## 4 Fingerprinting-Based Positioning with Spatial Side Information
### Pattern-Matching Methods
#### 4.4.4 Pattern-Matching Method 4-MultFingIn-ClassOut  
The pattern-matching method 4-MultFingIn-ClassOut uses spatial side information on the fingerprints. It produces a classification of the tiles as tile-classes based on fixed tiles by aggregating the fingerprints from all of the sub-tiles in the fingerprint domain. The aggregation of the fingerprints is carried out using a 2D CNN. The position estimate is calculated by relying on the classification of the fixed tiles and a mapping between the tile-class labels and the positions of the corresponding fixed tiles. This method is depicted in Figure 10e. The use of a CNN is promising for the problem at hand. The CNN presents an architecture implementing the convolution operation which may be suitable for exploiting the side information and offering an optimal representational capacity. The architecture of the CNN may require the use of a large number of parameters to generalize the model. In comparison, using an equivalent number of parameters in an FFNN would result in overfitting and thus the model not being generalized. From this perspective, it is expected that for the same number of parameters, a CNN can provide a higher performance than an FFNN in terms of minimizing the error distance. As mentioned in Section 5.7.1, we observed that increasing the width or depth of the layers in the FFNN, after certain point, does not produce an improvement in performance. The approach in this method is analogous to that used in image classification problems and pattern recognition in images, which apply a convolution operation using 2D CNNs. In traditional image processing, the images usually have one channel (monochrome images) or three channels (RGB colors). In contrast, we will use a 2D CNN as it is used in image classification problems; however, the images will be in the form of a tensor of fingerprints, as detailed next. The tensor input to the CNN has two dimensions for the 2D spatial position coordinates associated with the fingerprints measured by the 2D sensor array and a third dimension for the channels. The channels in this case represent each one of the fingerprints from \(N_{F}\) fingerprint sources. The training phase is carried out with fixed tiles, associated with definite tile-classes. The testing phase for the actual positioning is carried out with moving tiles. The objective is to estimate the positions of the moving tiles. We recall that there is a direct relationship between a tile and the 2D sensor array. Here, we expect from the CNN an output result showing a higher classification probability for the tile-classes (associated with fixed tiles) that are closer to the target input moving tile. Then, this method will combine the known positions of the fixed tiles and the hit probability for these to estimate the position of the target moving tile (2D sensor array). Figure 11 shows an example of the tile-class labels assigned to fixed tiles (the numbers inside circles) and the border of a superimposed random moving tile. For a given input of fingerprints, here that corresponding to a moving tile, the 2D CNN returns as its output the tile-class probabilities associated with each fixed tile. The figure shows as an example an ideal outcome where the 2D CNN returns as its output tile-class probabilities that are proportional to the areas of the fixed tiles covered by the overlapping part of the moving tile (percentages shown at the bottom of each fixed tile). A moving tile can overlap with 1 to 4 fixed tiles. However, moving tiles most likely will be shifted from the fixed tiles and thus will most likely overlap with 4 fixed tiles. Ideally, the RSS fingerprints in the overlapping sub-tiles of a moving tile and a fixed tile will match. In practice, these will differ due to the presence of noise and other effects. Noise and other effects contribute a random component to the fingerprints (for example, shadow fading in the case of radio signals).