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.