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.