## 6 Results of the Simulations
### Results with Pattern-Matching Method 4-MultFingIn-ClassOut  
The positioning results obtained with pattern-matching method 4-MultFingIn-ClassOut and different tile arrangements are shown in the three subfigures of Figure 20. Each subfigure groups the results for each one of the three selected side lengths of the sub-tiles, \(S_{S}\). Each subfigure shows the error distances from the cuts in the CDFs of the error distances at different percentiles for all of the sub-tiles per side of the tile \(N_{SS}\) considered for the given \(S_{S}\). The results for all of the \(N_{SS}\) considered are linked with a distinctive line for each percentile cut. Looking at the 95 th percentile in each subfigure, a result similar to that for the method 3-MultFingIn-PosOut is observed. Starting from a small tile (composed of a small number of sub-tiles), increasing the number of sub-tiles reduces the error distance. However, this trend reverses after a certain number of sub-tiles, which we call _the best_\(N_{SS}\). The error distance starts to grow after the best \(N_{SS}\) when increasing the number of sub-tiles further. In this method, the training is performed using a given number of tile-classes, which is determined by the number of tiles that covers the positioning area in the scenario. The total number of tiles in the scenario is a function of the size of the tiles. The size of the tiles is given by the number of sub-tiles per tile (i.e., a function of the number of sub-tiles per side of the tile, \(N_{SS}\)) and by the sub-tile sizes (i.e., a function of the side lengths of the sub-tiles, \(S_{S}\)). As with the previous method, the reasoning is that increasing the number of sub-tiles brings more information for determining the position more accurately, which results in a reduction in the error distance. However, on increasing the number of sub-tiles too much, or their size, the size of the tiles increases, the inter-tile distance increases, the number of tiles required to cover the whole positioning area decreases, and the number of tile-classes decreases. Because the estimated position of the moving tile is calculated from the weighted contributions of the center positions of the fixed tiles, it follows the hypothesis that the bigger the tile, the coarser the resolution for estimating the position. So, after a certain tile size, the performance starts to degrade. As a summary, it is hypothesized that the gains attained by increasing the number of sub-tiles are traded off by a coarser resolution of the reference points used to estimate the position. The coarser resolution is a consequence of the increment in the size of the tiles and the associated reduction in the density of tiles in the positioning area. The minima at the 95 th percentile are indicated using red circles in Figure 20. These occur at the following best \(N_{SS}\) for each \(S_{S}\):  
* \(N_{SS}=13\) sub-tiles per side of the tile, for \(S_{S}=30\) mm;
* \(N_{SS}=10\) sub-tiles per side of the tile, for \(S_{S}=50\) mm;
* \(N_{SS}=9\) sub-tiles per side of the tile, for \(S_{S}=70\) mm. Varying the side length of the sub-tiles, \(S_{S}\), and comparing the error distance at the 95 th percentile, we observe that the smaller the sub-tile size, the smaller the error distance. For example, the error for \(S_{S}=30\) mm with \(N_{SS}=13\) is close to 0.4 m, whereas the error for \(S_{S}=70\) mm with \(N_{SS}=9\) is close to 0.6 m.  
Figure 17: Error distances from the cuts in the CDF of the error distances at different percentiles for the pattern-matching method 1-SingFingIn-FosOut for different numbers of sub-tiles per side of the tile and the three side lengths of the sub-tiles considered. Figure 18: Error distances from the cuts in the CDF of the error distances at different percentiles for the pattern-matching method 2-SingFingIn-AggPosOut for different numbers of sub-tiles per side of the tile and the three side lengths of the sub-tiles considered. The red circles indicate the minima at the 95 th percentile for the interval of \(N_{SS}\) considered.