## 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
If, for example, there is a pattern in the error distances in which there is a concentration of a particular range of error distances close to the borders, the effect of the untiled stripes adjacent to the borders could lead to a change in the distribution of the error distances. In this case, a shift in the error distance CDFs would be a consequence of the different patterns of error distances contributing to the final distribution for a given tile arrangement and the resulting positioning area. We proceed to make an initial observation of the error distances in the positioning area. We use as reference the tile arrangement with \(S_{S}=50\) mm and \(N_{SS}=10\), which is the best result obtained using pattern-matching method 4-MultFingIn-ClassOut for \(S_{S}=50\) mm. Figure 27 shows with crosses the center positions of the moving tiles from the MTT dataset for this tile arrangement at the corresponding ground truth reference positions in the 2D positioning area in the scenario. The color of the crosses indicates the error distance according to the scale shown in the figure. In this figure, we do not observe any characteristic pattern that could lead to changes in the results. There is no characteristic concentration of the error distances close to the borders. Certainly, we can spot some clusters where certain ranges of error distances are concentrated in different parts of the positioning area; however, this is attributed to the radio channel realizations and a lack of enough samples. It should be noted that due to the symmetry of the scenario, the same statistics should be observed in the four quadrants of the positioning area. This observation is based on the symmetry of the scenario along the two coordinates. In this case, the density of the samples can be quadrupled in one-quarter of the scenario to obtain a more complete appreciation of the statistics of the results. Given the symmetry of the scenario, we can imagine dividing the scenario into four parts (in two halves, along each dimension) and then merging these four parts (mirroring along the vertical and/or horizontal axis accordingly) to increase the density of the samples. Figure 27: Positioning area in the selected scenario showing the center positions of the moving tiles from the MTT dataset, represented by crosses. The best result with pattern-matching method 4-MultFingIn-ClassOut for the tile arrangement with \(N_{SS}=10\) and \(S_{S}=50\) mm. The color of the crosses indicates the error distance according to the scale shown on the right side of the figure. Observing the other tile arrangements, we reached the same conclusions as those discussed above. For example, Figure 28 shows with crosses the center positions of the moving tiles from the MTT dataset at the corresponding ground truth reference positions in the positioning area in the scenario for a tile arrangement with \(S_{S}=30\) mm and \(N_{SS}=13\). In this figure, we do not observe any characteristic pattern that could lead to changes in the results. The observations above are based on a visual inspection of the samples. A formal study was carried out which consisted of removing a selection of samples from all of the samples covering the positioning area (the complete MTT dataset) to form a reduced dataset. This study was carried out for different tile arrangements. The samples removed were inside stripes of different widths, of up to 500 mm, adjacent to the inner borders of the area intended for positioning. Then, the error distance was calculated for the reduced dataset (without samples close to the borders). The CDF of the error distances corresponding to the reduced dataset was plotted and compared with the corresponding CDF considering all of the samples (the complete MTT dataset), such as the CDFs shown in Figure 26. We observed that the CDFs corresponding to the error distances from the reduced and complete datasets (the datasets without and with samples at the borders) almost overlapped, with negligible differences that could be attributed to the lack of enough samples.