## 4 Performance Evaluation
### Performance Evaluation Using Node MCU  
In this section, we apply and compare the performances of R-Curve, Arrow-Curve, and the previously proposed H-Curve. Parameter Settings: The proposed models were implemented in hardware using Node MCU (ESP 32 (Wi-Fi-Bluetooth module)) [37] as a mobile anchor node and Node MCU (ESP 8266 (Wi-Fi module)) [38] and (ESP 32 (Wi-Fi-Bluetooth module)) as unknown nodes. The network area is assumed to be a square area of size s = 20 \(\times\) 20 m\({}^{2}\) in the outdoor with communication range 28 m and has a size s = 8 \(\times\) 8 m\({}^{2}\) in indoor environment with communication range 9 m. A total of 20 unknown nodes are deployed in the outdoor square area and 10 unknown nodes are deployed in the indoor square area. The used sensors are Dust and Smoke sensors [39; 40], as shown in Figure 17a,b. We program the node using Arduino IDE software [41]. The experiment was run in an open-door environment where there are no obstacles and an indoor environment with obstacles. We find the distance between mobile node and the unknown node at each pausing point as illustrated in the following equation:  
\[\mathrm{D}=\mathrm{D}_{0}*10^{\frac{\mathrm{RSSI}-\mathrm{RSSI}_{0}}{10\mathrm{ p}}} \tag{23}\]  
where RSSI is the received signal strength indicated at distance \(\mathrm{D}\), RSSI\({}_{0}\) is the received signal strength indicated at the reference distance \(\mathrm{D}_{0}\), and n\({}_{\mathrm{p}}\) is the power loss exponent. The list of parameters is shown in Table 2.  
Figure 16: Power consumption (mw) corresponding to resolution (L) in Arrow-Curve model, R-Curve path model, and H-Curve. Figure 17: (**a**) Dust sensor; (**b**) smoke sensor. The performance of the proposed models is evaluated using the following metrics: average position error, standard deviation of localization error, localization coverage ratio, number of pausing points, path length, and power consumption. 1. Average localization error. Figure 18 shows the average localization error of the two path models compared to H-Curve. Arrow-Curve achieves high accuracy results in comparison to H-Curve and R-Curve in indoor and outdoor environments. Arrow-Curve achieves average localization error results less than H-Curve by 5% in outdoor and 9.6% in indoor. R-Curve is the worst model in both cases because it is not a symmetric path model. As shown in Figure 3, the non-localized nodes that exist in the second and the fourth sub-fields do not receive sufficient localization information from the mobile anchor node so, their position accuracy will decrease. In analysis of sub-field(s) (outdoor environment) as shown in Figure 19, the Arrow-Curve has the lowest average localization error in each sub-field because the locations of the mobile anchor node pausing points is at the middle of each edge. However, the R-Curve achieves the lowest results because it is non-symmetric in shape. Moreover, in sub-field (indoor environment) as shown in Figure 20, Arrow-Curve achieves high results in comparison to R-Curve and H-Curve as the mobile anchor node pausing points locations are at the corners of each sub-field. The value of localization error in each sub-field depends on the location status of the unknown node; whether it is in the corner of the sub-field or in the middle and the type of path model, and in indoor environment, it depends on the existence of obstacles in the mobile node path in each sub-field. Figure 19: Average localization error (m) corresponding to sub-field (S) number at resolution (L) in outdoor environment: (**a**) L = 20; (**b**) L = 17.5; (**c**) L = 15; (**d**) L = 12.5; (**e**) L = 10; (**f**) L = 7.5. Figure 20: _Cont._  
2. Standard deviation of position error. The standard deviation error is calculated at different values of resolution. Figure 21 illustrates the standard deviation error values at different resolutions in outdoor environment and indoor environment. Arrow-Curve achieves lower standard deviation values, which means it is very close to the average.