\newpage
\onecolumn

\appendix
\section*{Appendix}
\section{Experimental Details}\label{app:exp}
\subsection{Dataset Preprocessing and Description}\label{dataset}
This paper exploits real-world datasets provided by OpenSky from 2020 to 2022 to validate our proposed model. The data preprocessing steps are as follows:

(1) Data Extraction: We extract seven features from the raw data, including timestamp, longitude, latitude, altitude, horizontal flight speed, horizontal flight angle, and vertical speed. The timestamp is used to identify whether the trajectory points are continuous, and the other six features are further processed as inputs to the model.

(2) Data Filtering: Due to many missing values and outliers in the raw dataset, we select 100 consecutive points without missing values as a complete flight trajectory. Then, we adopt the z-score method to find out the outliers. If one flight trajectory contains any outliers, we discard the whole trajectory. The z-score formula is as follows:
\begin{equation}
	z = \frac{(\overline{x}-\mu)}{\sigma - \sqrt{n}}
	\tag{1}
\end{equation}
where $\overline{x}$ is the value of each feature point, $\mu$ is the mean of each feature, $\sigma$ is the variance of each feature, and $n$ is the number of feature points.

(3) Velocity Transformation: We transform the horizontal velocity into $V_x$ and $V_y$ according to the angle, where $V_x$ is the velocity in the longitude dimension and $V_y$ is the velocity in the latitude dimension. In this way, the features become longitude, latitude, altitude, $V_x$, $V_y$ and $V_z$.

(4) Data Segmentation: The dataset is randomly divided into three parts with a ratio of  8:1:1 for training, validation, and testing.

After the above preprocessing, 274,605 flight trajectories are selected into our dataset. The range of longitude, latitude and altitude are $[-179.86396^\circ, 178.82147^\circ]$, $[-46.42435^\circ, 70.32590^\circ]$ and $[0, 21031.00m]$, respectively. The interval between two adjacent flight trajectory points is 10 seconds.

\subsection{Baseline Methods}\label{baseline}
We briefly describe the selected 10 competitive baselines as follows:
\begin{itemize}
    \item LSTM \citep{LSTM8489734}: Based on two layers of LSTM (with 30 and 60 nodes respectively) to encode each trajectory point, and future trajectories are predicted through a fully connected layer.
    \item CNN-LSTM \citep{CNN-LSTM9145522}: Based on two layers of one-dimensional CNN (the convolution kernel size is $1 \times 3$) and two layers of LSTM (with 50 nodes) to encode each trajectory point, and future trajectories are predicted through a fully connected layer.
    \item Bi-LSTM \citep{Sahadevan}: Based on two layers of Bi-LSTM (with 200 and 50 nodes respectively) to encode each trajectory point, and future trajectories are predicted through a fully connected layer.
    \item FlightBERT \citep{Guo2023FlightBERT}: It utilizes a BE representation to convert the scalar attributes of the flight trajectory into binary vectors, considering the FTP task as a multi binary classification problem. It uses 18, 16, 11 and 11 bits to encode the real values (decimals) of longitude, latitude, altitude and velocities into BE representation respectively. 
    \item FlightBERT++ \citep{Guo2023FlightBERT++}: It inherits the BE representation from the FlightBERT and introduces a differential prediction paradigm, which aims to predict the differential values of the trajectory attributes instead of the absolute values.
    \item WTFTP \citep{Zhang2023FlightTP}: It is an IMS-based method that utilizes discrete wavelet transform (DWT) to decompose the input flight trajectory into wavelet coefficients and predicts future trajectories based on the generated wavelet coefficients by inverse discrete wavelet transform (IDWT).
    \item TimeMixer \citep{wang2024timemixer}: It is a fully MLP-based architecture that mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately and ensembles multiple predictors to utilize complementary forecasting capabilities in multi-scale observations.
    \item TimesNet \citep{wu2022timesnet}: It is a task-general foundational model for time series analysis, which disentangles complex temporal variations into multiple intra-period and inter-period variations. A parameter efficient inception block is employed to capture these temporal variations in 2D space.
    \item MICN \citep{wang2023micn}: It adopts a multi-scale branch structure to capture the underlying information in time series. Downsampling one-dimensional convolution is used for local feature extraction and isometric convolution is employed for global correlation discovery.
    \item Pathformer \citep{chen2024pathformer}: It is a multi-scale Transformer with adaptive pathways, which integrates both temporal resolution and temporal distance for multi-scale modeling. A multi-scale router with temporal decomposition and an aggregator work together to realize adaptive multi-scale modeling for time series.   
\end{itemize}

\subsection{Implementation Details}\label{app:implementation}
For fairness, all the models follow the same experimental setup with look-back window $L = 60$ and prediction horizon $T\in\{1,3,9,15\}$,  which means the observation time is 10 minutes and the forecasting time is 10 seconds, 30 seconds, 1.5 minutes, 2.5 minutes. The patch sizes in multi-scale patch mixer blocks are set to \{30, 20, 10, 6, 2\}. The dimension of temporal embedding $d$ is 128. For all the MSA in this paper, the head number is 8 and the attention layer $l$ is 3. The learning rate is set as $10^{-4}$ for all experiments.  Our method is trained with MSE loss, using the Adam optimizer. The training process is early stopped within 30 epochs. The training would be terminated early if the validation loss does not decrease for three consecutive rounds. The model is implemented in PyTorch 2.2.1 and trained on a single NVIDIA RTX 3090 GPU with 24GB memory.

\subsection{Evaluation Metrics}\label{metrics}
Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) are exploited to evaluate the proposed model and baselines, which are defined as:
\begin{equation*}
    \begin{aligned} 
    MAE &=\frac{1}{T}\sum_{i=1}^T|\mathbf{Y}_i-\hat{\mathbf{Y}}_i| \\
    RMSE&=\sqrt{\frac{1}{T}{\sum_{i=1}^T(\mathbf{Y}_i-\hat{\mathbf{Y}}_i)^2}}
    \end{aligned}
\end{equation*}
where  $\mathbf{Y}_i$, $\hat{\mathbf{Y}}_i$  are the ground truth and prediction result for  $i$-th future point, respectively.


\section{Additional Experimental Results}
\subsection{Hyper-Parameter Sensitivity }
\paragraph{Number of Scales}
We perform experiments on different number of scales and report the MAE and RMSE results. As shown in Figure~\ref{fig:different_scales_rmse}, we can observe that when the number of scales increases from 2 to 5, the performance of FlightPatchNet is constantly improved. This is because FlightPatchNet can capture diverse global and local temporal patterns under different scales. When the number of scales increases up to 6, the performance starts to deteriorate. This indicates that a certain number of scales is sufficient for temporal modeling, and excessive scales may lead to the overfitting problem.

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.8\linewidth]{figure/different_scales_rmse.pdf}
   \captionsetup{font=small}
    \caption{MAE and RMSE with different number of scales for prediction horizon $T \in \{1,3,9,15\}$.}
    \label{fig:different_scales_rmse}
\end{figure}
\paragraph{Number of Attention Layers }

We test the number of attention layers in $\{1,2,3,6\}$ for global temporal attention, scale fusion, and channel fusion. The results are shown in Figure~\ref{fig:different_temporal_attention_layer}, Figure~\ref{fig:different_scale_attention_layer}  and Figure~\ref{fig:different_channel_attention_layer}. We can observe that when the number of attention layers increases from 1 to 3, the values of MAE and RMSE decrease, demonstrating that our model can better capture the dependencies between different time steps, scale-wise correlations and inter-variable relationships with more layers of attention. When the number of attention layers increases up to 6, the prediction accuracy does not improve. Thus, we choose to use three layers of attention in these parts. 
\begin{figure}[htbp]
    \centering
    \subfigure[MAE and RMSE of different attention layers in global temporal attention.]{
       \centering
       \includegraphics[width=0.3\linewidth]{figure/different_temporal_attention_layersrmse.pdf}  
        \label{fig:different_temporal_attention_layer} 
    }
    \subfigure[MAE and RMSE of different attention layers in scale fusion.]{
     \centering
    \includegraphics[width=0.3\linewidth]{figure/scale_atten.pdf} 
        \label{fig:different_scale_attention_layer} 
    }
    \subfigure[MAE and RMSE of different attention layers in channel fusion.]{
     \centering
    \includegraphics[width=0.3\linewidth]{figure/different_channel_attention_layers.pdf}  
        \label{fig:different_channel_attention_layer} 
    }
    \captionsetup{font=small}
    \caption{MAE and RMSE of different attention layers for prediction horizon $T=15$}
    \label{fig:Attention_layers}
 \end{figure}   
 
\paragraph{Look-Back Window Size $\mathbf{L}$}
Figure~\ref{fig:different_input_length} demonstrates the MAE and RMSE results of our model with different look-back window sizes. We set the window size $L$ to $\{10, 20, 30, 40, 50, 60, 70, 80\}$. The overall performance of FlightPatchNet is significantly improved as the window size increases from 10 to 60, indicating that FlightPatchNet can thoroughly capture the temporal dependencies from long flight trajectories. Moreover, the performance of altitude fluctuates with the increase of the window size, suggesting that the series of altitude are non-stationary and easily affected by unexpected noise. Thus, we set $L$ as 60 to achieve the overall optimal performance.

\begin{figure}[htbp]
    \centering
    \subfigure[]{
        \centering
       \includegraphics[width=0.45\linewidth]{figure/different_input_length_mae.pdf}    
    }
    \subfigure[]{
        \centering
        \includegraphics[width=0.45\linewidth]{figure/different_input_length_rmse.pdf}    
    }
    \captionsetup{font=small}
    \caption{MAE and RMSE of different look-back window sizes $L$ for prediction horizon $T=15$.}
    \label{fig:different_input_length}
\end{figure}
\paragraph{Order of Scales}
We conduct experiments on the order of patch sizes and report the MAE and RMSE results. As shown in Table~\ref{table:effective of inverted pyramid}, we can observe that patch sizes in descending order can effectively improve the prediction performance, indicating that the macro knowledge from coarser scales can guide the temporal modeling of finer scales.
\begin{table*}[ht]
    \centering
    \captionsetup{font=small}
    \caption{ The results of flight trajectory prediction with scales in ascending and descending order. $\uparrow$ means scales in ascending order and $\downarrow$ means scales in descending order.  The better results are highlighted in \textbf{bold}.}
    \label{table:effective of inverted pyramid}
    \setlength{\tabcolsep}{1mm}{
        {
            \begin{tabular}{@{}c|cccccc|cccc|cccc@{}}
    \toprule
    \multirow{2}{*}{patch sizes}  & \multicolumn{6}{c|}{Lon($0.00001^\circ$)}                                                                                                                                                                     & \multicolumn{4}{c|}{Lat($0.00001^\circ$)}                                                                                 & \multicolumn{4}{c}{Alt(m)}                                                                                                           \\ \cmidrule(l){2-15} 
                                  & \multicolumn{1}{c|}{Style}                         & \multicolumn{1}{c|}{Horizon} & \multicolumn{1}{c|}{1}            & \multicolumn{1}{c|}{3}            & \multicolumn{1}{c|}{9}            & 15            & \multicolumn{1}{c|}{1}            & \multicolumn{1}{c|}{3}            & \multicolumn{1}{c|}{9}            & 15            & \multicolumn{1}{c|}{1}               & \multicolumn{1}{c|}{3}               & \multicolumn{1}{c|}{9}               & 15              \\ \midrule
    \multirow{4}{*}{2,6,10,20,30} & \multicolumn{1}{c|}{\multirow{2}{*}{$\uparrow$}}   & \multicolumn{1}{c|}{MAE}     & \multicolumn{1}{c|}{98}           & \multicolumn{1}{c|}{155}          & 548                               & 1008          & \multicolumn{1}{c|}{99}           & \multicolumn{1}{c|}{106}          & \multicolumn{1}{c|}{385}          & 697           & \multicolumn{1}{c|}{54.02}           & \multicolumn{1}{c|}{33.47}           & \multicolumn{1}{c|}{79.39}           & 127.51          \\ \cmidrule(l){3-15} 
                                  & \multicolumn{1}{c|}{}                              & \multicolumn{1}{c|}{RMSE}    & \multicolumn{1}{c|}{187}          & \multicolumn{1}{c|}{241}          & \multicolumn{1}{c|}{887}          & 1642          & \multicolumn{1}{c|}{131}          & \multicolumn{1}{c|}{183}          & \multicolumn{1}{c|}{656}          & 1197          & \multicolumn{1}{c|}{\textbf{81.92}}  & \multicolumn{1}{c|}{\textbf{110.68}} & \multicolumn{1}{c|}{184.54}          & 248.16          \\ \cmidrule(l){2-15} 
                                  & \multicolumn{1}{c|}{\multirow{2}{*}{$\downarrow$}} & \multicolumn{1}{c|}{MAE}     & \multicolumn{1}{c|}{\textbf{48}}  & \multicolumn{1}{c|}{\textbf{153}} & \multicolumn{1}{c|}{\textbf{546}} & \textbf{966}  & \multicolumn{1}{c|}{\textbf{32}}  & \multicolumn{1}{c|}{\textbf{105}} & \multicolumn{1}{c|}{\textbf{381}} & \textbf{678}  & \multicolumn{1}{c|}{\textbf{13.34}}  & \multicolumn{1}{c|}{\textbf{32.65}}  & \multicolumn{1}{c|}{\textbf{78.57}}  & \textbf{123.97} \\ \cmidrule(l){3-15} 
                                  & \multicolumn{1}{c|}{}                              & \multicolumn{1}{c|}{RMSE}    & \multicolumn{1}{c|}{\textbf{87}}  & \multicolumn{1}{c|}{\textbf{233}} & \multicolumn{1}{c|}{\textbf{885}} & \textbf{1577} & \multicolumn{1}{c|}{\textbf{64}}  & \multicolumn{1}{c|}{\textbf{175}} & \multicolumn{1}{c|}{\textbf{652}} & \textbf{1174} & \multicolumn{1}{c|}{129.65}          & \multicolumn{1}{c|}{121.78}          & \multicolumn{1}{c|}{\textbf{174.63}} & \textbf{244.34} \\ \midrule
    \multirow{4}{*}{3,4,6,20,40}  & \multicolumn{1}{c|}{\multirow{2}{*}{$\uparrow$}}   & \multicolumn{1}{c|}{MAE}     & \multicolumn{1}{c|}{98}           & \multicolumn{1}{c|}{155}          & \multicolumn{1}{c|}{556}          & 997           & \multicolumn{1}{c|}{64}           & \multicolumn{1}{c|}{105}          & \multicolumn{1}{c|}{383}          & 704           & \multicolumn{1}{c|}{\textbf{39.77}}  & \multicolumn{1}{c|}{32.15}           & \multicolumn{1}{c|}{\textbf{76.38}}  & \textbf{124.18} \\ \cmidrule(l){3-15} 
                                  & \multicolumn{1}{c|}{}                              & \multicolumn{1}{c|}{RMSE}    & \multicolumn{1}{c|}{188}          & \multicolumn{1}{c|}{247}          & \multicolumn{1}{c|}{901}          & 1631          & \multicolumn{1}{c|}{131}          & \multicolumn{1}{c|}{175}          & \multicolumn{1}{c|}{655}          & 1210          & \multicolumn{1}{c|}{64.86}           & \multicolumn{1}{c|}{124.20}          & \multicolumn{1}{c|}{177.46}          & \textbf{243.46} \\ \cmidrule(l){2-15} 
                                  & \multicolumn{1}{c|}{\multirow{2}{*}{$\downarrow$}} & \multicolumn{1}{c|}{MAE}     & \multicolumn{1}{c|}{\textbf{97}}  & \multicolumn{1}{c|}{\textbf{153}} & \multicolumn{1}{c|}{\textbf{542}} & \textbf{963}  & \multicolumn{1}{c|}{\textbf{63}}  & \multicolumn{1}{c|}{\textbf{104}} & \multicolumn{1}{c|}{\textbf{369}} & \textbf{670}  & \multicolumn{1}{c|}{43.46}           & \multicolumn{1}{c|}{\textbf{28.96}}  & \multicolumn{1}{c|}{79.27}           & 128.13          \\ \cmidrule(l){3-15} 
                                  & \multicolumn{1}{c|}{}                              & \multicolumn{1}{c|}{RMSE}    & \multicolumn{1}{c|}{\textbf{187}} & \multicolumn{1}{c|}{\textbf{245}} & \multicolumn{1}{c|}{\textbf{879}} & \textbf{1582} & \multicolumn{1}{c|}{\textbf{130}} & \multicolumn{1}{c|}{\textbf{174}} & \multicolumn{1}{c|}{\textbf{631}} & \textbf{1167} & \multicolumn{1}{c|}{\textbf{64.50}}  & \multicolumn{1}{c|}{\textbf{115.76}} & \multicolumn{1}{c|}{\textbf{176.96}} & 251.72          \\ \midrule
    \multirow{4}{*}{3,6,40}       & \multicolumn{1}{c|}{\multirow{2}{*}{$\uparrow$}}   & \multicolumn{1}{c|}{MAE}     & \multicolumn{1}{c|}{48}           & \multicolumn{1}{c|}{156}          & \multicolumn{1}{c|}{536}          & 994           & \multicolumn{1}{c|}{35}           & \multicolumn{1}{c|}{105}          & \multicolumn{1}{c|}{370}          & 691           & \multicolumn{1}{c|}{\textbf{14.96}}  & \multicolumn{1}{c|}{31.42}           & \multicolumn{1}{c|}{79.07}           & \textbf{117.43} \\ \cmidrule(l){3-15} 
                                  & \multicolumn{1}{c|}{}                              & \multicolumn{1}{c|}{RMSE}    & \multicolumn{1}{c|}{87}           & \multicolumn{1}{c|}{248}          & \multicolumn{1}{c|}{876}          & 1628          & \multicolumn{1}{c|}{65}           & \multicolumn{1}{c|}{176}          & \multicolumn{1}{c|}{634}          & 1193          & \multicolumn{1}{c|}{\textbf{107.43}} & \multicolumn{1}{c|}{118.36}          & \multicolumn{1}{c|}{177.40}          & 238.87          \\ \cmidrule(l){2-15} 
                                  & \multicolumn{1}{c|}{\multirow{2}{*}{$\downarrow$}} & \multicolumn{1}{c|}{MAE}     & \multicolumn{1}{c|}{\textbf{48}}  & \multicolumn{1}{c|}{\textbf{153}} & \multicolumn{1}{c|}{\textbf{534}} & \textbf{988}  & \multicolumn{1}{c|}{\textbf{33}}  & \multicolumn{1}{c|}{\textbf{103}} & \multicolumn{1}{c|}{\textbf{368}} & \textbf{685}  & \multicolumn{1}{c|}{16.81}           & \multicolumn{1}{c|}{\textbf{31.26}}  & \multicolumn{1}{c|}{\textbf{71.96}}  & 118.66          \\ \cmidrule(l){3-15} 
                                  & \multicolumn{1}{c|}{}                              & \multicolumn{1}{c|}{RMSE}    & \multicolumn{1}{c|}{\textbf{87}}  & \multicolumn{1}{c|}{\textbf{244}} & \multicolumn{1}{c|}{\textbf{870}} & \textbf{1620} & \multicolumn{1}{c|}{\textbf{64}}  & \multicolumn{1}{c|}{\textbf{173}} & \multicolumn{1}{c|}{\textbf{633}} & \textbf{1186} & \multicolumn{1}{c|}{145.25}          & \multicolumn{1}{c|}{\textbf{114.33}} & \multicolumn{1}{c|}{\textbf{175.63}} & \textbf{236.32} \\ \bottomrule
    \end{tabular}
        }
    }
\end{table*}





\subsection{Error Bar}\label{error_bar}
In this paper, we repeat all the experiments five times. Here we report the standard deviation of our model and the second best model in Table~\ref{table:exp_res_error}. 
\begin{table*}[htbp]
\centering
\captionsetup{font=small}
\caption{Error bar of our FlightPatchNet and the second best model FlightBERT++.}
\label{table:exp_res_error}

{
\setlength{\tabcolsep}{1mm}{
 {
    \begin{tabular}{@{}c|c|cc|cc|cc@{}}
\toprule
   
\multirow{2}{*}{Model}                                                           & \multirow{2}{*}{Horizon} & \multicolumn{2}{c|}{Lon($0.00001^\circ$)}                                                         & \multicolumn{2}{c|}{Lat($0.00001^\circ$)}                                                           & \multicolumn{2}{c}{Alt(m)}                                                   \\ \cmidrule(l){3-8} 
                                                                                 &                          & \multicolumn{1}{c|}{MAE}                          & RMSE                         & \multicolumn{1}{c|}{MAE}                           & RMSE                          & \multicolumn{1}{c|}{MAE}                      & RMSE                      \\ \midrule
\multirow{4}{*}{FlightBERT++}                                                    & 1                        & \multicolumn{1}{c|}{173$\pm$6.45}          & 360$\pm$8.28& \multicolumn{1}{c|}{85$\pm$3.33}              & 148$\pm$13.20& \multicolumn{1}{c|}{9.39$\pm$1.79}   & 175.29$\pm$29.09          \\ \cmidrule(l){2-8} 
                                                                                 & 3                        & \multicolumn{1}{c|}{317$\pm$26.10}          & 659$\pm$4.35& \multicolumn{1}{c|}{210$\pm$30.50}              & 425$\pm$12.40& \multicolumn{1}{c|}{21.89$\pm$5.58}  & 167.16$\pm$46.39          \\ \cmidrule(l){2-8} 
                                                                                 & 9                        & \multicolumn{1}{c|}{871$\pm$17.40}          & 1846$\pm$44.50& \multicolumn{1}{c|}{612$\pm$60.70}              & 959$\pm$21.90& \multicolumn{1}{c|}{47.84$\pm$2.87}  & 327.93$\pm$52.84          \\ \cmidrule(l){2-8} 
                                                                                 & 15                       & \multicolumn{1}{c|}{1187$\pm$5.91}          & 3131$\pm$53.30& \multicolumn{1}{c|}{1048$\pm$36.90}           & 2127$\pm$20.10& \multicolumn{1}{c|}{78.46$\pm$8.13}  & 384.18$\pm$51.82          \\ \midrule
\multirow{4}{*}{\begin{tabular}[c]{@{}c@{}}FlightPatchNet\\ (Ours)\end{tabular}} & 1                        & \multicolumn{1}{c|}{48$\pm$1.24} & 87$\pm$1.02& \multicolumn{1}{c|}{32$\pm$1.06} & 64$\pm$0.84& \multicolumn{1}{c|}{13.34$\pm$9.43}  & 123.78$\pm$15.13\\ \cmidrule(l){2-8} 
                                                                                 & 3                        & \multicolumn{1}{c|}{153$\pm$3.19} & 233$\pm$5.44e-4& \multicolumn{1}{c|}{105$\pm$1.19}  & 175$\pm$2.36& \multicolumn{1}{c|}{32.65$\pm$1.76}  & 121.48$\pm$2.81  \\ \cmidrule(l){2-8} 
                                                                                 & 9                        & \multicolumn{1}{c|}{546$\pm$15.40} & 885$\pm$21.60& \multicolumn{1}{c|}{381$\pm$7.47}  & 652$\pm$7.76& \multicolumn{1}{c|}{78.57$\pm$2.66}  & 174.63$\pm$6.87  \\ \cmidrule(l){2-8} 
                                                                                 & 15                       & \multicolumn{1}{c|}{966$\pm$36.50} & 1577$\pm$54.90& \multicolumn{1}{c|}{678$\pm$25.80}  & 1174$\pm$35.30& \multicolumn{1}{c|}{123.97$\pm$5.72} & 244.34$\pm$6.91  \\ \bottomrule
                                                                                 
\end{tabular} 
  }
}
}
\end{table*}


\section{3D Trajectory Visualization}\label{Visualization}

 We visualize the flight trajectory prediction results of FlightPatchNet and all the baselines when the prediction horizon is 15. As shown in Figure~\ref{fig:traj_pred}, FlightPatchNet can provide stable and the most accurate predictions in longitude and latitude while it suffers from slight fluctuations in altitude. 
 \begin{figure*}[htbp]
    \subfigure[]{
    
     \includegraphics[width=0.5\linewidth]{figure/traj52.pdf}
    
    }
    \subfigure[]{
      \centering
     \includegraphics[width=0.5\linewidth]{figure/traj192.pdf}
    
    }\\
     \subfigure[]{
    
     \includegraphics[width=0.5\linewidth]{figure/traj406.pdf}
    
    }
    \subfigure[]{
      \centering
     \includegraphics[width=0.5\linewidth]{figure/traj415.pdf}
    
    }  \\
     \subfigure[]{
      \centering
     \includegraphics[width=0.5\linewidth]{figure/trajectory_462.pdf}
    
    } 
    \subfigure[]{
      \centering
     \includegraphics[width=0.5\linewidth]{figure/traj398.pdf}
    
    } 
    \captionsetup{font=small}
     \caption{Visualization of flight trajectory prediction results when the prediction horizon $T=15$ and look-back window size $L=60$.}
     \label{fig:traj_pred}
 \end{figure*}



