## 6 Results of the Simulations
### Observations for Cases with Spatial Side Information and Aggregation in the Fingerprint Domain
#### 6.8.3 The Best Results and Border Conditions in the Positioning Area in the Scenario  
We discussed in Section 5.3 the border conditions in the area intended for positioning in the scenario. In the training phase, the whole positioning area will be covered with entire tiles that are contiguous to each other (fixed tiles); that is, the use of fractions of a tile (and the 2D sensor array) is not considered in our scope. Then, for cases with tile arrangements in which the dimensions of the area intended for positioning are not a multiple of the side length of the tile, some regions of the area intended for positioning will be uncovered, at the top or right borders or at both. Furthermore, we discussed in Section 5.10 that the size of the 2D sensor array limits the useful area in which the positioning can be performed. Considering the center of the 2D sensor array as the reference for determining the position, bigger 2D sensor arrays cannot come as close to the borders to perform positioning as smaller ones can. Thus, the useful area in which the positioning can be performed changes with the size of the 2D sensor array (and tile arrangement). Or, in other words, the uncovered areas adjacent to the borders appear as stripes with a width \(S_{T}/2\) (assuming the center of the 2D sensor array as the reference for determining the position). Now, we would like to study whether the fact that some tile arrangements do not fill the entire area intended for positioning and the fact that different tile arrangements produce more or less samples close to the borders of the positioning area cause any change in the results obtained using pattern-matching methods 3-MultFingIn-PosOut and 4-MultFingIn-ClassOut. So, in other words, we would like to know whether the CDF curves of the error distances shift due to a varying number of samples with different statistics close to the borders as a result of using different tile arrangements. The CDFs of the error distances obtained using these methods for the best results were discussed in Section 6.6.2 and are shown in Figure 22. For the particular case of the method 4-MultFingIn-ClassOut, the results were discussed in Section 6.7 and are shown in Figure 26. For convenience and simplicity, we will use as a reference the pattern-matching method 4-MultFingIn-ClassOut. Similar conclusions can be drawn for the method 3-MultFingIn-PosOut. First, we observe that the best result that minimizes the CDF of the error distances with \(S_{S}=50\) mm and the method 4-MultFingIn-ClassOut is obtained with \(N_{SS}=10\). This results in a tile with a side length of \(S_{T}=500\) mm. For this tile arrangement, the maximum allowed dimensions of the area intended for positioning (13,000 mm \(\times\) 5000 mm) are a multiple of \(S_{T}\), meaning that the area intended for positioning will be covered entirely by fixed tiles in the tiling process (through the execution of the function \(FTileCenters()\), listed in Pseudocode 1). Thus, for this tile arrangement, the positioning area is equivalent to the area intended for positioning; that is, there are no uncovered regions next to the borders. Hence, the results obtained for this tile arrangement cannot be affected by missing samples at the borders due to the impossibility of covering the entire area intended for positioning. Then, for this case (a tile arrangement with \(S_{S}=50\) mm and \(N_{SS}=10\)), the CDF curve depicted in Figure 26 can be considered a trusted reference; that is, it is not shifted by the effect of tiles not fitting into the scenario. Next, we aim to determine whether there is a characteristic pattern of the error distances when samples from the MTT dataset are observed in the positioning area. In this context, a characteristic pattern would be, for example, some kind of concentration of the error distances into some parts of the 2D positioning area. In particular, we will observe the pattern for the error distances in samples next to the borders.