## 4 Machine-Learning-Aided Positioning in 5G Networks
### Advances in Positioning Aided by Machine Learning
They investigated the sensitivity of the out-of-sample error to the number of hidden layers, the number of neurons per layer, the regularization constant, and the time window of the ACF using five-fold cross-validation. Their simulation results showed that both TDNNs and FFNNs offered RMSE reductions of 29.1% and 59.6%, respectively, over a conventional DLL over the test set. The results highlighted the importance of the available time history, which helped the TDNN extract information from the dynamics of the LOS and NLOS signals. In addition, the authors conducted an experiment to test the generalization ability of the TDNN in real environments. The TDNN showed an overall RMSE reduction of 27.1% with a reduction of 38% in the most severe multipath region. [PERSON] et al. [55] proposed a data-driven localization approach for narrow beam alignment for mmWave networks. According to real experiments, their methods achieve sub-meter localization accuracy (median squared error) both indoors (0.33-0.37 m) and outdoors (0.76 m). They argue that their domain-specific neural network approach can increase localization accuracy while minimizing the amount of real samples that need to be collected to train the model. Their approach consists of the following elements: the Structured Multilayer Perceptron model (SMLP), which addresses the problem of collinear regions (localization on the line between 2 BS), a quantized loss function that focuses on points with significant error, and a synthetic data generation procedure to limit the amount of measurements required for accurate localization. They confirm with simulations and real experiments that their methods are robust under different noise models, outperform the conventional NN model, meet the latency requirements of 5G networks, and solve the problem of collinear regions. [PERSON] et al. [56] proposed a densely connected NN-based solution for increasing the positioning accuracy in an urban beamforming-based network scenario with high RSS uncertainty. The authors combined RSS and GNSS localization data to enhance the positioning performance. They executed their experiments in a ray-tracing-based simulation setup using the Madrid grid layout [38] with 7 BS. The positioning performance of the NN model was evaluated with and without the combined localization data on six different RSS uncertainty levels. On the lowest uncertainty level, the utilization of both the GNSS and RSS data led to a 32% error reduction compared to using only the RSS signal. Moreover, in this case, the mean error is 0.74 m. On the highest uncertainty level, the error reduction is 49% and the mean error is 1.75 m with the fusion NN model. [PERSON] et al. [57; 68] used Deep Neural Networks (DNN) and decision tree regression for positioning based on BRSRP data. An outdoor urban environment was simulated, where the base stations had a 16 \(\times\) 16 antenna array. With a network-level DNN model (the DNN training was performed with all the data from all the sites at one location server), the average error is approximately 5 m. Additionally, the authors investigated the positioning accuracy by training individual cell-specific DNN models for each cell. In this scenario, the average error can be as low as 1.4 m.  
[PERSON] et al. [50] evaluated several NN architectures for Beamformed Fingerprint (BFF) data-based positioning. They also enhanced the positioning with tracking techniques, which leveraged short-term historical data. The BFF is a 2D matrix, where the data sequences along both dimensions carry valuable information. This is why the Convolutional Neural Network (CNN) and the hierarchical CNN were used for the single BFF positioning. For the BFF tracking problem, where the positioning has to be performed based on a sequence of BFFs, the Long Short-Term Memory Networks (LSTM) and Temporal Convolutional Networks (TCN) were considered.