## 2 Basic Concepts and Work Scope
### Fingerprinting-based Positioning  
Fingerprinting-based positioning is based on the ideal assumption that fingerprints, with these being a physical signal or any distinctive characteristic of the environment, alone or in a set, can be associated with a unique position in space. Figure 3 shows an example of fingerprints from three sources for positioning in 2D. In this figure, the fingerprints from each source are represented as a three-dimensional (3D) continuous surface, in which a fingerprint measure is a function of 2D position coordinates. A position is represented by an ideally unique combination of fingerprints. In practice, the presence of noise, interference, and other disturbances results in position estimates that contain a certain degree of positioning error. Different kinds of fingerprint sources are reported in the literature, for example, visible light [23; 24; 25], Fine Timing Measurement (FTM) ranging values [26], ultra-wideband signals [27], sound [28; 29], magnetic fields [30; 31], Channel State Information (CSI) [32] (and the references in Sections 3.1 and 3.2), and RSS (references in Sections 3.1 and 3.2). In addition, some authors treat visual images as fingerprints (see [33] and the references therein). Different types of fingerprints are, in some cases, combined together or are combined with other positioning methods through data fusion or other techniques to form hybrid positioning systems. For example, in [34], magnetic field fingerprints are fused with visual images, while in [35], the CSI amplitude is combined with the RSS. Fingerprinting-based positioning consists of two stages or phases. The first phase is commonly known in the literature as the offline or _training phase_. It consists of gathering fingerprints and constructing a suitable mapping from a sampled set of fingerprints to a \begin{table}
\begin{tabular}{l l} \hline \hline  & **Acronym** & **Description** \\ \hline
1D & One-dimensional/one-dimension \\
2D & Two-dimensional/two-dimensions \\
3D & Three-dimensional/three-dimensions \\ AoA & Angle of Arrival \\ CDF & Cumulative Distribution Function \\ CNN & Convolutional neural network \\ CSI & Channel State Information \\ FFNN & Feedforward neural network \\ FTM & Fine Timing Measurement \\ GNSS & Global Navigation Satellite System \\ ISAC & Integrated Sensing and Communications \\ kNN & k-Nearest Neighbors \\ LIS & Large Intelligent Surface \\ LOS & Line of Sight \\ LSTM & Long Short-Term Memory \\ MAE & Mean Absolute Error \\ MIMO & Multiple-Input Multiple-Output \\ (A)NN & (Artificial) neural network \\ RGB & Red–Green–Blue \\ RIS & Reconfigurable intelligent surface \\ RMSprop & Root Mean Square propagation \\ RNN & Recurrent neural network \\ RSS & Received signal strength \\ SNR & Signal-to-Noise Ratio \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Acronyms of general use in the article. ground truth reference position by means of a pattern-matching method. The ground truth position is usually obtained by other means in this phase, for example, with the aid of a secondary positioning system that it is known to produce a smaller positioning error. In Figure 4 (left), the training phase is represented in the case of a pattern-matching method based on supervised learning with an NN. A second phase, known in the literature on fingerprinting-based positioning as the online or _testing phase_, consists of mapping an input set of fingerprints to an output estimate of position coordinates, as depicted in Figure 4 (right) The mapping is performed using the pattern-matching method constructed or trained in the training phase. In the context of deep learning methods, this phase is referred to as the _inference phase_. In the inference phase, a trained NN model is used to make predictions based on input data. Hereafter, we refer to this phase as the testing phase, which is the terminology mainly used in the field of fingerprinting-based positioning and its literature.