## 7 Evaluation and Results
### Localization Accuracy
#### 7.1.1 Average Localization Error  
The average localization error is indicated as the calculated distance between the real location and the estimated location of the localized node. It is used to determine the degree to which the localization estimation is accurate. The node localization error is formulated as  
\[error_{(i)}=\sqrt{(x_{i}-u_{i})^{2}+(y_{i}-v_{i})^{2}} \tag{7}\]  
where \((x_{i},y_{i})\) are the true coordinates of the node \(i\), and \((u_{i},v_{i})\) are the estimated ones of the same node \(i\). Therefore, the average localization error, \(error_{avg}\), for the entire number of unknown nodes, \(N\), is calculated as:  
\[error_{avg}=\left(\sum_{i=1}^{N}error_{(i)}\right)/N \tag{8}\]  
where \(N\) is the total number of sensor nodes. However, to study the behaviour of the proposed model and compare it to the others, we first executed a test of 50 simulation runs with 250 unknown nodes, a maximum movement distance, \(d_{max}\), of 70 m, and a standard deviation of noise, \(\sigma\), of 3. Figure 11 shows the performance of the different models based on localization error when both WCL and WCWCL were used. Figure 11a shows that FLPPL offers lower error rate, thus, higher localization accuracy in most of the presented results when WCL was used. A range of localization errors between 0.434 m and 2.439 m were achieved. The dynamic path planning of NLA_MB also presented a better performance in comparison to the other static models of SCAN, LMAT and Z-curves. While LMAT was proposed  
Figure 11: Localization errors of all mobility models in (**a**) WCL, and (**b**) WCWCL, (\(d_{max}=70,\sigma=3\)). for a better performance as a static model [8; 10], when the MA movement is constrained, there is no significant difference to the other static models. This may help to prove that the dynamic path planning models are more suitable in such cases where the MA movement is limited and there is a need to take the network topology and nodes deployment into account in the movement decision making. The same assumptions were used again with WCWCL scheme, as shown in Figure 11b. Higher localization estimation was achieved by decreasing the localization error using WCWCL. FLPPL again provided higher performance of accuracy by offering lower localization error, which therefore means more accurate estimation. Once more, NLA_MB shows higher estimation of node locations with minimal locations error compared to the implemented static models. On average, WCWCL attained better results than WCL due to the fact of given the nearby anchors more impact on the estimation and calculation of the locations. For example, FLPPL yielded an average of 0.898 m with a range of errors between 0.345 m and 1.960 m in comparison to the higher results of the same assumptions in WCL. Moving on to the average localization error for all path models when different maximum movement distance, \(d_{max}\), are used, Figure 12 shows the performances when WCL and WCWCL are implemented. We conducted two experiments using the parameters shown in Table 7 with two changeable values, the maximum movement distance, \(d_{max}\), and the standard deviation of noise, \(\sigma\). In the first trial, we ran a test of 250 unknown nodes with different movement distances ranging between 35 m and 210 m and \(\sigma=3\). Figure 12 presents the average localization error for the proposed model along with the others when WCL is used, while Figure 12b shows the average localization error when WCWCL is used. FLPPL and NLA_MB offered the best results with slight distinctions in both WCL and WCWCL. FLPPL shows superior results with all movement allowances. In general, WCWCL provides better results with all path models including the statics. However, the difference between the dynamic models of FLPPL and NLA_MB, and the rest of SCAN, LMAT and Z-Curve is very significant. For example, the localization error of the models when only 35 m of distance is allowed are 7.41, 8.06, 8.15, 1.90 and 1.78 m for SCAN, LMAT, Z-Curve, NLA_MB and FLPPL respectively when WCL is used.