# Learning Approach for Angle Estimation Based on Characteristics of Phase Drift
## 4 Performance Evaluation
### Analysis of Experiment Results  
#### 4.3.1 Accuracy of Angle  
As shown in Figure 10, the relationship between the predicted and true angles for the test samples is illustrated, with the x-axis representing the true angles (degrees) and the y-axis representing the predicted angles (degrees). The blue dots represent the PLAE model predictions, while the orange dots represent the AoA predictions. The red dashed line indicates the ideal scenario where the predicted angles match the true angles. This visualization helps to assess how closely the model's predictions align with the actual angles, highlighting the model's accuracy in direction estimation. The PLAE model demonstrated a mean absolute error (MAE) of 0.031, which is significantly lower than the AoA's MAE of 96.12. The maximum deviation from the true angles was 6.77 degrees for the PLAE model, whereas the AoA exhibited a much larger maximum deviation of 216.42 degrees. These metrics suggest that the PLAE model provides more accurate and consistent angle predictions compared to the AoA. Figure 9: Comparison results of PLAE model predictions and actual angles: (**a**) before outlier removal and (**b**) after outlier removal. In open space environments where LOS is maintained, AoA typically performs well. However, in the measurement environment used in this study, obstacles, metallic objects, and various sources of interference such as propagation error, fading, and reflection adversely affect AoA accuracy. The AoA model operates by measuring the angle of arrival of signals, making it more susceptible to issues such as signal attenuation and multipath effects that are prevalent in indoor environments. As the angles move toward the extremes (i.e., closer to \(\pm 90\) degrees), these effects become more pronounced, leading to greater prediction errors, as shown by the larger deviations in the orange dots away from the ideal line. These environmental factors can lead to significant errors in AoA estimation, as indicated by the scattered orange dots that deviate from the ideal line. Conversely, the PLAE model, represented by the blue dots, shows a closer alignment with the true angles, suggesting that the PLAE model is more robust to the environmental factors. The PLAE model can incorporate these errors as features, enabling it to provide more accurate angle predictions despite the complex indoor environment. Figure 11 shows the evolution of the model loss during training and validation. The loss function used in this study is the mean squared error (_MSE_), which is defined as:  
\[MSE=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2} \tag{11}\]  
where \(y_{i}\) represents the true angle, \(\hat{y}_{i}\) represents the predicted angle, and \(n\) is the total number of samples. The _MSE_ measures the average squared difference between the true and predicted angles, with smaller values indicating better model performance. The unit of the loss is expressed in squared degrees (\({}^{\circ}\)2). Figure 11: PLAE model loss during training and validation. Figure 10: Comparison of PLAE Model predictions and AoA predictions for angle estimation. As observed in the graph, the training loss decreases significantly in the initial epochs and gradually stabilizes, indicating that the model is learning effectively. The validation loss follows a similar trend, decreasing consistently without sharp fluctuations. This suggests that the model is generalizing well to unseen data, with no significant signs of overfitting. The steady reduction in both losses implies that the model's parameter updates are well-controlled, preventing abrupt changes that could destabilize validation performance. Additionally, the consistent trend in validation loss indicates that the distributional differences between the training and validation datasets are minimal. The dataset split in a 7:1:2 ratio appears to provide a balanced representation, reducing variability in validation performance.