Fig. 10: Percentage of localization error vs. percentage of anchor nodes with 0-30% ranging error.
For better understanding, equation (1) is rewritten as equation (22).
\begin{equation} H_{\text{siz}e_{p}}=\frac{\text{Total\ distance\ between\ p\ and\ other\ anchor\ nodes}}{\text{Total\ HopCounts\ between\ p\ and\ other\ anchor\ nodes}}\ (22)\nonumber \\ \end{equation}
Here as per the equation (22), the hop size of an anchor node is dependent upon the hop counts only because the distance in between anchor nodes’ pair is an unmanaged value. If the hop counts value is less than the required value then the hop size is more than the necessary value. It implies that the distance estimated with the help of hop size is more than the exact straight line distance between a node pair. On the other side, if the hop counts value is more than the requisite value than the hop size leads to a less distance estimation. Therefore hop size calculation gets improved with an increase in the anchor nodes up-to a certain extent, which reflects improvement to localize a node. Since ODR is nearly free from equation (1) to estimates the distance between an anchor node and an unknown node as well as put efforts to approximate Euclidean distance, therefore, the effect of hop size assessment does not affect much in comparison to DV-Hop algorithm and IDV.
Fig. 7 shows the performance of the models when communication is not affected by ranging error, here ODR improves the results by more than 22% and 9% in comparison to DV-Hop and IDV respectively. The simulation results obtained through Fig. 8 to Fig. 10 shows the localization error in the presence of the random effect of ranging error. The simulation using ranging error shows the localization error for ODR is smaller by 23%, 27%, and 36% than DV-Hop as shown by figures 8, 9, and 10 respectively. Whereas at the same time experiment exhibits the reduction of error due to ODR is more than 11%, 10%, and 11% in comparison to IDV as plotted by Fig. 8, 9, and 10 respectively.
Here Experiment 1 infers a finding that the increases in ranging error increase the localization error also for all the models- DV-Hop, IDV, and ODR. But in all the results plotted by Fig. 7 to Fig. 10, it is also apparent that the proposed model ODR is more robust and less error-prone.