## 6 Results of the Simulations
### Results with Pattern-Matching Method 3-MultFingIn-PosOut  
The positioning results obtained with pattern-matching method 3-MultFingIn-PosOut and different tile arrangements are shown in the three subfigures of Figure 19. 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, it is observed that 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. One hypothesis about the best \(N_{SS}\) is that when increasing the number of sub-tiles, there is more information for determining the position more accurately, which results in minimization of the error distance. However, on increasing the number of sub-tiles too much, or their size, the size of the tile increases, and the inter-tile distance increases (hence, fewer tiles are required to cover the whole scenario). This contributes to fewer labeled samples in the training phase, meaning a lower number of trained positions with sparser reference positions from the fixed tiles. Thus, the NN has a smaller density of reference positions for interpolating the position of a moving tile. So, the greater the number of sub-tiles, the bigger the tile, the longer the inter-tile distance, the fewer the number of tiles and training points in the scenario, and the coarser the resolution for estimating the positions. Related to sparser reference positions, we recall that training is performed using the reference (center) positions of fixed tiles. From the perspective of ideally limiting the NN to returning as the estimated position the center of the nearest fixed tile, the longer the inter-tile distance, the higher the error in the estimated position. In practice, the NN may return an estimated position calculated mainly from the nearest fixed tile centers; thus, the longer the inter-tile distance, the higher the error in estimating the position of the moving tile. Another hypothesis about the best \(N_{SS}\) is that in this method, we are adjusting the size of the first layer of the NN according to the number of sub-tiles. However, we keep a constant size in the intermediate layers and a constant number of layers for all of the tile arrangements. So, we cannot discard the possibility that the NN has a lower representational capacity when increasing the number of sub-tiles. The hypotheses above may contribute to decreasing the resolution for estimating the position when the number of sub-tiles increases above the observed best \(N_{SS}\). The minima at the 95 th percentile are indicated using red circles in Figure 19. These occur at the following best \(N_{SS}\), for each \(S_{S}\):  
* \(N_{SS}=10\) sub-tiles per side of the tile, for \(S_{S}=30\) mm;
* \(N_{SS}=8\) sub-tiles per side of the tile, for \(S_{S}=50\) mm;
* \(N_{SS}=6\) 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 distances at the 95 th percentile, we observe that the smaller the sub-tile size, the smaller the error distance.