## 4 Experiments
### Experiment Settings
#### 4.1.3 Baselines  
To evaluate the performance of PESO, we make a comparison with several baseline models. RNN baselines models are utilized to predict the 5-track points in a sliding window manner with an input sequence of the previous 10 track points. When the RNN baseline predicts the first track point in the testing period, the process is shown in Equation (14). Note that \(Y_{10}=(y_{1},y_{2},\ldots,y_{10})\), \(\tilde{y}_{11}\) is the predicted track point, and \(\theta\) is the hidden state vector and cell memory.  
\[\widehat{y}_{11}=RNN(Y_{10},\theta) \tag{14}\]  
The twentieth trajectory point is shown in Equation (15) where \(\overline{Y}_{11}=(y_{2},y_{3},\ldots,y_{10},\overline{y}_{11})\).  
\[\overline{y}_{12}=RNN(\overline{Y}_{11},\theta) \tag{15}\]  
So we follow the rest of the sequence, and finally, we obtain the output \(\widehat{Y}_{RNN}=(\overline{y}_{11},\overline{y}_{12},\ldots,\overline{y}_ {15})\). The seq2 seq models in our baselines also predict a sequence of 10 position points but not in a recursive way.  
1. LSTM. An RNN variant is composed of five layers.
2. BiLSTM. An RNN variant is composed of five bidirectional layers.
3. GRU. Similar to LSTM.
4. BiGRU. Similar to BiGRU.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **RMSE** & **MAE** & **ADE** & **FDE** \\ \hline
1 layer & 0.000525 & 0.000369 & 0.000581 & 0.000865 \\
2 layers & 0.000614 & 0.000452 & 0.000699 & 0.001008 \\
3 layers & 0.000476 & 0.000325 & 0.000565 & 0.000774 \\
4 layers & 0.000469 & **0.000316** & 0.000542 & 0.000695 \\
5 layers & **0.000466** & 0.000327 & **0.000523** & **0.000681** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Explorations on the numbers of LSTM layers under the metrics of RMSE, MAE, ADE, and FDE. Note that 1 layer represents that the number of LSTM layers of encoder and decoder in PESO is 1.  
Figure 4: The details of training loss and testing loss during the the training process. The X-axis represents the number of training epochs, and the Y-axis represents the RMSE loss value.  
* LSTM-LSTM. A Seq2 Seq-based model with five LSTM layers in the encoder and the decoder. LSTM-LSTM and PESO are both LSTM as the encoder and LSTM as the decoder. The difference is that the input of baseline LSTM-LSTM is longitude and latitude, while PESO's input includes multiple semantic features and an oriental vector.
* BiLSTM-LSTM. A Seq2 Seq-based model with five BiLSTM layers in the encoder and five LSTM layers in the decoder.
* GRU-GRU. Similar to LSTM-LSTM.
* BiGRU-GRU. Similar to BiLSTM-LSTM.  
In addition to RNN-based and Seq2 Seq-based methods for trajectory prediction, this paper also considers time-series models. These models include traditional models and deep learning models: Autoregressive Integrated Moving Average model (ARIMA) [38], Kalman Filter [39], Vector Auto-Regression model (VAR) [40], and Spatial and Temporal Normalization (ST-Norm) [41]. Note that the ARIMA, Kalman Filter, and VAR are traditional methods, while ST-Norm is based on neural networks.  
* ARIMA. A statistical time-series forecasting model.
* Kalman Filter. A linear optimal estimation model.
* VAR. A statistical model for multivariate time-series prediction.
* ST-Norm. A deep learning model for time-series forecasting.