# Learning Approach for Angle Estimation Based on Characteristics of Phase Drift
## 3 Data Analysis and Model Construction  
### Radio Signal Analysis for Training Model  
To collect the training data, we utilized the BOOSTXL-AOA kit [41] from Texas Instruments [42], as shown in Figure 1. The experimental setup involved securing the sender at a fixed location while rotating the receiver around it to collect data at precise distances, ensuring accurate angle measurements. The data collection was conducted indoors utilizing six antennas organized into two groups of three. Signals were gathered at 10-degree intervals, ranging from \(-90\) to 90 degrees, with a signal interval of 625 \(\upmu\)s. A Jetson Nano [43] was used for data acquisition, producing CSV files that included RSSI values, phase drift values (pa1 and pa2), and the corresponding AoA results. Each angle was measured approximately 20,000 times to ensure reliability. Prior to data transformation, an in-depth examination of the phase drift values (pa1 and pa2 from antenna 1 and 2, respectively) was conducted to understand their characteristics and correlations. This analysis was essential to validate the use of the mean and difference between phase drift values as features in the regression model for angle prediction. The phase drift values exhibited consistent patterns over time, indicating a strong correlation between them. As shown in Figure 2, when analyzing the phase drift values at a fixed angle (e.g., 90 degrees) over 100 time steps (each time step is 625 \(\upmu\)s), although overall patterns are unstable, both phase drift values demonstrated similar trends. This correlation suggests that phase drift values are influenced by similar underlying factors. Consistent patterns highlight that the phase drift values are not random but have an underlying systematic behavior. The variations in phase drift values are likely due to the same environmental factors, such as multipath propagation, delay, reflection, fading, and refraction, which consistently affect the phase of the signals. The correlation between phase drift values indicates their potential to be effectively used together to improve the accuracy of angle estimation. Figure 1: Experimental setup for training data acquisition. Figure 2: Comparative analysis of phase drift values over time for phase drift values. As shown in Figure 3, the comparative analysis of phase drift values across various angles revealed distinct patterns for each angle. For instance, dataset-40 shows phase drift values that are almost similar, while dataset-90 reveals a significant difference of about 50 units between phase drift values. This finding supports the hypothesis that phase drift values are angle-dependent and can effectively differentiate between different angles. The clear differentiation between the datasets at different angles highlights the phase drift values' sensitivity to angular changes. The distinct patterns observed across different angles indicate that phase drift values can serve as reliable features for angle estimation, providing information that enhances the prediction accuracy in complex indoor environments. To better capture these angle-specific features, the mean of phase drift values ((pa1 + pa2)/2) and the difference between phase drift values (pa1 \(-\) pa2) were calculated. Calculating the mean helps reflect the general trend and combined effect of phase drift values, while the difference captures the unique interaction and divergence between them, reflecting the nuanced variations due to different angles. As shown in Figures 4 and 5, the mean and difference in phase drift values across different datasets provide insights into their angle-specific patterns. The analysis revealed that phase drift values for different angles exhibit distinct characteristics, which are better captured by considering their mean and difference. These observations underscore the importance of using both the mean and difference values to capture angle-specific features more effectively.