# Learning Approach for Angle Estimation Based on Characteristics of Phase Drift
## 1 Introduction  
In response to the increasing demand for reliable indoor positioning systems (IPSs), a variety of techniques have been developed, including time of arrival (ToA) [1], angle of arrival (AoA) [2], and received signal strength indicator (RSSI) [3]. These methods employed some communication interfaces such as ultra-wideband (UWB) [4], Wi-Fi [5], and Bluetooth low energy (BLE) [6] to enhance the precision of indoor positioning [7, 8]. However, the current generation of IPSs faces several challenges, including signal fluctuations, multipath effects, and high infrastructure costs, which collectively limit the accuracy and widespread adoption of these systems [9, 10]. UWB offers centimeter-level accuracy and performs well in environments with minimal multipath interference. Nevertheless, the high cost and infrastructure requirements of this technology present considerable obstacles to its widespread adoption [11]. Wi-Fi-based positioning systems benefit from existing infrastructure and cost-effectiveness. However, these systems are susceptible to multipath effects and signal attenuation, which can impact the accuracy of the results obtained [12]. Bluetooth-based systems offer low power consumption and high compatibility with mobile devices; however, they are also prone to signal attenuation and multipath effects, which can affect the accuracy of the positioning results [13]. Despite the advancements in IPS, the accuracy of RSSI-based distance estimation methods is constrained by signal fluctuations, multipath effects, and environmental factors, particularly in complex indoor environments [7; 10]. Significant progress has been made in developing AI and machine learning (ML) models for indoor positioning. The integration of AI-based models for Wi-Fi, BLE, and other wireless technologies led to notable improvements in the precision and robustness of indoor positioning systems [14; 15; 16]. However, research on AI models specifically designed for AoA estimation remains limited. The objective of this study is to utilize artificial intelligence (AI) for the precise prediction of AoA, particularly in complex indoor environments where traditional RSSI-based methods struggle due to instability and environmental factors. Conventional AoA estimation methods typically attempt to mitigate multipath effects, as these distortions are considered a primary source of error. However, in complex indoor environments, completely eliminating the multipath is often impractical. Instead, an alternative approach is to exploit these distortions as useful features rather than treating them as noise. The need for accurate direction and angle estimation has been increased with applications such as smart glasses for gaze tracking, indoor navigation for the visually impaired, and augmented reality (AR) systems. Traditionally, RSSI has been more commonly used for distance estimation rather than angle [17]. However, with new use cases, the importance of AoA emerged. UWB using high-frequency signals, BLE, and Wi-Fi often faces significant challenges in maintaining precision in indoor environments due to fading and reflection. Leveraging phase drift values, which have not been widely applied before, could improve precision. Phase drift occurs due to slight variations in the signal phase as it propagates. By accurately measuring these variations, AoA estimation accuracy can be enhanced. Incorporating machine learning techniques to analyze and interpret phase drift values offers a promising solution against the limitations of traditional methods. This study aims to apply machine learning to identify features and perform angle estimation based on phase drift values. By exploring this approach, we aim to develop a phase drift-dependent lightweight angle estimation (PLAE) model that enhances the accuracy of AoA predictions in indoor settings, providing a more reliable solution compared to traditional methods. To date, no ML-based models effectively utilized phase drift for this purpose, highlighting the aspect of this research.