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.