基于Informer的客机长时4D航迹预测方法

客机长时4D航迹预测是基于航迹运行的重要基础，对于改善空中交通系统安全性能和优化空域结构有重要意义。针对现有长时4D航迹预测未充分考虑长序列航迹数据之间存在隐式关联信息等问题，借助Informer模型的自注意力机制，研究构建了基于Informer的长时4D航迹预测模型。为提取航迹数据的全局特征信息，增强数据独立性和时间序列特征学习能力，在数据嵌入层中增加全局时间戳模块，并利用航迹点序列等分层时间戳突破Informer模型固有的嵌入层时间刻度限制；为更好地捕捉非相邻时序序列点之间的隐式相关性，采用自注意力机制提取航迹数据特征，并运用概率稀疏方法降低自注意力机制的计算复杂度至O（LlogL），同时在编码器中增加蒸馏机制以减少计算维度和网络参数量；为避免传统的逐步预测输出方法造成的误差累积现象，提高航迹预测精度，采用全连接层对预测输出数据进行维度调整，完成一步生成式输出。对历史4D航迹数据进行三次样条插值等预处理后，与时序特征数据同时输入到航迹预测模型中，经过模型迭代训练，输出航迹预测结果。实验结果表明：在同时预测航迹的4D特征时，基于Informer模型的预测表现优于LSTnet方法，其均方根误差和欧氏距离误差分别为0.218 5和15.980 km，相较于LSTnet网络分别减少了1.48%和2.44%。此外，对于分别预测航迹特征的任务，Informer模型的欧氏距离误差为13.248 km，相较于LSTnet网络减少了3.11%，相较于传统LSTM网络减少了34.99%。

A Method for Predicting Long-term 4D Trajectory of Airplanes Based on Informer

Prediction of long-term 4D trajectory is an important foundation for trajectory-based operation, which is significant for improving safety of air transportation system and optimizing airspace. The existing methods for predicting long-term 4D trajectory do not fully consider implicit association among trajectory data with a long sequence. To address this problem, a long-term 4D trajectory prediction model based on Informer model with the self-attention mechanism is developed. To extract the global feature from trajectory data, enhance data independence and the capability to learn the feature of time series, a global timestamp module is added into the data embedding layer. Moreover, the layered timestamps, such as trajectory point sequences, are utilized to overcome the inherent time scale limitation of the Informer model. To better capture the implicit correlations between non-adjacent temporal sequence points, a self-attentive mechanism is employed to extract the features of trajectory data, and a probabilistic sparse method is applied to reduce the computational complexity of the self-attentive mechanism to O(LlogL). Additionally, a distillation mechanism is incorporated into the encoder to reduce the computational dimensions and the number of network parameters. To avoid the error accumulation arising from traditional step-by-step prediction models and improve the accuracy of trajectory prediction, a fully connected layer is applied to adjust the dimensions of the predicted data, achieving one-step generative output. After three-time spline interpolation, the pre-processed historical 4D trajectory data are inputted to the trajectory prediction model along with the data presenting the feature of time-series. Through iterative training of the model, the trajectory prediction results are generated and output. Study results show that, the Informer-based model outperforms the LSTnet method when predicting the trajectory of 4D features simultaneously. The root mean square error and Euclidean distance error is 0.2185 and 15.980 km, respectively, which is a reduction of 1.48% and 2.44% compared to that of the LSTnet network. In addition, when predicting the trajectory features separately, the Euclidean distance error of the Informer-based model is 13.248 km, with a reduction of 3.11% compared to the LSTnet network and a reduction of 34.99% compared to the traditional LSTM network.