## 6 Results of the Simulations
### Results with Pattern-Matching Method 2-SingFingIn-AggPosOut  
The positioning results obtained with pattern-matching method 2-SingFingIn-AggPosOut and different tile arrangements are shown in the three subfigures of Figure 18. 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 increasing the number of sub-tiles per tile reduces the error distance. In this method, the trend shows that in the interval of the number of sub-tiles considered, the greater the spatial side information, the smaller the error distance. We did not calculate any results beyond \(N_{SS}=15\), so it is unknown whether this trend continues or whether it reaches a minimum for a certain number of sub-tiles. However, for the scenario considered, bigger tiles are not of much interest to practical applications, and in addition, we observe later that other methods perform better than this one. Therefore, we do not investigate how the error distance varies for bigger tile sizes.  
The minima at the 95 th percentile for the interval of \(N_{SS}\) considered are indicated using red circles in Figure 18. These occur at the following values:  
* \(N_{SS}=14\) sub-tiles per side of the tile, for \(S_{S}=30\) mm;
* \(N_{SS}=15\) sub-tiles per side of the tile, for \(S_{S}=50\) mm;
* \(N_{SS}=15\) sub-tiles per side of the tile, for \(S_{S}=70\) mm.  
In the case of \(S_{S}=30\) mm, the minimum error is at \(N_{SS}=14\), in contrast to \(N_{SS}=15\) for the other two cases. Either we did not find a good representative result with a minimum error for \(N_{SS}=15\) or there is effectively a minimum for \(N_{SS}=14\).  
Varying the side length of the sub-tiles \(S_{S}\) and comparing the error distances at the 95 th percentile, we observe that the bigger the sub-tile size, the smaller the error distance. For example, the error for \(S_{S}=30\) mm with \(N_{SS}=14\) is close to 1.16 m, whereas the error for \(S_{S}=70\) mm with \(N_{SS}=15\) is close to 0.93 m. One hypothesis for this behavior is based on the fact that there are more samples contributing to a better estimation of the position. However, this may be not the case, as in the cases with \(S_{S}=50\) and \(S_{S}=70\), both have a minimum error with the same number of samples (the same number of sub-tiles per side of the tile, \(N_{SS}=15\)); however, the latter has a smaller minimum error distance than the former. Yet, another hypothesis can be formulated in the sense that the bigger the sub-tile size, the further apart the fingerprints are located from each sub-tile; thus, it would be possible to obtain more distinctive patterns of fingerprints for estimating a position with less error. The pattern-matching methods that follow present more interesting results, so we did not study this method further.