基于Transformer模型的空战飞行器轨迹预测误差补偿方法

doi:10.7527/S1000-6893.2022.27413

Abstract

Abstract:

Accurate prediction results of the target aircraft trajectory can greatly improve the ability of our aircraft to gain air superiority in the process of air combat. This paper proposes a Transformer-based Prediction Error Compensation （TFPEC） method to further improve the accuracy of the trajectory prediction results based on the benchmarks generated by mature trajectory prediction algorithms. Firstly， a Transformer-based feature extraction model is established to process the historical trajectory sequence of the target aircraft， so as to obtain the trajectory feature matrix. Secondly， the multi-layer perceptron structure is used to perform regression calculation of the feature matrix， so as to calculate the trajectory prediction error compensation value. Thirdly， the Fourier transform is used to transform the trajectory into the frequency domain for modulo analysis， and to calculate the error compensation coefficient. Finally， the benchmark， the error compensation value， and the compensation coefficient are comprehensively calculated to obtain the final prediction result. The proposed method is tested on the one-on-one data set generated by pilots. The simulation results show that compared with the four existing trajectory prediction algorithms， the proposed method can effectively improve the accuracy of trajectory prediction results， and is applicable for aircraft trajectory prediction tasks in the air combat environment.

Key words: air combat trajectory prediction, sequence feature extraction, error compensation, Transformer, Fourier transform

CLC Number:

V249

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.

Figures/Tables 16

Fig. 1

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Table 1

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
数据集编号	预测步长 /ms	轨迹预测算法	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	预测精度提升/%	运行时间增加/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

Table 2

Table 3

Fig. 6

Fig. 7

Table 4

Fig. 8

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Fig. 10

Fig. 11

References 22

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数据集编号	最大速度/（m·s^-1）	最大加速度/（m·s^-2）	数据集长度/s
Ⅰ	63.58	49.98	3 139.6
Ⅱ	366.38	86.21	3 890.4

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
数据集编号	预测步长 /ms	轨迹预测算法	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	预测精度提升/%	运行时间增加/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

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
数据集编号	预测步长 /ms	平均绝对误差 /m	平均运行时间 /ms	误差补偿方法	平均绝对误差 /m	平均运行时间 /ms	预测精度提升/%	运行时间增加/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

频率阈值/Hz	平均绝对误差/m
0.25	505.583 8
0.5	233.185 2
0.75	165.333 7
1	114.223 7
1.25	144.388 4
1.5	146.482 9
1.75	149.548 7
2	153.265 0

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Transformer-based error compensation method for air combat aircraft trajectory prediction

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