## 5 Performance Evaluations
### Scalability  
Scalability means localization performance is independent of the number of UNNs in the ROI. In this paper, the number of UNNs has been changed from 50 to 250 and uses the resolution of 1 and a std of noise \(\sigma=7\) to test the path planning models' scalability. Figure 17a shows the change of the path planning models' average error performance according to different node volume for the WCL method. First of all, it can be seen from Figure 17a that the H-curve and the proposed NHHexCurves models show the best error performance of all the node numbers. Additionally, it can be said that the localization error values of NHHexCurves are almost unchanged and remain constant against the changing number of nodes. When the scalability performance of the models for WCL is evaluated, it is observed that the error performance of all models does not change much with the  
Figure 16: Localization ratio of the path planning models by resolution (\(\sigma=7\)) (**a**) WCL, and (**b**) APT.  
changing volume in nodes. This can be explained by the fact that the localization method used is WCL and the statistical distribution of UNNs deployed on the network is uniform. In terms of localization error performance, it can be said that all mobile path planning models are largely scalable for the WCL method. If the same evaluation is applied to the APT localization method, it cannot be said that the error performance of all models varies significantly with the changing number of nodes again. The error values are lower due to the nature of the APT method, and again, the H-curve showed the best error performance in all node count cases. Although the models' error values are similar, the Z-curve is set apart from the other models because it produces a slightly higher error value. The error value of the proposed model NHexCurves changed much less than other models with the changing volume of nodes. Therefore, it can be said that NHexCurves is the best model in terms of scalability performance compared to other models for both WCL and APT localization methods.  
Figure 17: Scalability of the path planning models in terms of localization error performance (**a**) WCL, and (**b**) APT.  
Figure 18a shows the localization ratio performances of the path planning schemes for the WCL according to the varying number of nodes. As seen from the figure, each path planning model has localized almost all of its nodes in this resolution value. Moreover, the localization ratios of each method have not changed with the changing number of nodes. The same determination can be made for the APT method; the same scenario for APT appears in Figure 18b. Using this method, NHexCurves has the best localization ratio for all node numbers among path planning models. This ratio is approximately 90% and has not changed much according to the number of nodes. M-curves and Z-curve models produced results very close to NHexCurves. When considering the changing volume of nodes, the localization ratio performance of these three models is better than the other models. However, according to the changing number of nodes, the HILBERT model's localization ratio performance was noticeably worse than the other models, which is an expected result as explained in the previous chapters.  
Figure 18: Scalability of the path planning models in terms of localization ratio performance (**a**) WCL, and (**b**) APT.