Target maneuver trajectory prediction based on RBF neural network optimized by hybrid algorithm

doi:10.23919/JSEE.2021.000042

Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (2): 498-516.doi: 10.23919/JSEE.2021.000042

• CONTROL THEORY AND APPLICATION • Previous Articles

Target maneuver trajectory prediction based on RBF neural network optimized by hybrid algorithm

Zhifei XI*(), An XU, Yingxin KOU, Zhanwu LI, Aiwu YANG

¹ Aeronautics Engineering College, Air Force Engineering University, Xi’an 710038, China

Received:2020-03-18 Online:2021-04-29 Published:2021-04-29
Contact: Zhifei XI E-mail:18149365256@163.com
About author:|XI Zhifeiwas born in 1996. He graduated from the Aeronautics Engineering College, Air Force Engineering University in 2018. He is currently a master student in the same university. His research mainly focuses on air combat, machine intelligent and artificial intelligence. E-mail: 18149365256@163.com||XU An was born in 1984. He received his M.S. and Ph.D. degrees from Air Force Engineering University, Xi’an, China, in 2009 and 2012, respectively. He is currently a postdocotoral researcher at the Electronic Information College of Northwestern Polytechnical University, Xi’an, China, as well as a researcher with the Aeronautics Engineering College of Air Force Engineering University. His research interests include nonlinear and adaptive control, artificial intelligence and pattern recognition. E-mail: 18157494594@163.com||KOU Yingxin was born in 1965. He received his M.S. and Ph.D. degrees from Air Force Engineering University, Xi’an, China, in 1997 and 2010, respectively. He is currently a professor with the Aeronautics Engineering College of Air Force Engineering University. His research interests include air combat, nonlinear and adaptive control, artificial intelligence, multi-sensor data fusion, and optimized target assignment. E-mail: kgykyx@hotmail.com||LI Zhanwu was born in 1978. He received his M.S. degree from Air Force Engineering University, Xi’an, China, in 2007. He is currently an associate professor with the Aeronautics Engineering College of Air Force Engineering University. His research mainly focuses on multi-sensor data fusion, machine intelligent and artificial intelligence. E-mail: afeulzw@189.cn||YANG Aiwu was born in 1996. He graduated from the Aeronautics Engineering College of Air Force Engineering University in 2018. He is currently a master student in the same university. His research mainly focuses on air combat, machine intelligent and artificial intelligence.E-mail: 15349215326@163.com

Abstract

Abstract:

Target maneuver trajectory prediction plays an important role in air combat situation awareness and threat assessment. To solve the problem of low prediction accuracy of the traditional prediction method and model, a target maneuver trajectory prediction model based on phase space reconstruction-radial basis function (PSR-RBF) neural network is established by combining the characteristics of trajectory with time continuity. In order to further improve the prediction performance of the model, the rival penalized competitive learning (RPCL) algorithm is introduced to determine the structure of RBF, the Levenberg-Marquardt (LM) and the hybrid algorithm of the improved particle swarm optimization (IPSO) algorithm and the k-means are introduced to optimize the parameter of RBF, and a PSR-RBF neural network is constructed. An independent method of 3D coordinates of the target maneuver trajectory is proposed, and the target manuver trajectory sample data is constructed by using the training data selected in the air combat maneuver instrument (ACMI), and the maneuver trajectory prediction model based on the PSR-RBF neural network is established. In order to verify the precision and real-time performance of the trajectory prediction model, the simulation experiment of target maneuver trajectory is performed. The results show that the prediction performance of the independent method is better, and the accuracy of the PSR-RBF prediction model proposed is better. The prediction confirms the effectiveness and applicability of the proposed method and model.

Key words: trajectory prediction, k-means, improved particle swarm optimization (IPSO), Levenberg-Marquardt (LM), radial basis function (RBF) neural network

Zhifei XI, An XU, Yingxin KOU, Zhanwu LI, Aiwu YANG. Target maneuver trajectory prediction based on RBF neural network optimized by hybrid algorithm[J]. Journal of Systems Engineering and Electronics, 2021, 32(2): 498-516.

Figures/Tables 26

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 1

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Table 2

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Fig.21

Fig.22

Fig.23

Table 3

References 30

1	MA G B, XUE A K Application of data mining technology in predicting the track of moving object. Computer Engineering and Applications, 2004, 40 (11): 210- 212.
2	YOU H H, YU M J, LV Y, et al Application of UKF optimized by improved gray wolf algorithm in air combat trajectory prediction. Tactical Missile Technology, 2020, (1): 91- 98.
3	KIM B M, CHOI K C, KIM B S. Trajectory tracking controller design using neural networks for Tiltrotor UAV. Proc. of the AIAA Guidance, Navigation and Control Conference and Exhibit, 2007: 1–17.
4	WANG C, GUO J X, SHEN Z P Prediction of 4D trajectory based on basic flight models. Journal of Southwest Jiaotong University, 2009, 44 (2): 295- 300.
5	ZHANG M J, SHAO P N, YU M H Pattern-based moving target trajectory prediction in hyperspace. Computer System & Applications, 2018, 27 (1): 113- 119.
6	QIAO S J, HAN N, ZHU X W, et al A dynamic trajectory prediction algorithm based on Kalman filter. Acta Electronica Sinica, 2018, 46 (2): 418- 423.
7	IOANNIS L, JOHN L. Adaptive aircraft trajectory prediction using particle filters. Proc. of the AIAA Guidance, Navigation and Control Conference and Exhibit, 2008. DOI: 10.2514/6.2008-7387.
8	XIE L, ZHANG J F, SUI D Aircraft trajectory prediction based on interacting multiple model filtering algorithm. Aeronautical Computing Technique, 2012, 42 (5): 68- 71.
9	YAN H W, ZOU D Short-term wind speed forecasting based on PSO-Elman optimized by association rule. Computer Engineering and Applications, 2017, 53 (23): 261- 266.
10	QIAN K, ZHOU Y, YANG L J, et al Aircraft target track prediction model based on BP neural network. Command Information System and Technology, 2017, 8 (3): 54- 58.
11	TAN W, LU B C, HUANG M L Track prediction based on neural networks and genetic algorithm. Journal of Chongqing Jiaotong University, 2010, 29 (1): 147- 150.
12	GAN X S, DUANMU J S, MENG Y B, et al Aerodynamic modeling from flight data based on WNN optimized by particle swarm. Acta Aeronautica et Astronautica Sinica, 2012, 33 (7): 1209- 1217.
13	YANG R N, ZHANG Z X, ZHANG Y, et al Prediction of aircraft flight performance model based on NARX neural network. Journal of Northwest University, 2017, 47 (1): 7- 12.
14	FAN G F, PENG L L, HONG W C Short term load forecasting based on phase space reconstruction algorithm and bi-square kernel regression model. Applied Energy, 2018, 224, 13- 33. doi: 10.1016/j.apenergy.2018.04.075
15	WANG H Z, WANG G B, LI G Q, et al Deep belief network based deterministic and probabilistic wind speed forecasting approach. Applied Energy, 2016, 182, 80- 93. doi: 10.1016/j.apenergy.2016.08.108
16	KIM H S, EYKHOLT R, SALAS J D Nonlinear dynamics, delay times, and embedding windows. Physica D: Nonlinear Phenomena, 1999, 127 (1/2): 48- 60.
17	KIM H S, KANG D S, KIM J H The BDS statistic and residual test. Stochastic Environmental Research & Risk Assessment, 2003, 17 (1/2): 104- 115. doi: 10.1007/s00477-002-0118-0
18	YAN Z, JIAN Y, CAI Y J. Initializing k-means clustering using affinity propagation. Proc. of the International Conference on Hybrid Intelligent Systems, 2009, 1: 338–343.
19	HUA X, HU X, YUAN W W Research optimization on logistics distribution center location based on adaptive particle swarm algorithm. Optik, 2016, 127 (20): 8443- 8450. doi: 10.1016/j.ijleo.2016.06.032
20	GAO W F, LIU S Y, HUANG L L Particle swarm optimization with chaotic opposition-based population initialization and stochastic search technique. Communications in Nonlinear Science & Numerical Simulation, 2012, 17 (11): 4316- 4327.
21	TURGUT O E, TURGUT M S, COBAN M T Chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations. Computers & Mathematics with Applications, 2014, 68 (4): 508- 530.
22	LI P, XU D, ZHOU Z Y, et al Stochastic optimal operation of microgrid based on chaotic binary particle swarm optimization. IEEE Trans. on Smart Grid, 2016, 7 (1): 66- 73. doi: 10.1109/TSG.2015.2431072
23	CUANG L Y, YANG C S, WU K C, et al Gene selection and classification using Taguchi chaotic binary particle swarm optimization. Expert Systems with Application, 2011, 38 (10): 13367- 13377. doi: 10.1016/j.eswa.2011.04.165
24	HUANG G B, SIEW C K Extreme learning machine with randomly assigned RBF kernels. International Journal of Information Technology, 2005, 11 (1): 16- 24.
25	XU L, KRZYZAK A, OJA E Rival penalized competitive learning for clustering analysis, RBF net, and curve detection. IEEE Trans. on Neural Networks, 1993, 4 (4): 636- 649. doi: 10.1109/72.238318
26	SUN Y X, XIA H W Rival penalized competitive learning-based neural network model for wind power forecasting. Journal of Beijing University of Technology, 2016, 42 (5): 674- 678.
27	WANG J S, GAO Z W Network traffic modeling and prediction based on RBF neural network. Computer Engineering and Applications, 2008, 44 (13): 6- 11.
28	NOMAN S, SHAMSUDDIN S M, HASSANIEN A E. Hybrid learning enhancement of RBF network with particle swarm optimization. Foundations of Computational Intelligence, Volume 1: Learning and Approximation, 2009, 201: 381–397.
29	HU Y M, LI D C, HE Y Q, et al Q-learning algorithm based on incremental RBF network. Robot, 2019, 41 (5): 562- 573.
30	WOLPERT D H, MACREADY W G No free lunch theorems for optimization. IEEE Trans. on Evolutionary Computation, 1997, 1 (1): 67- 82. doi: 10.1109/4235.585893

Algorithm	Parameter
PSO	$\begin{array}{l} {\rm{Population}} \;{\rm{size}} = 50, \\ \omega {\rm{ = }}0.8, {c_1} = {c_2} = 2 \end{array} $
IPSO	$\begin{array}{l} {\rm{Population}} \;{\rm{size}} = 50, {H_0} = 1.5 \\ thr{e_{\rm{p}}}{\rm{ = }}4 , thr{e_{\rm{g}}}{\rm{ = }}5 , {t_{\max }}{\rm{ = }}100, \\ threshol{d_\sigma }{\rm{ = }}0.1, {c_1} = {c_2} = 2.5 \end{array} $

Coordinate	Algorithm	MAE	NMSE	Perr	Cor	Time
X	Hybrid algorithm	16.0787	0.0020	9.8677×10^?5	0.9987	14.350948
	k-means-RBF	54.2051	0.0237	0.0011	0.9923	2.393672
	KRLS-RBF	36.6747	0.0110	5.2293×10^?4	0.9967	8.118918
	PSO-RBF	22.5727	0.0044	2.1902×10^?4	0.9980	2.157142
	BP	28.2177	0.0053	2.5598×10^?4	0.9987	4.232382
	RBF	84.2022	0.0519	0.0024	0.9972	5.316289
Y	Hybrid algorithm	29.5963	0.0017	5.9124×10^?5	0.9988	7.500620
	k-means-RBF	50.3425	0.0059	2.0235×10^?4	0.9967	1.9489286
	KRLS-RBF	38.0530	0.0033	1.1197×10^?4	0.9980	9.833438
	PSO-RBF	35.6712	0.0029	1.0072×10^?4	0.9979	2.279306
	BP	59.2305	0.0071	2.4251×10^?4	0.9979	4.901085
	RBF	49.7448	0.0053	1.8278×10^?4	0.9971	5.310010
Z	Hybrid algorithm	2.6647	0.0169	5.6031×10^?7	0.9926	7.971086
	k-means-RBF	5.4294	0.0977	3.2308×10^?6	0.9517	2.292306
	KRLS-RBF	3.9263	0.0344	1.1381×10^?6	0.9830	8.561687
	PSO-RBF	23.8547	1.0174	3.3684×10^?5	0.1953	2.328323
	BP	8.4035	0.1028	3.4118×10^?6	0.9849	4.102884
	RBF	10.2155	0.1689	5.5776×10^?6	0.9439	9.192351

Coordinate	Algorithm	MAE	NMSE	Perr	Cor	Time
X	Hybrid algorithm	40.2672	0.0144	7.1105×10^?4	0.9933	29.616218
	k-means-RBF	136.1964	0.1450	0.0081	0.9968	17.959766
	KRLS-RBF	170.9212	0.2210	0.0093	0.9957	25.521019
	PSO-RBF	23.0470	0.0041	2.0694×10^?4	0.9988	13.886920
	BP	106.2750	0.0797	0.0035	0.9923	26.891305
	RBF	123.7173	0.1101	0.0050	0.9743	12.254671
Y	Hybrid algorithm	47.1890	0.0041	1.4496×10^?4	0.9988	29.616218
	k-means-RBF	89.4069	0.0139	4.6373×10^?4	0.9987	17.959766
	KRLS-RBF	69.8827	0.0120	4.0600×10^?4	0.9987	25.521019
	PSO-RBF	79.8018	0.0141	5.0993×10^?4	0.9989	13.886920
	BP	170.0623	0.0651	0.0024	0.9920	26.891305
	RBF	330.4476	0.1861	0.0056	0.9918	12.254671
Z	Hybrid algorithm	12.1015	0.2226	7.3642×10^?6	0.9515	29.616218
	k-means-RBF	36.8691	2.8773	9.4013×10^?5	0.0574	17.959766
	KRLS-RBF	18.6878	0.7032	2.3306×10^?5	0.6510	25.521019
	PSO-RBF	58.3648	5.3875	1.7416×10^?4	0.1688	13.886920
	BP	5.1186	0.0529	1.7464×10^?6	0.9933	26.891305
	RBF	36.7159	2.1721	7.082×10^?5	0.8511	12.254671

[1]	Fan WANG, Pengfei FAN, Yonghua FAN, Bin XU, Jie YAN. Robust adaptive control of hypersonic vehicle considering inlet unstart [J]. Journal of Systems Engineering and Electronics, 2022, 33(1): 188-196.
[2]	Fan LI, Jiajun XIONG, Xuhui LAN, Hongkui BI, Xin CHEN. NSHV trajectory prediction algorithm based on aerodynamic acceleration EMD decomposition [J]. Journal of Systems Engineering and Electronics, 2021, 32(1): 103-117.
[3]	Mengfan XUE, NLei HA, Dongliang PENG. A combined algorithm of K-means and MTRL for multi-class classification [J]. Journal of Systems Engineering and Electronics, 2019, 30(5): 875-885.
[4]	Yang LI, Mingyong LIU, Xiaojian ZHANG, Xingguang PENG. Global approximation based adaptive RBF neural network control for supercavitating vehicles [J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 797-804.
[5]	Jing Yang and Jun Wang. Tag clustering algorithm LMMSK: improved K-means algorithm based on latent semantic analysis [J]. Systems Engineering and Electronics, 2017, 28(2): 374-384.
[6]	Ling Wang?, Dongmei Fu, Qing Li, and Zhichun Mu. Modelling method with missing values based on clustering and support vector regression [J]. Journal of Systems Engineering and Electronics, 2010, 21(1): 142-147.
[7]	Yi Qingming. Blind source separation by weighted K-means clustering [J]. Journal of Systems Engineering and Electronics, 2008, 19(5): 882-887.

Target maneuver trajectory prediction based on RBF neural network optimized by hybrid algorithm

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 26

References 30

Related Articles 7

Recommended Articles

Metrics

Comments