ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2023, Vol. 44 ›› Issue (9): 327413-327413.doi: 10.7527/S1000-6893.2022.27413
• Electronics and Electrical Engineering and Control • Previous Articles Next Articles
Baichuan ZHANG, Wenhao BI(), An ZHANG, Zeming MAO, Mi YANG
Received:
2022-05-10
Revised:
2022-05-22
Accepted:
2022-06-10
Online:
2022-06-20
Published:
2022-06-17
Contact:
Wenhao BI
E-mail:biwenhao@nwpu.edu.cn
Supported by:
CLC Number:
Baichuan ZHANG, Wenhao BI, An ZHANG, Zeming MAO, Mi YANG. Transformer-based error compensation method for air combat aircraft trajectory prediction[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(9): 327413-327413.
Table 2
Overall evaluation of performance of Transformer-based prediction error compensation method
数据集 编号 | 预测步长 /ms | 轨迹预 测算法 | 基准预测值 | 误差补偿后结果 | 预测精度 提升/% | 运行时间增加/ms | |||
---|---|---|---|---|---|---|---|---|---|
平均绝对误差 /m | 平均运行时间 /ms | 平均绝对误差 /m | 平均运行时间 /ms | ||||||
Ⅰ | 1 000 | CAPM | 1.420 6 | 0.012 6 | 1.178 7 | 8.857 2 | 17.026 4 | 8.844 6 | |
KFTP | 4.536 2 | 0.042 4 | 3.506 6 | 8.183 5 | 22.697 4 | 8.141 1 | |||
PBTT-LSTM | 3.309 7 | 1.447 9 | 2.022 0 | 10.407 4 | 38.906 8 | 8.959 5 | |||
OIF-Elman | 4.121 0 | 0.818 7 | 3.129 9 | 9.594 9 | 25.690 9 | 8.776 2 | |||
2 000 | CAPM | 6.005 6 | 0.011 9 | 5.709 9 | 9.066 1 | 4.923 7 | 9.054 2 | ||
KFTP | 9.007 0 | 0.039 4 | 6.744 1 | 8.116 9 | 26.123 8 | 8.077 5 | |||
PBTT -LSTM | 9.893 7 | 1.396 8 | 7.307 9 | 10.022 8 | 26.135 8 | 8.626 0 | |||
OIF-Elman | 8.514 0 | 0.812 4 | 7.880 1 | 9.637 8 | 7.445 4 | 8.825 4 | |||
3 000 | CAPM | 14.984 4 | 0.011 0 | 13.190 1 | 8.921 6 | 11.974 5 | 8.910 6 | ||
KFTP | 12.732 7 | 0.044 9 | 9.243 6 | 8.030 9 | 27.402 6 | 7.986 0 | |||
PBTT -LSTM | 13.085 5 | 1.399 3 | 9.410 9 | 10.075 9 | 28.081 5 | 8.676 6 | |||
OIF-Elman | 12.104 2 | 0.846 5 | 11.346 8 | 9.952 4 | 6.257 3 | 9.105 9 | |||
4 000 | CAPM | 27.801 1 | 0.011 3 | 21.125 6 | 8.779 9 | 24.011 6 | 8.768 6 | ||
KFTP | 15.292 0 | 0.051 8 | 10.222 7 | 8.311 7 | 33.150 0 | 8.259 9 | |||
PBTT -LSTM | 14.943 1 | 1.408 7 | 10.136 0 | 10.098 3 | 32.169 4 | 8.689 6 | |||
OIF-Elman | 20.998 8 | 0.847 1 | 19.235 1 | 9.927 9 | 8.399 1 | 9.080 8 | |||
5 000 | CAPM | 44.099 6 | 0.014 4 | 27.955 4 | 8.746 2 | 36.608 0 | 8.731 8 | ||
KFTP | 17.023 9 | 0.039 8 | 10.935 1 | 8.405 5 | 35.766 2 | 8.365 7 | |||
PBTT -LSTM | 16.161 9 | 1.397 0 | 10.973 9 | 10.116 4 | 32.100 2 | 8.719 4 | |||
OIF-Elman | 21.848 8 | 0.848 1 | 18.748 4 | 9.808 4 | 14.190 3 | 8.960 3 | |||
Ⅱ | 1 000 | CAPM | 3.401 2 | 0.059 9 | 3.230 8 | 8.798 1 | 5.009 9 | 8.738 2 | |
KFTP | 2.855 2 | 0.041 7 | 2.594 9 | 8.930 1 | 9.116 7 | 8.888 4 | |||
PBTT -LSTM | 3.830 4 | 1.466 1 | 3.173 2 | 11.185 9 | 17.157 5 | 9.719 8 | |||
OIF-Elman | 3.750 0 | 0.821 3 | 2.746 1 | 8.904 7 | 26.770 7 | 8.083 4 | |||
2 000 | CAPM | 18.993 5 | 0.074 1 | 16.779 7 | 9.651 7 | 11.655 6 | 9.577 6 | ||
KFTP | 12.918 2 | 0.040 7 | 10.378 8 | 8.910 3 | 19.657 5 | 8.869 6 | |||
PBTT -LSTM | 14.709 6 | 1.537 8 | 12.700 8 | 10.176 1 | 13.654 6 | 8.638 3 | |||
OIF-Elman | 18.842 3 | 0.824 4 | 16.501 1 | 8.983 2 | 12.425 2 | 8.158 8 | |||
3 000 | CAPM | 53.831 9 | 0.061 5 | 43.501 6 | 9.723 3 | 19.189 9 | 9.661 8 | ||
KFTP | 49.523 3 | 0.056 8 | 38.275 4 | 9.249 7 | 22.712 3 | 9.192 9 | |||
PBTT -LSTM | 48.170 4 | 1.578 9 | 31.658 6 | 10.341 4 | 34.277 9 | 8.762 5 | |||
OIF-Elman | 50.093 2 | 0.824 9 | 43.568 5 | 8.837 9 | 13.025 1 | 8.013 0 |
数据集 编号 | 预测步长 /ms | 轨迹预 测算法 | 基准预测值 | 误差补偿后结果 | 预测精度 提升/% | 运行时间增加/ms | |||
---|---|---|---|---|---|---|---|---|---|
平均绝对误差 /m | 平均运行时间 /ms | 平均绝对误差 /m | 平均运行时间 /ms | ||||||
4 000 | CAPM | 112.764 1 | 0.072 9 | 85.975 7 | 9.724 7 | 23.756 1 | 9.651 8 | ||
KFTP | 106.332 9 | 0.051 4 | 68.892 8 | 9.241 0 | 35.210 3 | 9.189 6 | |||
PBTT-LSTM | 97.392 9 | 1.538 0 | 62.933 5 | 10.158 9 | 35.381 8 | 8.620 9 | |||
OIF-Elman | 94.344 9 | 0.812 6 | 79.078 3 | 8.861 4 | 16.185 6 | 8.048 8 | |||
5 000 | CAPM | 200.407 3 | 0.058 6 | 114.223 7 | 8.513 1 | 43.004 2 | 8.454 5 | ||
KFTP | 172.614 5 | 0.053 0 | 129.040 0 | 9.144 6 | 25.248 3 | 9.091 6 | |||
PBTT -LSTM | 159.042 8 | 1.525 8 | 104.025 8 | 10.174 2 | 33.335 1 | 8.648 4 | |||
OIF-Elman | 188.424 1 | 0.742 4 | 101.633 9 | 8.439 5 | 46.061 1 | 7.697 1 |
Table 3
Comparison of performance of error compensation methods
数据集 编号 | 预测步长 /ms | 基准预测值 | 误差补偿方法 | 误差补偿后结果 | 预测精度 提升/% | 运行时间增加/ms | ||
---|---|---|---|---|---|---|---|---|
平均绝对误差 /m | 平均运行时间 /ms | 平均绝对误差 /m | 平均运行时间 /ms | |||||
Ⅰ | 1 000 | 1.420 6 | 0.012 6 | BPNN | 1.179 2 | 4.384 7 | 16.992 8 | 4.372 1 |
GRU | 1.221 1 | 6.002 6 | 14.043 4 | 5.990 0 | ||||
TFPEC | 1.178 7 | 8.857 2 | 17.026 4 | 8.844 6 | ||||
2 000 | 6.005 6 | 0.011 9 | BPNN | 5.610 8 | 4.876 6 | 6.573 9 | 4.864 7 | |
GRU | 5.287 3 | 6.004 4 | 11.960 5 | 5.992 5 | ||||
TFPEC | 5.709 9 | 9.066 1 | 4.923 7 | 9.054 2 | ||||
3 000 | 14.984 4 | 0.011 0 | BPNN | 13.814 5 | 4.847 5 | 7.807 5 | 4.836 5 | |
GRU | 13.159 3 | 5.987 9 | 12.180 0 | 5.976 9 | ||||
TFPEC | 13.190 1 | 8.921 6 | 11.974 5 | 8.910 6 | ||||
4 000 | 27.801 1 | 0.011 3 | BPNN | 23.780 1 | 4.858 8 | 14.463 5 | 4.847 5 | |
GRU | 24.603 2 | 5.797 3 | 11.502 8 | 5.786 0 | ||||
TFPEC | 21.125 6 | 8.779 9 | 24.011 6 | 8.768 6 | ||||
5 000 | 44.099 6 | 0.014 4 | BPNN | 35.348 0 | 5.019 9 | 19.845 1 | 5.005 5 | |
GRU | 40.299 7 | 5.864 4 | 8.616 6 | 5.850 0 | ||||
TFPEC | 27.955 4 | 8.746 2 | 36.608 0 | 8.737 8 | ||||
Ⅱ | 1 000 | 3.401 2 | 0.059 9 | BPNN | 3.325 5 | 4.843 9 | 2.225 7 | 4.784 0 |
GRU | 3.273 8 | 6.023 1 | 3.745 7 | 5.963 2 | ||||
TFPEC | 3.230 8 | 8.798 1 | 5.009 9 | 8.738 2 | ||||
2 000 | 18.993 5 | 0.074 1 | BPNN | 17.333 2 | 4.671 2 | 8.741 4 | 4.597 1 | |
GRU | 17.243 5 | 6.138 0 | 9.213 7 | 6.063 9 | ||||
TFPEC | 16.779 7 | 9.651 7 | 11.655 6 | 9.577 6 | ||||
3 000 | 53.831 9 | 0.061 5 | BPNN | 46.001 3 | 4.807 6 | 14.546 4 | 4.746 1 | |
GRU | 45.081 3 | 5.908 4 | 16.255 4 | 5.846 9 | ||||
TFPEC | 43.501 6 | 9.723 3 | 19.189 9 | 9.661 8 | ||||
4 000 | 112.764 1 | 0.072 9 | BPNN | 92.779 2 | 4.791 8 | 17.722 8 | 4.718 9 | |
GRU | 88.630 9 | 5.829 4 | 21.401 5 | 5.756 5 | ||||
TFPEC | 85.975 7 | 9.724 7 | 23.756 1 | 9.651 8 | ||||
5 000 | 200.407 3 | 0.058 6 | BPNN | 179.852 2 | 4.127 1 | 10.256 7 | 4.068 5 | |
GRU | 159.692 6 | 5.983 4 | 20.315 9 | 5.924 8 | ||||
TFPEC | 114.223 7 | 8.513 1 | 43.004 2 | 8.454 5 |
1 | 张昊, 金琳乘, 王胜男. 基于OODA环的对地攻击流程半实物仿真验证方法[J]. 航空学报, 2021, 42(8): 525788. |
ZHANG H, JIN L C, WANG S N. Semi-physical simulation verification method of air-to-ground attacking process with OODA loop[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(8): 525788 (in Chinese). | |
2 | 蒲志强, 易建强, 刘振, 等. 知识和数据协同驱动的群体智能决策方法研究综述[J]. 自动化学报, 2022, 48(3): 627-643. |
PU Z Q, YI J Q, LIU Z, et al. Knowledge-based and data-driven integrating methodologies for collective intelligence decision making: A survey[J]. Acta Automatica Sinica, 2022, 48(3): 627-643 (in Chinese). | |
3 | 奚之飞, 徐安, 寇英信, 等. 基于改进粒子群算法辨识Volterra级数的目标机动轨迹预测[J]. 航空学报, 2020, 41(12): 324183. |
XI Z F, XU A, KOU Y X, et al. Target maneuver trajectory prediction based on Volterra series identified by improved particle swarm algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(12): 324183 (in Chinese). | |
4 | 张博伦, 周荻, 吴世凯. 临近空间高超声速飞行器机动模型及弹道预测[J]. 系统工程与电子技术, 2019, 41(9): 2072-2079. |
ZHANG B L, ZHOU D, WU S K. Maneuver model and trajectory prediction of near space hypersonic aircraft[J]. Systems Engineering and Electronics, 2019, 41(9): 2072-2079 (in Chinese). | |
5 | BARRATT S T, KOCHENDERFER M J, BOYD S P. Learning probabilistic trajectory models of aircraft in terminal airspace from position data[J]. IEEE Transactions on Intelligent Transportation Systems, 2019, 20(9): 3536-3545. |
6 | WIEST J, HÖFFKEN M, KREßEL U, et al. Probabilistic trajectory prediction with Gaussian mixture models[C]∥ 2012 IEEE Intelligent Vehicles Symposium. Piscataway: IEEE Press, 2012: 141-146. |
7 | 郑天宇, 姚郁, 贺风华. 基于可学习EKF的高超声速飞行器航迹估计[J]. 哈尔滨工业大学学报, 2020, 52(6): 160-170. |
ZHENG T Y, YAO Y, HE F H. Trajectory estimation of a hypersonic flight vehicle via L-EKF[J]. Journal of Harbin Institute of Technology, 2020, 52(6): 160-170 (in Chinese). | |
8 | LI M, LU F, ZHANG H, et al. Predicting future locations of moving objects with deep fuzzy-LSTM networks[J]. Transportmetrica A Transport Science, 2020, 16(1): 119-136. |
9 | ZYNER A, WORRALL S, NEBOT E. Naturalistic driver intention and path prediction using recurrent neural networks[J]. IEEE Transactions on Intelligent Transportation Systems, 2019, 21(4): 1584-1594. |
10 | 张宏鹏, 黄长强, 唐上钦, 等. 基于卷积神经网络的无人作战飞机飞行轨迹实时预测[J]. 兵工学报, 2020, 41(9): 1894-1903. |
ZHANG H P, HUANG C Q, TANG S Q, et al. CNN-based real-time prediction method of flight trajectory of unmanned combat aerial vehicle[J]. Acta Armamentarii, 2020, 41(9): 1894-1903 (in Chinese). | |
11 | MA Z M, YAO M F, HONG T, et al. Aircraft surface trajectory prediction method based on LSTM with attenuated memory window[J]. Journal of Physics: Conference Series, 2019, 1215(1): 012003. |
12 | 王德运, 陈奕青, 耿亮. 基于模态分解与误差修正策略的原油价格组合预测研究[J]. 南昌工程学院学报, 2022, 41(1): 22-31. |
WANG D Y, CHEN Y Q, GENG L. A novel hybrid model based on mode decomposition and error compensation strategy for crude oil price forecasting[J]. Journal of Nanchang Institute of Technology, 2022, 41(1): 22-31 (in Chinese). | |
13 | 王增平, 赵兵, 贾欣, 等. 基于差分分解和误差补偿的短期电力负荷预测方法[J]. 电网技术, 2021, 45(7): 2560-2568. |
WANG Z P, ZHAO B, JIA X, et al. Short-term power load forecasting method based on difference decomposition and error compensation[J]. Power System Technology, 2021, 45(7): 2560-2568 (in Chinese). | |
14 | LIU H, TIAN H Q, LI Y F. Four wind speed multi-step forecasting models using extreme learning machines and signal decomposing algorithms[J]. Energy Conversion and Management, 2015, 100: 16-22. |
15 | 刘帅, 朱永利, 张科, 等. 基于误差修正ARMA-GARCH模型的短期风电功率预测[J]. 太阳能学报, 2020, 41(10): 268-275. |
LIU S, ZHU Y L, ZHANG K, et al. Short-term wind power forecasting based on error correction ARMA-GARCH model[J]. Acta Energiae Solaris Sinica, 2020, 41(10): 268-275 (in Chinese). | |
16 | VASWANI A, SHAZEER N, PARMAR N, et al. Attention is all You need[C]∥ Proceedings of the 31st International Conference on Neural Information Processing Systems. New York: ACM, 2017: 6000-6010. |
17 | 周哲韬, 刘路, 宋晓, 等. 基于Transformer模型的滚动轴承剩余使用寿命预测方法[J/OL]. 北京航空航天大学学报, 1-17 [2021-08-28]. . |
ZHOU Z T, LIU L, SONG X, et al. Remaining useful life prediction method of rolling bearing based on Transformer model [J/OL]. Journal of Beijing University of Aeronautics and Astronautics, 1-17 [2021-08-28]. (in Chinese). | |
18 | IMMAS A, DO N, ALAM MR. Real-time in situ prediction of ocean currents[J]. Ocean Engineering, 2021, 228: 108922. |
19 | 罗棕, 杜春, 陈浩, 等. 基于Transformer层次预测的多星应急观测任务规划方法[J]. 航空学报, 2021, 42(4): 524721. |
LUO Z, DU C, CHEN H, et al. Multi-satellite scheduling approach for emergency scenarios based on hierarchical forecasting with Transformer network[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524721 (in Chinese). | |
20 | 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). | |
21 | ZHU Y, LIU J L, GUO C, et al. Prediction of battlefield target trajectory based on LSTM[C]∥2020 IEEE 16th International Conference on Control & Automation (ICCA). Piscataway: IEEE Press, 2020: 725-730. |
22 | XU X M, YANG R N, ZHANG T, et al. Trajectory prediction of target aircraft in air combat based on GA-OIF-Elman neural network[C]∥2019 IEEE International Conference on Artificial Intelligence and Computer Applications (ICAICA). Piscataway: IEEE Press, 2019: 108-113. |
[1] | Wei ZHENG, Yusong WANG, Kun JIANG, Yidi WANG. Overview of X-ray pulsar-based navigation methods [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(3): 527451-527451. |
[2] | QI Liangang, HAN Yanze, WANG Yani, GUO Qiang, Kaliuzhny MYKOLA. Multi-component LFM interference suppression method based on chirp rate turning point and FrFT [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 326840-326840. |
[3] | WANG Zi, SUN Xiaoliang, LI Zhang, CHENG Zilong, YU Qifeng. Transformer based monocular satellite pose estimation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 325298-325298. |
[4] | TIAN Wei, CHENG Simiao, LI Bo, LIAO Wenhe. An error compensation method of an industrial robot with joint backlash [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 625569-625569. |
[5] | YING Tao, WANG Xuebao, TIAN Wei, ZHOU Cheng, HOU Xiaoyang. A novel algorithm for reference signal purification in non-cooperative passive detection [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(2): 325025-325025. |
[6] | WANG Dayi, HOU Bowen, WANG Jiongqi, GE Dongming, LI Maodeng, XU Chao, ZHOU Haiyin. State estimation method for spacecraft autonomous navigation: Review [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(4): 524310-524310. |
[7] | LUO Zong, DU Chun, CHEN Hao, PENG Shuang, LI Jun. Multi-satellite scheduling approach for emergency scenarios based on hierarchical forecasting with Transformer network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(4): 524721-524721. |
[8] | SHI Lin, HAN Ning, SONG Xiangjun, WANG Libing, CUI Donghui. Bistatic ISAR imaging algorithm based on virtual slow time [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(5): 322683-322683. |
[9] | LIN Xiaojun, CUI Tong, YANG Biying, YANG Rui, XIN Xiaopeng. Method for establishing machining and inspection model of multi-stage machining processes of thin-walled blades [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(11): 423034-423034. |
[10] | WANG Longfei, ZHANG Liyan, YE Nan. An on-line compensation technology for robotic drilling error suitable for curved structure [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(10): 422871-422871. |
[11] | ZHANG Yaojia, WANG Li, YIN Zhendong, GAO Yang, WANG Bangting. Characteristics extraction method of aviation DC serial arc fault based on HHT [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(1): 522404-522404. |
[12] | LUO Changxin, ZHANG Dongyang, LEI Humin, BU Xiangwei, YE Jikun. Robust backstepping control of input-constrained hypersonic vehicle [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(4): 321801-321801. |
[13] | WANG Guohong, SUN Dianxing, BAI Jie, ZHANG Xiangyu. Radio frequency noise interference suppression based on estimation-feedback integration [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(3): 321500-321500. |
[14] | MENG Qian, LIU Jianye, ZENG Qinghua, FENG Shaojun, LI Rongbing. BeiDou navigation receiver weak signal acquisition aided by block improved DBZP [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(8): 320833-320833. |
[15] | HE Xiaoxu, TIAN Wei, ZENG Yuanfan, LIAO Wenhe, XIANG Yong. Robot positioning error and residual error compensation for aircraft assembly [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(4): 420538-420538. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||||||
Full text 564
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Abstract 1652
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Address: No.238, Baiyan Buiding, Beisihuan Zhonglu Road, Haidian District, Beijing, China
Postal code : 100083
E-mail:hkxb@buaa.edu.cn
Total visits: 6658907 Today visits: 1341All copyright © editorial office of Chinese Journal of Aeronautics
All copyright © editorial office of Chinese Journal of Aeronautics
Total visits: 6658907 Today visits: 1341