## 1 Introduction
The analytical model assumes a magnetic dipole approximation and incorporates the unknown sensor positions and magnetic moment as optimization variables. Using single- and multi-objective optimization approaches, the study achieves localization accuracy within 25 to 35 cm, demonstrating the efficacy of these algorithms for realistic underwater conditions. Other deterministic approaches like the LMA [17; 18; 19] were also used. [PERSON] et al. [19] introduced a real-time magnetic tracking system that was designed to locate a swallowable endoscopic capsule in the gastrointestinal tract using a small permanent magnet and a reduced number of magnetic sensors. The system calculates the capsule's position by solving an inverse problem using a mathematical model of the magnetic field generated by the magnet. LMA refines the solution, offering fast and accurate localization while minimizing system complexity. This approach was validated through laboratory tests and in vivo animal trials, demonstrating its potential for precise and practical in-body tracking applications. Other studies utilized a positioning technique called Simultaneous Localization and Mapping (SLAM) [20]. [PERSON] et al. showed that SLAM contributes significantly by enabling the creation of magnetic field maps while localizing users or robots in real time, effectively integrating mapping and positioning tasks. Techniques like particle filters and Gaussian processes are employed to model the magnetic environment, improving positioning accuracy and map consistency. The survey highlights advancements in SLAM, such as efficient map updates and reduced computational demands, which enhance the scalability and practicality of magnetic field localization systems. Additional classification schemes based on ML solutions include both unsupervised methods such as clustering and supervised methods such as k-nearest neighbor (KNN) [21]). [PERSON] et al. [21] investigated magnetic field (MF)-based indoor positioning, addressing challenges like device heterogeneity and MF disturbances. They highlighted the application of the KNN algorithm for MF classification, demonstrating its ability to improve location discernibility in indoor environments. By using calibrated magnetic data, the KNN method achieves higher positioning accuracy compared to other classifiers, effectively reducing the impact of MF anomalies and enhancing the practical feasibility of MF-based positioning systems. Supervised methods such as the Support Vector Machine (SVM) [22] have also been regarded as accurate. [PERSON] et al. [22] proposed an adaptive Magnetic Anomaly Detection (MAD) method using SVM. They utilized Orthonormal Basis Function (OBF) energy and magnetic entropy as features to classify anomalies in low-signal-to-noise-ratio environments. The SVM model, with a radial basis function (RBF) kernel, achieves high accuracy and robustness by reducing false alarms and improving detection performance compared to traditional MAD methods. This approach eliminates the need for manual threshold settings and adapts effectively to varying noise conditions, enhancing its applicability in real-world scenarios. Currently, the state-of-the art solution appears to rely on Neural Networks. Some use Convolutional Neural Networks (CNNs) to determine the position of a magnetic source [23; 24]. [PERSON] et al. [24] proposed an indoor location estimator that relies on the distinctive and quasi-static magnetic fields found in rooms. By transforming the magnetic field data into a two-dimensional heat map and applying a Fourier transform, temporal dependencies are minimized. The processed data are then used to train a CNN model for building location estimation. Others employ Recurrent Neural Networks (RNNs) to detect anomalies in magnetic time-series data [25; 26]. [PERSON] et al. [25] proposed a deep learning technique for geomagnetic field forecasting, utilizing an RNN architecture with Long Short-Term Memory (LSTM).