## 6 Results of the Simulations
### Comparison of the Results Among the Pattern-Matching Methods
#### 6.6.1 Comparison of the Results Obtained Using the Smallest 2D Sensor Array Considered  
From the results for all of the pattern-matching methods, we select the ones resulting from the smallest 2D sensor array considered for the three side lengths of the sub-tiles considered, namely the following:  
* \(S_{S}=30\) mm with \(N_{SS}=6\);
* \(S_{S}=50\) mm with \(N_{SS}=5\);
* \(S_{S}=70\) mm with \(N_{SS}=5\).  
Next, we compare how the different pattern-matching methods perform against one another in these cases in terms of minimizing the error distance. This comparison is presented in Figure 21. The results present the same pattern for the three side lengths of the sub-tiles \(S_{S}\) considered. The methods 3-MultFingIn-PosOut and 4-MultFingIn-ClassOut perform better than the other methods. The method 4-MultFingIn-ClassOut performs slightly better than the method 3-MultFingIn-PosOut, although the difference may be negligible for practical considerations. The method 2-SingFingIn-AggPosOut performs better than 1-SingFingIn-PosOut but worse than 3-MultFingIn-PosOut and 4-MultFingIn-ClassOut.  
The results found for each sub-tile size and pattern-matching method for the case of the smallest 2D sensor array are summarized in Table 15. The table lists the number of NN parameters for each combination of \(S_{S}\) and \(N_{SS}\) and pattern-matching method.  
The first and most important observation is that all of the methods that include spatial side information perform much better than the method that does not use side information, 1-SingFingIn-PosOut. The second observation is that by relying on a more expensive NN model, in terms of the number of NN parameters, a better performance result can be obtained for the same input data. A third observation is that aggregating the results in the fingerprint domain (with the methods 3-MultFingIn-PosOut and 4-MultFingIn-ClassOut) produces better results than aggregating the position results in the position domain (with the method 2-SingFingIn-AggPosOut).  
As discussed above, we observe in Figure 21 that the methods 3-MultFingIn-PosOut and 4-MultFingIn-ClassOut perform almost the same in terms of the practical considerations. Assuming an equal distribution of the error distances for both methods, we can conclude that pattern-matching method 3-MultFingIn-PosOut is less expensive to implement than the method 4-MultFingIn-ClassOut in terms of the number of parameters required by the respective NN models. That is, the method 4-MultFingIn-ClassOut requires about 3.8 to 5.2 times more parameters than the method 3-MultFingIn-PosOut to produce presumably equal results. Thus, when adopting spatial side information, if the performance of the smallest sensor array is suitable for a given use-case, pattern-matching method 3-MultFingIn-PosOut would be the choice when aiming for a lighter method in terms of the computing resources.  
It is noted that the column in Table 15 indicating the number of NN parameters for the method 2-SingFingIn-AggPosOut includes the number of instances of, or calls to, the NN model implemented in this method. The NN model is executed for each one of the \(N_{ST}\) sub-tiles in the tile. This is provided to indicate that for this method, the number of NN parameters alone is not representative of the computing cost of this method.