## 6 Results of the Simulations
### Results with Pattern-Matching Method 1-SingFingIn-PosOut  
The smaller the size of the tile, the higher the number of tiles that are required to cover the whole positioning area, and the higher the number of positions that are sampled. The size of the tile is determined by the number of sub-tiles per side of the tile, \(N_{SS}\), and the side length of the sub-tile, \(S_{S}\).  
Pattern-matching 1-SingFingIn-PosOut does not exploit side information. It takes a pointwise sample of the fingerprints from one sub-tile in the whole tile. So, it would be expected that in varying the size of the tile, the statistics of the positioning error will not change. However, the smaller the size of the tile, the higher the number of samples in the whole positioning area that contribute to the statistics.  
The CDF of the error distances obtained using the MTT dataset, from the simulations with this pattern-matching method, for a given tile arrangement (that is, a given sub-tile size and number of sub-tiles per side of the tile) is calculated. Then, the CDF is cut at  
Figure 16: Baseline reference performance of the error distance in two trivial solutions and comparison to the error distance obtained with the fingerprinting method based on pointwise samples (pattern-matching method 1-SingFingIn-PosOut). CDF(\(e\)) is the Cumulative Distribution Function (CDF) of the error distances \(e\) corresponding to each case.  
different percentiles. The error distances resulting from the cuts in the CDFs of the error distances at different percentiles are plotted for each number of sub-tiles considered, \(N_{SS}\), in the three subfigures in Figure 17. Each subfigure groups the results for each one of the three selected side lengths of the sub-tiles, \(S_{S}\). The results for all of the \(N_{SS}\) considered are linked with a distinctive line for each percentile cut.  
It is observed in Figure 17 that, ignoring minor variations, there is a trend in which the error distance seems constant for all numbers of sub-tiles and sizes of the sub-tiles considered. In fact, we expect these results to be constant for any number of sub-tiles and sub-tile sizes. As explained above, in reducing the size of the sub-tiles and the number of sub-tiles per tile, a higher density of samples is obtained (that is, a higher number of tiles) than when increasing the size of the sub-tiles and the number of sub-tiles per tile. Nevertheless, the statistics should not change when varying these parameters. Thus, ideally, the cuts in the CDF of the error distances at different percentiles, for all cases considered, should appear as horizontal lines. However, in practice, the bigger the size of the tiles, the smaller the number of samples that contribute to the statistics. Therefore, the results observed may be the result of the statistics. In addition, we may observe the possible non-optimal training of the NN model for this method, as discussed in Section 5.7.  
From the comparisons of the results obtained using the method 1-SingFingIn-PosOut, we take the results for the tile arrangement with \(N_{SS}=6\) and \(S_{S}=30\) mm as a reference for comparison against the other pattern-matching methods. The complete CDF for this pattern-matching method and the selected reference tile arrangement is shown in Figure 16 and in the figures presented in Sections 6.6.1 and 6.6.2.