Simulation Method of Target Track Based on Embedded Particle Swarm Optimization Algorithm

doi:10.3969/j.issn.1009-086x.2024.05.007

Abstract

Abstract:

A target track simulation method based on embedded PSO is proposed to address the fidelity and universal applicability issues of radar-moving target track simulation. Firstly， the principle of simulation moving target track by UAV is analyzed， the motion model and coupling relationship between the UAV and the simulated target is discussed and the control quantity and control equation are determined. Then， based on constraint conditions of target motion track simulation， the objective optimization fitness function is proposed by UAV performance and energy consumption， and the optimal control model of target track simulation is established. Finally， in order to improve the accuracy and practicality of the model solution， the particle swarm optimization algorithm is improved and embedded in the model solution， achieving effective simulation of different motion tracks of the target. The simulation results indicate that this method can have wide applicability for simulating the track of moving targets.

Key words: radar target, moving track, simulation, PSO, UAV

摘要：

针对雷达运动目标轨迹模拟逼真度和普遍适用性问题，提出一种基于嵌入式粒子群算法的目标航迹模拟方法。分析了无人机模拟运动目标航迹的基本原理，论述了无人机和模拟目标之间的运动模型和耦合关系，确定了耦合因子和控制量。分析了目标运动轨迹模拟的约束条件，并结合无人机性能和能耗等因素给出了目标优化适应度函数，建立了目标航迹模拟的最优控制模型。为提高模型解算的精确度和实用性，将粒子群算法进行改进，并嵌入到模型求解中，实现了对目标航迹的有效模拟。仿真结果表明：该方法对实现运动目标轨迹模拟具有广泛适用。

关键词: 雷达目标, 运动轨迹, 模拟仿真, 粒子群算法, 无人机

CLC Number:

TN97

Yanyan MA, Qiang LIN, Chuang NIU, Haida YANG. Simulation Method of Target Track Based on Embedded Particle Swarm Optimization Algorithm[J]. Modern Defense Technology, 2024, 52(5): 51-60.

马艳艳, 林强, 牛闯, 杨海达. 基于嵌入式粒子群算法的目标航迹模拟方法[J]. 现代防御技术, 2024, 52(5): 51-60.

Figures/Tables 8

Fig. 1 Dynamic relationship between UAV and the simulated targets

Fig. 2 Solution flowchart

Table 1 Constraint conditions

参数	v_e /（m/s）	v_p /（m/s）	$u 1$ /（m/s²）	$u 2$ /（rad/s）	$σ$
最大值	100	400	30	0.4	0.50
最小值	10	200	-30	-0.4	0.25

Table 1 Constraint conditions

参数	v_e /（m/s）	v_p /（m/s）	$u 1$ /（m/s²）	$u 2$ /（rad/s）	$σ$
最大值	100	400	30	0.4	0.50
最小值	10	200	-30	-0.4	0.25

Fig. 3 Effect of UAV simulation of target track

Fig. 4 Variation diagram of velocity and accelerated velocity

Fig. 5 Variation diagram of angle and angle speed

Fig. 6 Variation diagram of altitude angle and altitude angle speed

Table 2 Maximum and minimum values of parameters

参数	直线航迹		曲线航迹		环形航迹
参数	最大值	最小值	最大值	最小值	最大值	最小值
v_p /（m/s）	344.314 1	203.699 5	398.584 9	256.109 6	394.679 7	218.487 0
v_e /（m/s）	86.648 1	72.280 9	87.413 9	63.628 6	90.180 3	62.058 7
$v ˙$ _p /（m/s²）	14.924 7	-3.984 9	24.399 9	-28.579 2	29.117 6	-29.668 8
$v ˙$ _e /（m/s²）	0.103 1	0.039 5	13.715 9	-8.585 4	29.723 0	-26.565 3
$α ˙$ _p /（rad/s）	3.992 7×10^-18	-2.964 7×10^-18	0.399 7	-0.375 3	0.250 1	-0.303 4
$α ˙$ _e /（rad/s）	3.204 4×10^-18	-3.961 5×10^-18	0.397 2	-0.400 0	0.395 5	-0.381 5

Table 2 Maximum and minimum values of parameters

参数	直线航迹		曲线航迹		环形航迹
参数	最大值	最小值	最大值	最小值	最大值	最小值
v_p /（m/s）	344.314 1	203.699 5	398.584 9	256.109 6	394.679 7	218.487 0
v_e /（m/s）	86.648 1	72.280 9	87.413 9	63.628 6	90.180 3	62.058 7
$v ˙$ _p /（m/s²）	14.924 7	-3.984 9	24.399 9	-28.579 2	29.117 6	-29.668 8
$v ˙$ _e /（m/s²）	0.103 1	0.039 5	13.715 9	-8.585 4	29.723 0	-26.565 3
$α ˙$ _p /（rad/s）	3.992 7×10^-18	-2.964 7×10^-18	0.399 7	-0.375 3	0.250 1	-0.303 4
$α ˙$ _e /（rad/s）	3.204 4×10^-18	-3.961 5×10^-18	0.397 2	-0.400 0	0.395 5	-0.381 5

References 25

1	WU Xiaochao， WANG Liandong， YAN Liaoliao， et al. Simulation of Radar Track Based on Data Mining Techniques［J］. Telkomnika Indonesian Journal of Electrical Engineering， 2013， 11（7）： 3780-3788.
2	NAM J H， KOH I S， PARK S H， et al. Target Detection and Tracking Simulation of Air Defense Radar in High-Density Clutter Environments Using a Real-Time Simulator［J］. The Journal of Korean Institute of Electromagnetic Engineering and Science， 2020， 31（8）： 738-745.
3	XIAO Qiang， GAO Tengfei， XU Yongshi， et al. Design of Target Detection and Tracking Simulation System of Networking Fire Control Radar［C］∥Proceedings of the 2016 International Conference on Computer Engineering， Information Science & Application Technology （ICCIA 2016）. Dordrecht： Atlantis Press， 2016： 154-157.
4	SARKAR B K， KAKATKAR S S， AGARWAL A. Target Movement Simulation for Testing Monopulse Radar［C］∥IEEE Antennas and Propagation Society International Symposium.Piscataway： IEEE， 1995： 1822-1825.
5	吴鹏. 基于DRFM技术的雷达飞行目标模拟及评估方法研究［D］. 成都：电子科技大学， 2022.
	WU Peng. Research on Radar Flight Target Simulation and Evaluation Method Based on DRFM Technology［D］. Chengdu： University of Electronic Science and Technology of China， 2022.
6	蒙广元. 雷达目标跟踪模拟系统设计与实现［D］. 武汉：武汉大学， 2017.
	MENG Guangyuan. Design and Implementation of Radar Target Tracking Simulation System［D］. Wuhan： Wuhan University， 2017.
7	MAITHRIPALA D H A， JAYASURIYA S. Radar Deception Through Phantom Track Generation［C］∥Proceedings of the 2005， American Control Conference， Piscataway： IEEE， 2005： 4102-4106.
8	MAITHRIPALA D H A， JAYASURIYA S. Phantom Track Generation in 3D through Cooperative Control of Multiple ECAVs Based on Geometry［C］∥First International Conference on Industrial and Information Systems. Piscataway： IEEE， 2006： 255-260.
9	MAITHRIPALA D H A， JAYASURIYA S. Feasibility Considerations in Formation Control： Phantom Track Generation Through Multi-UAV Collaboration［C］∥2008 47th IEEE Conference on Decision and Control. Piscataway： IEEE， 2008： 3959-3964.
10	PURVIS K B， ASTROM K J， KHAMMASH M. Online Control Strategies for Highly Coupled Cooperative UAVs［C］∥2007 American Control Conference. Piscataway： IEEE， 2007： 3961-3966.
11	范振宇，王磊，陈越，等. 组网雷达航迹欺骗技术研究［J］. 中国电子科学研究院学报， 2010， 5（2）： 179-181， 186.
	FAN Zhenyu， WANG Lei， CHEN Yue， et al. A Technique of Track Deception Against Netted Radars［J］. Journal of China Academy of Electronics and Information Technology， 2010， 5（2）： 179-181， 186.
12	FENG Cong， FENG Qi， LI Hui. A Flight Path Planning for Cooperative Generation of a Phantom Radar Track［C］∥2018 37th Chinese Control Conference （CCC）. Piscataway： IEEE， 2018： 4913-4916.
13	李飞，周中良，苟新禹，等. 基于多机协同航迹欺骗的组网雷达突防技术［J］. 系统工程与电子技术， 2013， 35（11）： 2309-2313.
	LI Fei， ZHOU Zhongliang， GOU Xinyu， et al. Technology for Penetrating Radar Net Based on Multiple Combat Air Vehicles Cooperation Track Deception［J］. Systems Engineering and Electronics， 2013， 35（11）： 2309-2313.
14	束坤，刘宇蕊，李迪，等. 多无人机协同航迹欺骗群体智能算法研究［J］. 现代雷达， 2022， 44（11）： 18-23.
	SHU Kun， LIU Yurui， LI Di， et al. A Study on Swarm Intelligence Algorithm for Multi-UAV Cooperative Track Deception［J］. Modern Radar， 2022， 44（11）： 18-23.
15	郭淑芬，余国文，熊鑫，等. 基于无人机协同的航迹欺骗干扰方法研究［J］. 空军预警学院学报， 2018， 32（1）： 44-47， 54.
	GUO Shufen， YU Guowen， XIONG Xin， et al. Research on Method of Track Deception Jamming Based on Cooperative Control of UAVs［J］. Journal of Air Force Early Warning Academy， 2018， 32（1）： 44-47， 54.
16	袁天，陶建锋，李兴成. 飞行器编队协同的虚假航迹产生仿真研究［J］. 计算机仿真， 2017， 34（8）： 100-104.
	YUAN Tian， TAO Jianfeng， LI Xingcheng. Simulation Research of Phantom Track Generation Based on Cooperative Control of a Team of Aircrafts［J］. Computer Simulation， 2017， 34（8）： 100-104.
17	LEE I H， BANG H. Optimal Phantom Track Generation for Multiple Electronic Combat Air Vehicles［C］∥2008 International Conference on Control， Automation and Systems. Piscataway： IEEE， 2008： 29-33.
18	KENNEDY J， EBERHART R. Particle Swarm Optimization［C］∥Proceedings of ICNN'95-International Conference on Neural Networks. Piscataway： IEEE， 1995： 1942-1948.
19	SHI Y， EBERHART R. A Modified Particle Swarm Optimizer［C］∥1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence. Piscataway： IEEE， 1998： 69-73.
20	CLERC M. The Swarm and the Queen： Towards a Deterministic and Adaptive Particle Swarm Optimization［C］∥Proceedings of the 1999 Congress on Evolutionary Computation-CEC99. Piscataway： IEEE， 1999： 1951-1957.
21	CLERC M， KENNEDY J. The Particle Swarm-Explosion， Stability， and Convergence in a Multidimensional Complex Space［J］. IEEE Transactions on Evolutionary Computation， 2002， 6（1）： 58-73.
22	李明. 标准粒子群算法的收敛性分析及改进研究［D］. 锦州：渤海大学， 2017.
	LI Ming. Convergence Analysis and Improvement Research of Standard Particle Swawrm Optimization Algorithm［D］. Jinzhou： Bohai University， 2017.
23	倪庆剑，邢汉承，张志政，等. 粒子群优化算法研究进展［J］. 模式识别与人工智能， 2007， 20（3）： 349-357.
	NI Qingjian， XING Hancheng， ZHANG Zhizheng， et al. Survey of Particle Swarm Optimization Algorithm［J］. Pattern Recognition and Artificial Intelligence， 2007， 20（3）： 349-357.
24	秦媛. 粒子群算法改进及其应用研究［D］. 南京：南京邮电大学， 2018.
	QIN Yuan. Improved Particle Swarm Algorithm and Its Applications［D］. Nanjing： Nanjing University of Posts and Telecommunications， 2018.
25	SHI Yuhui， EBERHART R C. Parameter Selection in Particle Swarm Optimization［C］∥Evolutionary Programming VII. Berlin： Springer Berlin Heidelberg， 1998： 591-600.

[1]	Qianli FENG, Xianming SHI, Xiongfei QIU, Shuai LÜ, Yu ZHANG. Optimization Analysis of Ammunition Reserve Quantity in Wartime Based on System Dynamics Model [J]. Modern Defense Technology, 2024, 52(5): 173-181.
[2]	Jiutao WU, Zhiqian WU, Chao YANG. Digital Research and Development Methods for Electronic Information Equipment [J]. Modern Defense Technology, 2024, 52(5): 25-30.
[3]	Wenbiao HE, Yongjiang HU, Wenguang LI. Review of Optimization Algorithms for UAV Routes [J]. Modern Defense Technology, 2024, 52(4): 24-32.
[4]	Jingyu HE, Jizheng LIU, Zhichen YANG, Dongdong WANG, Ping OU. Development and Testing of Multi Rotor Unmanned Aerial Vehicle Noise Source Tracking and Positioning System [J]. Modern Defense Technology, 2024, 52(3): 1-8.
[5]	Zonghui WANG, Yunjun YANG, Hongrui ZHAO, Jiaxiang ZHAO. Numerical Simulation of Tilting Wing and Rotor UAV During Transition Flight [J]. Modern Defense Technology, 2024, 52(3): 9-19.
[6]	Jing WU, Yaqiang ZHUANG, Peng NI, Haifeng CAI, Sen LI. Research on the Operation Influence of MALD on the Ground Air Defense Equipment [J]. Modern Defense Technology, 2024, 52(2): 13-21.
[7]	Linan WANG, Guanghui WEN, Xiaojian YI. Finite-time Attitude Consensus Control of Multiple Unmanned Aerial Vehicles Under State Constraints [J]. Modern Defense Technology, 2024, 52(2): 124-131.
[8]	Xiaofeng AI, Jing WU, Jingke ZHANG, Yiqi ZHU, Zhiming XU, Qihua WU. Design and Implementation of Radar Intelligent Recognition Simulation System for Aerospace Targets [J]. Modern Defense Technology, 2024, 52(2): 151-162.
[9]	Cheng SHANG, Zhiming XU, Yang ZHANG, Kaiyu ZHANG, Qihua WU, Yiqi ZHU, Xiaofeng AI. Design and Realization of an Dynamic Electromagnetic Scattering Data Simulation System for Air Target [J]. Modern Defense Technology, 2024, 52(2): 163-171.
[10]	Wenru FAN, Quanwei LIU, Bailing TIAN. Trajectory Tracking Control of Quadrotor UAV Based on Disturbance Compensation [J]. Modern Defense Technology, 2024, 52(2): 87-93.
[11]	Wenqiang DING, Hao DING, Zhiyun ZHAO. Research on Simulation of Submarine Evading Torpedo Attack Through Changing Depth by Strong Movement [J]. Modern Defense Technology, 2024, 52(1): 124-129.
[12]	Jianchao LIU, Fei DONG, Siyu JI, Qiong WU. Design of Carrier-Based Aircraft Operational Command Training System Based on LVC [J]. Modern Defense Technology, 2024, 52(1): 130-138.
[13]	Baojie HU, Fuhong GONG, Fangjun HE, Pan WANG. An Integrated Training Implementation Method Based on Virtual-Real Combination of Inside and Outside Field [J]. Modern Defense Technology, 2024, 52(1): 16-23.
[14]	Ye XU, GuoSheng XU, Yukun WANG, Gang WANG, Jingwang LIU, BoJun FAN, Miao WU. Stepwise Deployable Mechanism Design and Dynamics Analysis of UAV Folding Wing [J]. Modern Defense Technology, 2024, 52(1): 24-33.
[15]	Yang TAO, Yi ZHOU, Huangtao JIANG. Application of Improved Ant Colony Algorithm to Terrain Following Route Planning Problem [J]. Modern Defense Technology, 2024, 52(1): 34-40.