Electronics and Electrical Engineering and Control

Target maneuver trajectory prediction based on Volterra series identified by improved particle swarm algorithm

  • XI Zhifei ,
  • XU An ,
  • KOU Yingxin ,
  • LI Zhanwu ,
  • YANG Aiwu
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  • Aeronautics Engineering College, Air Force Engineering University, Xi'an 710038

Received date: 2019-05-05

  Revised date: 2020-05-21

  Online published: 2020-07-17

Supported by

Air Force Engineering University President Fund (XZJK2019040)

Abstract

Target maneuver trajectory prediction plays an important role in air combat situation awareness and target threat assessment. Aiming at the problems of high complexity and low prediction accuracy in the traditional method, this paper proposes a target maneuvering trajectory prediction model based on the phase space reconstruction theory and Volterra functional series, combining the chaotic characteristics of the target maneuvering trajectory time series. The 0-1 test method is firstly used to verify the chaotic characteristics of the target maneuvering trajectory time series, followed by determination of the embedding dimension and time delay by the C-C method. The target maneuvering trajectory time series is further reconstructed. The Volterra functional series prediction model is introduced. However, the identification of higher-order Volterra kernel function is difficult. To solve this problem, we propose a Modified Particle Swarm Optimization algorithm (MPSO) combining the chaotic strategy and adaptive strategy, construct a Volterra series prediction model identified by the MPSO, and apply the model to target maneuvering trajectory prediction. Finally, the algorithm proposed in this paper is compared with the Kalman filter and machine learning algorithm for single-step and multi-step prediction. Meanwhile, the performance of MPSO is compared with that of other intelligent algorithms. The simulation results show good performance of the proposed prediction model in both single-step and multi-step prediction, and fast, accurate identification of the Volterra series model parameters by the MPSO.

Cite this article

XI Zhifei , XU An , KOU Yingxin , LI Zhanwu , YANG Aiwu . Target maneuver trajectory prediction based on Volterra series identified by improved particle swarm algorithm[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020 , 41(12) : 324183 -324183 . DOI: 10.7527/S1000-6893.2020.24183

References

[1] 寇英信, 李战武, 陈哨东, 等. 火控系统在航空作战中的作用——作战飞机之"魂"[J]. 电光与控制, 2013, 20(12):1-5. KOU Y X, LI Z W, CHEN S D, et al. The important role of fire control system in air combat——Soul of fighters[J]. Electronics Optics & Control, 2013, 20(12):1-5(in Chinese).
[2] 姜佰辰, 关键, 周伟, 等. 基于多项式卡尔曼滤波的船舶轨迹预测算法[J]. 信号处理, 2019, 35(5):741-746. JIANG B C, GUAN J, ZHOU W, et al. Vessel trajectory prediction algorithm based on polynomial fitting Kalman filtering[J]. Journal of Signal Processing, 2019, 35(5):741-746(in Chinese).
[3] 赵帅兵, 唐诚, 梁山, 等. 基于改进卡尔曼滤波的控制河段船舶航迹预测[J]. 计算机应用, 2012, 32(11):3247-3250. ZHAO S B, TANG C, LIANG S, et al. Track prediction of vessel in controlled waterway based on improved Kalman filter[J]. Journal of Computer Applications, 2012, 32(11):3247-3250(in Chinese).
[4] 乔少杰, 韩楠, 朱新文, 等. 基于卡尔曼滤波的动态轨迹预测算法[J]. 电子学报, 2018, 46(2):418-423. QIAO S J, HAN N, ZHU X W, et al. A dynamic trajectory prediction algorithm based on Kalman filter[J]. Acta Electronica Sinica, 2018, 46(2):418-423(in Chinese).
[5] 翟岱亮, 雷虎民, 李炯, 等. 基于自适应IMM的高超声速飞行器轨迹预测[J]. 航空学报, 2016, 37(11):3466-3475. ZHAI D L, LEI H M, LI J, et al. Trajectory prediction of hypersonic vehicle based on adaptive IMM[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(11):3466-3475(in Chinese).
[6] 杨彬, 贺正洪. 一种GRNN神经网络的高超声速飞行器轨迹预测方法[J]. 计算机应用与软件, 2015, 32(7):239-243. YANG B, HE Z H. Hypersonic vehicle track prediction based on GRNN[J]. Computer Applications and Software, 2015, 32(7):239-243(in Chinese).
[7] 谭伟, 陆百川, 黄美灵. 神经网络结合遗传算法用于航迹预测[J]. 重庆交通大学学报, 2010, 291(1):147-150. TAN W, LU B C, HUANG M L. Track prediction based on neural networks and genetic algorithm[J]. Journal of Chongqing Jiaotong University, 2010, 291(1):147-150(in Chinese).
[8] 甘旭升, 端木京顺, 孟月波, 等. 基于粒子群优化的WNN飞行数据气动力建模[J]. 航空学报, 2012, 33(7):1209-1217. GAN X S, DUANMU J S, MENG Y B, et al. Aerodynamic modeling from flight data based on WNN optimized by particle swarm[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(7):1209-1217(in Chinese).
[9] SLATTERY R, ZHAO Y. Trajectory synthesis for air traffic automation[J]. Journal of Guidance, Control and Dynamic, 1997, 20:232-238.
[10] 张雪清, 梁军. 风电功率时间序列混沌特性分析及预测模型研究[J]. 物理学报, 2012, 61(19):70-81. ZHANG X Q, LIANG J. Chaotic characteristics analysis and prediction model study on wind power time series[J]. Acta Physica Sinica, 2012, 61(19):70-81(in Chinese)
[11] CHATTERJEE A. Parameter estimation of Duffing oscillator using Volterra series and multi-tone excitation[J]. Neural Networks, 2009, 22(1):343-347.
[12] 张家良, 曹建福, 高峰. 大型装备传动系统非线性频谱特征提取与故障诊断[J]. 控制与决策, 2012, 27(1):135-138. ZHANG J L, CAO J F, GAO F. Feature extraction and fault diagnosis of large-scale equipment transmission system based on nonlinear frequency spectrum[J]. Control and Decision, 2012, 27(1):135-138(in Chinese).
[13] 孔祥玉, 韩崇昭, 马红光, 等. 一种总体最小二乘算法及在Volterra滤波器中的应用[J]. 西安交通大学学报, 2004, 38(4):339-342. KONG X Y, HAN C Z, MA H G, et al. Total least square algorithm and its application to Volterra filter[J]. Journal of Xi'an Jiao Tong University, 2004, 38(4):339-342.
[14] 唐浩, 屈梁生, 温广瑞. 基于Volterra级数的转子故障诊断研究[J]. 中国机械工程, 2009, 20(4):447-454. TANG H, QU L S, WEN G R. Fault diagnosis for rotor system based on volterra series[J]. China Mechanical Engineering, 2009, 20(4):447-454(in Chinese).
[15] ABBAS H M, BAYOUMI M M. Volterra system identification using adaptive genetic algorithms[J]. Applied Soft Computing, 2004(5):75-86
[16] 李志农, 唐高松, 肖尧先, 等. 基于自适应蚁群优化的Volterra核辨识算法研究[J]. 振动与冲击, 2011, 30(10):35-38. LI Z N, TANG G S, XIAO Y X, et al. Volterra series identification method based on adaptive ant colony optimizations[J]. Journal of Vibration and Hock, 2011, 30(10):35-38(in Chinese).
[17] 李志农, 蒋静, 陈金刚, 等. 基于量子粒子群优化的Volterra核辨识算法研究[J]. 振动与冲击, 2013, 32(3):60-63. LI Z N, JIANG J, CHEN J G, et al. Volterra series identification method based on quantum particle swarm optimization[J]. Journal of Vibration and Hock, 2013, 32(3):60-63(in Chinese).
[18] 李志农, 蒋静, 冯辅周, 等. 基于量子粒子群优化Volterra时域核辨识的隐Markov模型识别方法[J]. 仪器仪表学报, 2011, 32(12):2693-2698. LI Z N, JIANG J, FENG F Z, et al. Hidden Markov model recognition method based on Volterra kernel identified with particle swarm optimization[J]. Chinese Journal of Scientific Instrument, 2011, 32(12):2693-2698(in Chinese).
[19] EBERHART R, KENNEDY J. A new optimizer using particle swarm theory[C]//Proceedings of the Sixth International Symposium on Micro Machine and Human Science. Piscataway:IEEE Press, 1995:39-43.
[20] KENNEDY J, EBERHART R. Particle swarm optimization[C]//International Conference on Neural Networks. Piscataway:IEEE Press, 1995:1942-1948.
[21] 毛鹏轩, 肖扬. 粒子群算法在稳定时滞系统设计中的应用[J]. 计算机应用研究, 2012, 29(1):214-216. MAO P X, XIAO Y. Application of PSO algorithm for stable time-delay system design[J]. Application Research of Computers, 2012, 29(1):214-216(in Chinese).
[22] 崔志华, 曾建潮. 微粒群优化算法[M]. 北京:科学出版社, 2011:85-86. CUI Z H, ZENG J C. Particle swarm optimization[M]. Beijing:Science Press, 2011:85-86(in Chinese).
[23] 商云龙, 张奇, 崔纳新, 等. 基于AIC准则的锂离子电池变阶RC等效电路模型研究[J]. 电工技术学报, 2015, 30(17):55-62. SHANG Y L, ZHANG Q, CUI N X, et al. Research on variable-order RC equivalent circuit model for lithium-ion battery based on the AIC criterion[J]. Transactions of China Electrotechnical Society, 2015, 30(17):55-62(in Chinese).
[24] SAVI M A, PEREIRA-PINTO F H I, VIOLA F M, et al. Using 0-1 test to diagnose chaos on shape memory alloy dynamical systems[J]. Chaos Solitons & Fractals, 2017, 103:307-324
[25] ARMAND E F J S, BODO B, SABAT S L, et al. A modified 0-1 test for chaos detection in oversampled time series observations[J]. International Journal of Bifurcation and Chaos, 2014, 24(5):1450063.
[26] TAKENS F. Determing strang attractors in turbulence[J]. Lecture Notes in Math, 1981, 898:361-381.
[27] SONG J, MENG D, WANG Y. Analysis of chaotic behavior based on phase space reconstruction methods[C]//Proceedings of the IEEE 6th International Symposium on Computational Intelligence and Design. Piscataway:IEEE Press, 2014:414-417
[28] 陆振波, 蔡志明, 姜可宇. 基于改进的C-C方法的相空间重构参数选择[J]. 系统仿真学报, 2007, 19(11):2527-2529. LU Z B, CAI Z M, JIANG K Y. Determination of embedding parameters for phase space reconstruction based on improved C-C methods[J]. Journal of System Simulation, 2007, 19(11):2527-2529(in Chinese).
[29] CUI Z H, CAI X J, ZENG J C, et al. Particle swarm optimization with FUSS and RWS for high dimensional functions[J]. Applied Mathematics and Computation, 2008, 205(1):98-108.
[30] HARISH G. A hybrid PSO-GA algorithm for constrained optimization problems[J]. Applied Mathematics and Computation, 2016, 274:292-395.
[31] 张浩, 张铁男, 沈继红, 等. Tent混沌粒子群算法及其在结构优化决策中的应用[J]. 控制与决策, 2008, 23(8):857-862. ZHANG H, ZHANG T N, SHEN J H, et al. Research on decision-makings of structure optimization based on improved Tent PSO[J]. Control and Decision, 2008, 23(8):857-862(in Chinese).
[32] 魏玉琴, 戴永寿, 张亚南, 等. 基于Tent映射的自适应混沌嵌人式粒子群算法[J]. 计算机工程与应用, 2013, 49(10):45-49. WEI Y Q, DAI Y S, ZHANG Y N, et al. Adaptive chaotic embedded particle swarm optimization algorithm based on Tent mapping[J]. Computer Engineering and Applications, 2013, 49(10):45-49(in Chinese).
[33] NOMAN S, SHAMSUDDIN S, HASSANIEN A. Hybrid learning enhancement of RBF network with particle swarm optimization[J]. Foundations of Computational, Intelligence, 2009, 1:381-397.
[34] 甘慧萍. 基于IGA的Volterra核辨识及机械振动信号消噪方法研究[D]. 兰州:兰州交通大学, 2015. GAN H P. Research of Volterra kernel identification method based on IGA and its application in cancellation of mechanical vibration signal noise[D]. Lanzhou:Lanzhou Jiaotong University, 2015(in Chinese).
[35] 唐高松. 基于Volterra级数模型辨识的旋转机械故障诊断方法研究[D]. 郑州:郑州大学, 2010. TANG G S. Rotating machine fault diagnosis method based on Volterra series identification[D]. Zhengzhou:Zhengzhou University, 2010(in Chinese).
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