## 7 Evaluation and Results
### Localization Accuracy
#### 7.1.2 Standard Deviation of the Localization Error  
In addition to low localization error, a low standard deviation in localization error is desirable. The standard deviation of localization error is formulated as  
\[error_{std}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(error_{(i)}-error_{avg})^{2}} \tag{9}\]  
where \(N\) is the UNs number, \(error(i)\) is the localization error for each node \(i\), and \(error_{avg}\) is the average localization error. We examined the standard deviation of error from two aspects as in past experiments, the change of maximum movement distance, \(d_{max}\), and the change of standard  
Figure 13: Average localization error versus the standard deviation of noise (\(\sigma\)) of the mobility models in (**a**) WCL, and (**b**) WCWCL.  
deviation of noise, \(\sigma\). Figure 14 depicts the standard deviation of localization error rate for WCL and WCWCL, when \(d_{max}=70\) and \(\sigma=3\) for each run time.  
When WCL is used, as shown in Figure 14a, both FLPPL and NLA_MB interchangeably present low standard deviation of error results ranging between 0.68 m and 1.66 m in FLPPL, and 0.49 m and 1.59 m in NLA_MB. However, this is not the case when SCAN, LMAT or Z-Curve are used. Higher standard deviations of error are offered in all the 50 runs. One reason behind that is the nature of the design of the static models that does not consider the requirements of the network and the movement constraints. Even in the other scenario, where WCWCL was used, FLPPL and NLA_MB provided very small deviations with minimum values that could reach 0.38 m in FLPPL and 0.22 m in NLA_MB. Figure 14b shows the results of the all movement paths behaviour in WCWCL over the 50 simulation runs. However, while WCWCL improved the standard deviation of error results in both dynamic models, it increases the deviations in all the static models.  
We also calculated the average standard deviation of error of 50 simulation runs using different maximum distances, \(d_{max}\) which are shown in Figure 15.  
Figure 14: Standard deviation of errors of all mobility models in (**a**) WCL, and (**b**) WCWCL.  
Figure 15: Standard deviation of errors versus maximum movement in (**a**) WCL, and (**b**) WCWCL, (\(d_{max}=70,\sigma=3\)).  
In Figure 15a, the average standard deviations of error are shown when different maximum distances, \(d_{max}\) of 35 m, 70 m, 105 m, 140 m, 175 m and 210 m are used with WCL and \(\sigma\) is 3. Broadly, increasing the maximum movements increases the standard deviation of error especially when the static models are used. LMAT and Z-Curve show better results than SCAN when 35 m is used, however, the results change gradually till SCAN surpassed the other two when 210 m of movement is used. Both dynamic models kept the deviations around 1 m regardless of the value of \(d_{max}\). When WCWCL is applied, as shown in Figure 15b, the dynamic models again outperformed the other models with lower deviations this time with less than 1 m in all run times. However, the deviations increased in the static models when using WCWCL compared to WCL. Still, the deviations increase when the movement increases in all models.