China Safety Science Journal ›› 2024, Vol. 34 ›› Issue (12): 74-83.doi: 10.16265/j.cnki.issn1003-3033.2024.12.0497
• Safety engineering technology • Previous Articles Next Articles
LIU Hong1(
), ZHANG Xindi1, LU Fei1, ZHANG Chengyu2
Received:2024-09-11
Revised:2024-11-08
Online:2024-12-28
Published:2025-06-28
CLC Number:
LIU Hong, ZHANG Xindi, LU Fei, ZHANG Chengyu. Research on 4D flight trajectory prediction based on improved Transformer model[J]. China Safety Science Journal, 2024, 34(12): 74-83.
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URL: http://www.cssjj.com.cn/EN/10.16265/j.cnki.issn1003-3033.2024.12.0497
Table 1
Preprocessing longitude
| 时间 | 原始数据 | 插值后 | 归一化后 |
|---|---|---|---|
| 2023-11-11 T7:51:08 | -118.409 8 | -118.409 8 | 0.005 203 874 |
| 2023-11-11 T7:51:13 | NA | -118.399 1 | 0.005 440 012 |
| 2023-11-11 T7:51:18 | NA | -118.407 | 0.005 265 667 |
| 2023-11-11 T7:51:23 | NA | -118.421 4 | 0.004 947 873 |
| 2023-11-11 T7:51:24 | -118.424 | NA | NA |
| 2023-11-11 T7:51:28 | NA | -118.431 3 | 0.004 729 39 |
| 2023-11-11 T7:51:33 | NA | -118.435 6 | 0.004 634 493 |
| 2023-11-11 T7:51:38 | NA | -118.437 5 | 0.004 592 562 |
| 2023-11-11 T7:51:40 | -118.4384 | NA | NA |
| 2023-11-11 T7:51:43 | NA | -118.440 3 | 0.004 530 769 |
| 2023-11-11 T7:51:48 | NA | -118.444 9 | 0.004 429 251 |
| 2023-11-11 T7:51:53 | NA | -118.450 6 | 0.004 303 458 |
| 2023-11-11 T7:51:56 | -118.454 1 | NA | NA |
| 2023-11-11 T7:51:58 | NA | -118.456 4 | 0.004 175 457 |
| 2023-11-11 T7:52:03 | NA | -118.462 1 | 0.004 049 664 |
| 2023-11-11 T7:52:08 | NA | -118.467 5 | 0.003 930 491 |
Table 5
Prediction data comparison with benchmark models
| 模型 | MAE | RMSE | ||||||
|---|---|---|---|---|---|---|---|---|
| 纬度 | 经度 | 高度 | 平均 | 纬度 | 经度 | 高度 | 平均 | |
| F1 | 0.044 | 0.092 | 0.116 | 0.084 | 0.05 | 0.113 | 0.136 | 0.099 |
| F2 | 0.028 | 0.032 | 0.047 | 0.035 | 0.035 | 0.041 | 0.055 | 0.043 3 |
| F3 | 0.034 | 0.058 | 0.062 | 0.047 | 0.042 | 0.075 | 0.077 | 0.0656 |
| F4 | 0.026 | 0.018 | 0.026 | 0.023 | 0.034 5 | 0.032 | 0.028 | 0.032 |
| F | 0.018 | 0.027 | 0.015 | 0.021 | 0.029 | 0.030 | 0.020 | 0.027 |
Table 6
Prediction data comparison with benchmark models in three stages(length of prediction series is 1)
| 阶段 | 起始爬升阶段 | 巡航阶段 | 进近下降阶段 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 模型 | 纬度 | 经度 | 高度 | 平均 | 纬度 | 经度 | 高度 | 平均 | 纬度 | 经度 | 高度 | 平均 | ||
| F1 | RMSE | 0.132 | 0.015 | 0.091 | 0.079 | 0.051 | 0.108 | 0.145 | 0.101 | 0.027 | 0.120 | 0.030 | 0.059 | |
| MAE | 0.125 | 0.013 | 0.086 | 0.074 | 0.034 | 0.125 | 0.050 | 0.069 | 0.034 | 0.125 | 0.149 | 0.102 | ||
| F2 | RMSE | 0.146 | 0.031 | 0.119 | 0.098 | 0.078 | 0.155 | 0.097 | 0.33 | 0.015 | 0.116 | 0.11 | 0.08 | |
| MAE | 0.128 | 0.026 | 0.114 | 0.089 | 0.155 | 0.096 | 0.038 | 0.096 | 0.013 | 0.113 | 0.108 | 0.078 | ||
| F3 | RMSE | 0.014 | 0.045 | 0.118 | 0.059 | 0.066 | 0.072 | 0.052 | 0.063 | 0.040 | 0.048 | 0.045 | 0.044 | |
| MAE | 0.012 | 0.030 | 0.100 | 0.047 | 0.038 | 0.065 | 0.064 | 0.055 | 0.038 | 0.038 | 0.037 | 0.038 | ||
| F4 | RMSE | 0.029 | 0.005 | 0.031 | 0.022 | 0.029 | 0.024 | 0.030 | 0.028 | 0.072 | 0.06 | 0.027 | 0.053 | |
| MAE | 0.027 | 0.010 | 0.029 | 0.022 | 0.022 | 0.015 | 0.030 | 0.027 | 0.071 | 0.059 | 0.026 | 0.052 | ||
| F | RMSE | 0.071 | 0.014 | 0.024 | 0.036 | 0.020 | 0.038 | 0.021 | 0.026 | 0.016 | 0.060 | 0.019 | 0.031 | |
| MAE | 0.055 | 0.01 | 0.019 | 0.028 | 0.015 | 0.029 | 0.018 | 0.020 | 0.018 | 0.048 | 0.010 | 0.025 | ||
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