# Learning Approach for Angle Estimation Based on Characteristics of Phase Drift
## 2 Related Work  
IPS significantly advanced with the integration of ML and deep learning techniques, addressing various challenges such as multipath effects, signal attenuation, and environmental interference. This section reviews various ML-based approaches for IPS, highlighting methods and technologies employed in different studies. Recent research effectively utilized deep neural networks and ML algorithms to enhance BLE-based indoor positioning. To mitigate multipath-induced RSSI fluctuations, a fingerprinting technique using random forest was introduced in [18], achieving 96% accuracy. A comparative analysis of distance estimation using BLE in [19] integrated TX power into ML models, while a deep neural network-based approach in [20] combined RSSI and IQ components, achieving a localization accuracy of 70 cm, demonstrating robustness against changes in room content and AP configurations. UWB is known for its fine delay resolution and obstacle penetration capabilities, making it ideal for indoor localization. A non-parametric ML regressor was applied in [21] to mitigate ranging errors directly in the physical layer, showing superior performance in real-world scenarios. Classification techniques such as support vector machine (SVM), random forest (RF), and multi-layer perceptron (MLP) in [22] effectively distinguished between line-of-sight (LOS), non-line-of-sight (NLOS), and multipath (MP) conditions. Furthermore, ref. [23] demonstrated that MLP and boosted decision trees (BDT) were effective for NLOS mitigation, particularly for mobile objects. Wi-Fi technology is ubiquitous and widely used for indoor positioning. In [24], a Wi-Fi fingerprinting system using principal component analysis (PCA) [25] and various classifiers (KNN [26], decision tree [27], RF, and SVM [28]) improved localization accuracy while reducing computational costs. In [29], an approach combining relative and absolute RSS values mitigated device heterogeneity and RSSI variance, achieving a 0.87 m average localization error and reducing large errors by 30-50%. In [30], a method integrating kernel direct discriminant analysis (KDDA) [31] and relevance vector regression (RVR) [32] addressed RSSI-based inaccuracies, yielding notable accuracy improvements. Traditional AoA estimation methods, such as multiple signal classification (MUSIC [33] and ESPRIT [34]), have been widely used due to their high resolution and computational efficiency. These algorithms leverage the spatial covariance matrix to estimate angles and have been extensively studied in theoretical research. While effective in many scenarios, their performance can degrade in complex indoor environments where multipath interference, phase noise, and low SNR conditions introduce challenges. AoA-based localization is particularly beneficial in indoor environments due to its high accuracy and independence from extensive infrastructure. Compared to RSSI-based fingerprinting and ToA methods, AoA provides robust positioning with fewer anchor nodes [35; 36]. AoA estimation is a critical technique in indoor localization, offering high accuracy by determining the direction of incoming signals. In [37], a hybrid approach combining signal processing and machine learning trained regression models on snapshot data from multiple antennas, achieving at least 20% improvement over traditional MUSIC algorithms across various channel conditions. In [38], a convolutional neural network (CNN) was trained on the spatial covariance matrix's eigenvectors, significantly outperforming MUSIC in low-SNR environments. Despite advancements in AoA estimation techniques, there are relatively few machine learning models specifically designed to address this challenge, particularly those capable of handling the complexities introduced by phase drift. Most existing models fail to consider phase drift values, limiting their effectiveness in addressing fundamental issues such as multipath fading, which can significantly distort angle estimations.