗颖思, 周书宇, 等. 现代浮空器军事应用[J]. 科技导报, 2022, 45 (2): 28- 31.
	HUANG W N, LI Y S, ZHOU S Y, et al. The application of airborne balloons in military confrontation[J]. Ship Electronic Countermeasures, 2022, 45 (2): 28- 31.
4	JIAN L Z, XIN D, YONG Z, et al. An estimation method of unmanned aerial vehicle rotor spin frequency based on laser micro-Doppler effect[J]. Optics Communications, 2023, 526, 128926. doi: 10.1016/j.optcom.2022.128926
5	URS B, WELLIG P. Numerical RCS and micro Doppler investigations of a consumer UAV[C]//Proc. of the Target and Background Signatures II, 2016.
6	TING D, SHI Y X, BIAO T, et al. Extraction of micro-Doppler feature using LMD algorithm combined supplement featurefor UAVs and birds classification[J]. Remote Sensing, 2022, 14 (9): 2196. doi: 10.3390/rs14092196
7	ZHAO Y C, SU Y. The extraction of micro-Doppler signal with EMD algorithm for radar-based small UAVs’ detection[J]. IEEE Trans. on Instrumentation and Measurement, 2019, 69, 929- 940.
8	RAO N G, RAO J P, DUVVURU R. A Drone remote sensing for virtual reality simulation system for forest fires: semantic neural-network approach[J]. IOP Conference Series: Materials Science and Engineering, 2024, 149, 012011.
9	RAKSHIT R H, ZADAH B P. A new approach to classify drones using a deep convolutionalneural network[J]. Drones, 2016, 8 (7): 319.
10	LE N P, KANG J H. Robot manipulator calibration using a model based identification technique and a neural network with the teaching learning-based optimization[J]. IEEE Access, 2020, 8, 105447- 105454. doi: 10.1109/ACCESS.2020.2999927
11	MA Y M, MUSTAPHA F, ISHAK M R, et al. Structural fault diagnosis of UAV based on convolutional neural network and data processing technology[J]. Nondestructive Testing and Evaluation, 2024, 39 (2): 426- 445. doi: 10.1080/10589759.2023.2206655
12	殷加鹏, 黄建开, 李永祯, 等. 双极化雷达的空飘气球快速检测方法及装置[P]. 中国: CN202210488113.5, 2023-11−23.
	YIN J P, HUANG J K, LI Y Z, et al. Rapid detection method and device for airborne balloons using dual-polarization radar[P]. China: CN202210488113.5, 2023-11−23.
13	CHEN Y Y, JIANG J, CAO Z L, et al. Exploration of moiré tomography in spatial distribution measurement of wind velocity[J]. Optics and Lasers in Engineering, 2025, 184 (P1): 108579.
14	李健兵, 周洁, 高航. 基于多经纬仪的三维风场反演方法, 装置, 设备和介质[P]. 中国: CN113281826A, 2025-05−30.
	LI J B, ZHOU J, GAO H. Three-dimensional wind field inversion method, device, equipment, and medium based on multi-geodetic instruments[P]. China: CN113281826A, 2025-05−30.
15	YUE F Z, XIAO J Z, YU R Z, et al. Data processing and analysis of eight-beam wind profile coherent wind measurement lidar[J]. Remote Sensing, 2021, 13 (18): 3549. doi: 10.3390/rs13183549
16	ABARI C F, XIN Z C, HARDESTY R M, et al. A reconfigurable all-fiber polarization-diversity coherent Doppler lidar: principles and numerical simulations[J]. Applied Optics, 2015, 54 (30): 8999- 9009. doi: 10.1364/AO.54.008999
17	WANG Y, DENG J Y, SHI L H, et al. Analysis of a dust-floating process based on the vertical distribution of aerosol optical properties[J]. Environmental Science, 2014, 35 (3): 830- 838.
18	CAYA D, ZAWADZKI L. VAD analysis of nonlinear wind fields[J]. Journal of Atmospheric & Oceanic Technology, 2008, 9 (5): 575- 587.
19	LIANG X D, WANG B. An integrating VAP method for single-Doppler radar wind retrieval[J]. Meteorological Journal: English Edition, 2009, (2): 166- 174.
20	WALDTEUFEL P, CORBIN H. On the analysis of single-Doppler radar data[J]. Journal of Applied Meteorology, 1979, 18 (4): 532- 542. doi: 10.1175/1520-0450(1979)018<0532:OTAOSD>2.0.CO;2
21	郎需兴, 魏鸣, 葛文忠, 等. 一种新的单多普勒雷达风场反演方法[J]. 气象科学, 2001, (4): 417- 424. doi: 10.3969/j.issn.1009-0827.2001.04.005
	LANG X X, WEI M, GE W Z, et al. A new method for wind field inversion using single Doppler radar[J]. Meteorological Science, 2001, (4): 417- 424. doi: 10.3969/j.issn.1009-0827.2001.04.005
22	高航, 周洁, 胡健, 等. 基于激光雷达探测的三维风场变分反演算法[J]. 光学学报, 2021, 41 (20): 203- 215.
	GAO H, ZHOU J, HU J, et al. Varying inversion algorithm for three-dimensional wind field based on lidar detection[J]. Acta Optica Sinica, 2021, 41 (20): 203- 215.
23	周洁, 高航, 张旭晖, 等. 一种基于激光雷达探测的风场多特征反演方法[J]. 激光与红外, 2022, 52 (4): 488- 496.
	ZHOU J, GAO H, ZHANG X H, et al. Amulti-feature inversion method for wind field based on lidar detection[J]. Laser and Infrared, 2022, 52 (4): 488- 496.
24	WON S P, MELEK W W. A Kalman/particle filter-based position and orientation estimation method using a position sensor/inertial measurement unit hybrid system[J]. IEEE Trans. on Industrial Electronics, 2010, 57 (5): 1787- 1798. doi: 10.1109/TIE.2009.2032431
25	KAO C F, CHEN T L. Design and analysis of an orientation estimation system using coplanar gyro-free inertial measurement unit and magnetic sensors[J]. Sensors & Actuators A Physical, 2008, 144 (2): 251- 262.
26	WANG H G, WILLIANMS T C. Strategic-inertial navigation systems-high-accuracy inertially stabilized platforms for hostile environments[J]. IEEE Control Systems Magazine, 2008, 28 (1): 65- 85. doi: 10.1109/MCS.2007.910206
27	牛莉霞, 刘谋兴, 李乃文, 等. HVB惯性度的MPHMADM评价[J]. 中国安全科学学报, 2017, 27 (7): 48- 52.
	NIU L X, LIU M X, LI N W, et al. Evaluation of HVB inertial degree using MPHMADM[J]. Journal of Safety Science and Technology, 2017, 27 (7): 48- 52.
28	张金凤, 何重阳, 梁彦. 面向再入目标跟踪的估计与辨识联合优化算法[J]. 航空学报, 2016, 37 (5): 1634- 1643.
	ZHANG J F, HE C Y, LIANG Y. Joint optimization algorithm for measurement and identification aimed at tracking reentry targets[J]. Journal of Aviation, 2016, 37 (5): 1634- 1643.
29	李陆军, 丁建江, 胡磊, 等. 基于运动特征的弹道导弹目标识别技术[J]. 飞航导弹, 2017, (8): 89- 96.
	LI L J, DING J J, HU L, et al. Technology for missile target recognition based on motion features[J]. Flight Navigation Missile, 2017, (8): 89- 96.
30	金文彬, 刘永祥, 黎湘, 等. 再入目标质阻比估计算法研究[J]. 国防科技大学学报, 2004, 26 (5): 46- 51. doi: 10.3969/j.issn.1001-2486.2004.05.011
	JIN W B, LIU Y X, LI X, et al. Study on estimating the mass-to-drag ratio of reentry targets[J]. Journal of National University of Defense Technology, 2004, 26 (5): 46- 51. doi: 10.3969/j.issn.1001-2486.2004.05.011
31	INCROPERA F P, DEWITT D P, BERGMAN T L, et al. Fundamentals of heat and mass transfer[M]. 4th ed. New York: Wiley, 1996.
32	薛大同. 对地球大气密度随高度分布规律的讨论[J]. 真空科学与技术学报, 2009, 29 (S1): 1- 8. doi: 10.3969/j.issn.1672-7126.2009.z1.01
	XUE D T. Discussion on the distribution law of atmospheric density with altitude[J]. Journal of Vacuum Science and Technology, 2009, 29 (S1): 1- 8. doi: 10.3969/j.issn.1672-7126.2009.z1.01
33	达道安, 杨亚天, 涂建辉. 太阳系行星及行星际大气环境特性研究[J]. 宇航学报, 2006, (6): 1306- 1313.
	DA D A, YANG Y T, TU J H. Research on the environmental characteristics of planets and interplanetary atmospheres in the solar system[J]. Journal of Astronautics, 2006, (6): 1306- 1313.
34	王贵, 谭凯, 曹成. 形状差异的岩屑颗粒沉降规律及曳力系数模型[J]. 钻井液与完井液, 2022, 39 (6): 707- 713.
	WANG G, TAN K, CAO C. Settling laws of rock fragment particles with shape differences and drag coefficient model[J]. Drilling Fluid and Completion Fluid, 2022, 39 (6): 707- 713.
35	SHIROKOV D. Non commutative vieta theorem in clifford geometric algebras[J]. Mathematical Methods in the Applied Sciences, 2023, 47 (14): 11305- 11320.

M	ρ	ρ_a	M1	M2	DOI	MRR
5	1	5000	5	0	0	1.0960
			4.95	0.05	2.6789	1.0760
			4.90	0.1	2.8421	1.0762
			4.85	0.15	2.6062	1.0786
			4.80	0.2	1.3758	1.0820
			4.75	0.25	1.1690	1.0861
			4.70	0.3	0.7323	1.0906
			4.65	0.35	0.0660	1.0956
			4.60	0.4	0.6266	1.1009
			4.55	0.45	1.4509	1.1065
			4.50	0.5	2.0582	1.1124

M	ρ_a	M1	M2	DOI	MRR
5	5000	5	0	0	1.0960
		4.5	0.5	2.0582	1.1124
		4	1	12.9336	1.1831
		3.5	1.5	38.3362	1.2753
		3	2	81.6467	1.3946
		2.5	2.5	102.6159	1.5529
		2	3	122.7093	1.7735
		1.5	3.5	147.2192	2.1063
		1	4	175.3374	2.6835
		0.72	4.28	194.1257	3.2618
		0.5	4.5	218.8550	4.0438
		0.1	4.9	331.3871	10.0935
5	7000	5	0	0	1.0960
		4.5	0.5	3.2117	1.1189
		4	1	16.8395	1.1920
		3.5	1.5	41.2953	1.2868
		3	2	84.0287	1.4091
		2.5	2.5	103.2932	1.5713
		2	3	124.6424	1.7974
		1.5	3.5	149.2474	2.1389
		1	4	175.5328	2.7325
		0.72	4.28	198.3456	3.3219
		0.5	4.5	222.9136	4.1385
		0.1	4.9	337.2699	10.4819
	20000	5	0	0	1.0960
		4.5	0.5	5.8094	1.1352
		4	1	19.8990	1.2148
		3.5	1.5	58.2606	1.3161
		3	2	88.7963	1.4462
		2.5	2.5	105.1802	1.6184
		2	3	129.8776	1.8588
		1.5	3.5	152.4744	2.2232
		1	4	184.1869	2.8605
		0.72	4.28	202.8230	3.5060
		0.5	4.5	228.4909	4.3890
		0.1	4.9	349.8054	11.5513

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