## 6 Results of the Simulations
### Pattern-Matching Method 4-MultFingIn-ClassOut Details  
We study in detail the results obtained using pattern-matching method 4-MultFingIn-ClassOut since this is the method that produces the best result in terms of minimizing the error distance when compared with those of the other methods. A selection of CDF curves of the error distances for different numbers of sub-tiles and sub-tile sizes is presented in Figures 23-25. These figures depict the actual CDF curves from which we took the cuts at different percentiles depicted in Figure 20. Each CDF curve in Figures 23-25 contains more information about the results for all of the percentiles than that presented in Figure 20; however, some curves were removed for legibility. In the CDF curves shown in Figures 23-25, the curves depicted with continuous lines correspond to low \(N_{\text{SS}}\) values. More specifically, curves with continuous lines correspond to \(N_{SS}\) values ranging from the smallest number of sub-tiles considered to the \(N_{SS}\) that minimizes the error distance (regarded as the best \(N_{SS}\)). The CDF curve for the best \(N_{SS}\) sets an upper bound on the performance, meaning that the results for any other \(N_{SS}\) will perform worse than those obtained for the best \(N_{SS}\). This upper bound is depicted as a thicker continuous line. The curves for results with a number of sub-tiles, \(N_{SS}\), greater than the best \(N_{SS}\) show a worse performance than this upper bound. These curves are observed on the right side of the curve for the best \(N_{SS}\). These curves are represented using dashed lines, for legibility, to distinguish them from the curves representing the results for a lower \(N_{SS}\) (which are plotted using continuous lines). From these results, we can observe that it is meaningless to increase the number of sub-tiles to a greater number than the best \(N_{SS}\) since the performance starts to degrade. Therefore, the use of \(N_{SS}\) values greater than the best \(N_{SS}\), that is, corresponding to the curves represented with dashed lines, is not a good option in the context of our study. This is because to obtain the performance represented by the dashed lines, a bigger 2D sensor array is required, plus the associated computing resources, for a performance that could be attained using a smaller 2D sensor array. Figure 23: Comparison of the results for the pattern-matching method 4-MultFingIn-ClassOut with a side length of the sub-tiles \(S_{S}=30\) mm and different numbers of sub-tiles per side of the tile, \(N_{SS}\). Figure 24: Comparison of the results for the pattern-matching method 4-MultFingIn-ClassOut with a side length of the sub-tiles \(S_{S}=50\) mm and different numbers of sub-tiles per side of the tile, \(N_{SS}\). From the curves, we can also study the difference in the error at different percentiles to decide whether increasing the complexity and computing cost using a bigger 2D sensor array, that is, with more sub-tiles, is worth the reduction in the positioning error. It is noted that pattern-matching method 3-MultFingIn-PosOut shows similar results to those of the method 4-MultFingIn-ClassOut, with the difference being that the former performs worse than the latter. Then, similar conclusions to those discussed above can be drawn for the pattern-matching method 3-MultFingIn-PosOut based on the results presented in Figure 19.  
Finally, Figure 26 gathers the CDF curves for the best results (continuous lines) and for the results using the smallest 2D sensor array (dashed lines) for each side length of the sub-tiles \(S_{S}\) using the method 4-MultFingIn-ClassOut. In this figure, we can observe the differences in the error distance when changing the side length of the sub-tiles, \(S_{S}\), for these distinctive cases.