## 4 Performance Evaluation
### Performance Evaluation Using MATLAB Simulation  
The performance of the proposed path models is first compared using MATLAB simulation. For wireless model, the specifications of wireless nodes that was equipped with ESP 23 node are employed in simulation. The network area is assumed to be a square area of size s = 50 \(\times\) 50 m\({}^{2}\), 40 unknown nodes deployed with communication range 15 m, and one mobile anchor node is used. Each point in the results is the average of 10 experimental runs. The distance between the mobile node and the unknown node at each pausing point is calculated as follows:  
\[\mathrm{D}=\mathrm{D}_{0}*10^{\frac{RSSI-RSSI_{0}}{10\mathrm{p}}}+\sigma \tag{22}\]  
where RSSI is the received signal strength indicated at distance D, RSSI\({}_{0}\) is the received signal strength indicated at the reference distance D\({}_{0}\), n\({}_{\mathrm{P}}\) is the power loss exponent, and \(\sigma\) is the standard deviation of noise. Estimating the distance using RSSI measurement suffers from high errors caused by signal fading and blockage of the signal by obstacles. To overcome the problem of blockage of signals due to obstacles, in the path design, the mobile node has to move around obstacle and not crash with it. For noise fading through simulation, we should guarantee that \(\sigma\) and n\({}_{\mathrm{P}}\) values chosen during calculations are suitable to the nature of the noise and obstacles in the environment. The list of parameters is shown in Table 1.  
Figure 10: Mobile anchor node with MAX471 Voltage and Current Sensor Module Consume Voltage Load Detection Module. The performance of the proposed of the proposed models is evaluated using the following metrics: average localization error, standard deviation of localization error, localization coverage ratio, path length, and power consumption. 1. Average localization error. Figure 11 shows the average localization error of the two path models compared to H-Curve. In simulation results, as observed from Figure 11, the Arrow-Curve achieves higher accuracy results in comparison to H-Curve and R-Curve. Arrow-Curve achieves an average localization error less than H-Curve by 11%. R-Curve model has the lowest accuracy values in most resolutions near to H-Curve model results, however, because it is not a symmetric path model as shown previously in Figure 3, where the non-localized nodes that exist in the second and fourth sub-fields do not receive sufficient localization information from the mobile anchor node and, hence, their position accuracy will decrease. In the analysis of sub-field(s) shown in Figure 12, 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. 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 also depends on the type of path model. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network area size & \(50\times 50\) m\({}^{2}\) \\ Number of mobile anchor nodes & 1 \\ Number of unknown nodes & 40 \\ Resolution L & L = 10, 12.5, 15, 17.5 \\ Path loss exponent (n\({}_{\text{p}}\)) & 3.3 \\ RSSI\({}_{0}\) (D\({}_{0}\)) & \(-59\) \\ D\({}_{0}\) & 1 m \\ Standard deviation of noise (\(\sigma\)) & 4 \\ Communication range & 15 \\ Simulation run times & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental Parameters. Figure 11: Average localization error (m) corresponding to resolution (L) in Arrow-Curve model, R-Curve model, and H-Curve. 2. Standard deviation of position error. The standard deviation error is calculated at different values of resolution. Figure 13 illustrates the standard deviation error values at different resolutions. Arrow-Curve achieves lower standard deviation values, which means it is very close to average.