Fig. 14: Percentage of localization error vs. communication range with 0-30% ranging error.
It is shown with the help of Fig. 11 to Fig. 14 that the localization error falls with the rise of communication range for ODR and as well as for DV-Hop and IDV also. The localization gets better with the increase in communication range because an unknown node comes closer by some hop counts to more anchor nodes. As more and more anchor nodes cover an unknown node with lesser hops the distance estimated between them is calculated with less number of hops. The lesser number of hops contributes less error because hop size is estimated as an average value only (equation (1)) with an inherent error. This localization improvement can be answered by the equation (2). Here the equation (2) is rewritten as equation (23).
\begin{equation} d_{i}=Hop\ Size\ per\ unit\ hop\ \times number\ of\ hops\ (23)\nonumber \\ \end{equation}
The localization accuracy is dependent upon the correctness of distance\(d_{i}\) between an anchor node and an unknown node. As the number of hop counts value reduces with the increase in the communication range so as the value \(d_{i}\) also reduces. Therefore with less number of hop counts up-to a certain value the distance \(d_{i}\) is estimated with more accuracy.
Here the equation (2) and (23) is applicable for the DV-Hop algorithm and IDV only. Therefore the correction in \(d_{i}\) with an increase in communication-range improves the localization accuracy for these two models gently. But IDV is completely away from the equations (2) and (23). IDV gets the benefit of the increased communication range just because of the improvement in calculating the point\(\text{CN}\left(\frac{\sum_{\forall i\epsilon K}x_{i}}{N(K)},\ \ \frac{\sum_{\forall i\epsilon K}y_{i}}{N(K)}\right)\ \)due to the increase in the arity of \({}^{\prime}K^{\prime}\).
The proposed model ODR is able to perform better than DV-Hop and IDV by 7% and 3% respectively when the network is considered to be immune to any kind of ranging error effect as shown by Fig. 11. The adverse effects of different ranging errors slabs (i.e. 0-10%, 0-20%, and 0-30%) are highlighted through Fig. 12 to Fig. 14. The network simulation under the influence of different ranging error slabs shows the localization error for ODR is lesser by 24%, 28%, and 37% than DV-Hop as shown by Fig. 12, Fig. 13, and Fig. 14 respectively. However, on the same configurations, the experiment (i.e. Experiment 2) exhibits the reduction of error by 12%, 11%, and 12% because of ODR in comparison to IDV as plotted by Fig. 12, Fig. 13, and Fig. 14 respectively.
Although Experiment 2 establishes the adverse effect of ranging error similar to Experiment 1 also but still ODR can localize the unknown nodes with better accuracy than DV-Hop and IDV. Furthermore, it is demonstrated that ODR is more robust even in the presence of ranging error and yields less localization error.