## 5 Feasibility Study Through System Simulations
### Mechanisms to Optimize the Models and Minimize the Error Distance
#### 5.7.1 Mechanism 1: Selection of the NN Structure  
The first mechanism consists of the selection of the structure of the NN. The goal is to select a suitable NN structure such that the model can deliver results with a minimum positioning error. In this regard, we tested a number of NN structures to determine those to be used in each pattern-matching method. The selection of the NN structures was carried out using two tile arrangements (introduced in Section 5.9) for evaluation. The first tile arrangement uses \(N_{SS}=7\) and \(S_{S}=50\) mm. The second tile arrangement uses \(N_{SS}=11\) and \(S_{S}=50\) mm. The simulation process presented in Section 5.6 was executed for each one of the four pattern-matching methods, with different NN structures and using the two selected tile arrangements, for at least 200 different sets of random initial weights. We kept the bestresult in each case, measured by the minimum error distance at the 95 th percentile (\(P_{R}\) cut) of the CDF of the error distances resulting from the MTV dataset. Actually, for the method 1-SingFingIn-PosOut, we considered the error distances resulting from all of the sub-tiles in the whole positioning area on the basis that there were more pointwise samples contributing to the statistics. For the method 2-SingFingIn-AggPosOut, we did not compute the aggregation of the estimated position results. In this particular case, the method 2-SingFingIn-AggPosOut is equivalent to executing the method 1-SingFingIn-PosOut considering all of the sub-tiles in the whole positioning area. The rationale is that if we select an optimal NN structure considering the minimization of the error distances for all of the sub-tiles in the whole positioning area, any possible enhancement in minimizing the positioning error attained from the aggregation of the results (positions) in the method 2-SingFingIn-AggPosOut is independent of the selection of the NN structure. Therefore, we selected the same NN structure for the methods 1-SingFingIn-PosOut and 2-SingFingIn-AggPosOut. For each pattern-matching method and tile arrangement, we tested different NN structures by changing the activation functions, the number of layers, and layer width in a quest to find the NN structure that minimized the error distance. Initially, we searched for an optimal NN structure through systematic experimentation with a grid search [210]. Then, from the best NN structure found by the grid search, we tested making corrections by changing the NN structure as a function of the results observed. In the case of the FFNNs, we observed that adding more layers or increasing their width resulted either in overfitting or in larger error distances in the estimated position results. After several cycles of changing the NN structure, we found the suitable the NN structures shown in the next subsection. In the actual process, we tested the lighter pattern-matching methods many more times, and with many more combinations in the NN structure, than the heavier ones, in the order 1-SingFingIn-PosOut, 3-MultFingIn-PosOut, and 4-MultFingIn-ClassOut. This approach was carried out in an attempt to minimize the possibility of not identifying a case in which a lightweight method could perform as well as a heavier one. It is noted that this process was carried out only in the tests with the two tile arrangements mentioned above. The best-performing NN structures found from these tests were reused for different tile arrangements in the benchmark tests that follow. Mechanism 1 is shown in step 4 of the block diagram describing the model training execution flow, in Figure 15. It is noted that in the block diagram, Mechanism 1 appears with a label drawn with a dashed line. This is to distinguish that Mechanism 1 is not programmed as part of the simulation process for the final benchmarking of all of the pattern-matching methods and tile arrangements considered.