Fig. 20: Percentage of localization error vs. Average Hop Counts
vs. Communication Range.
For the analysis of the data presented by Table 5, the equation (24)
modifies by replacing a variable \({}^{\prime}m^{{}^{\prime}}\) by another variable\({}^{\prime}R^{{}^{\prime}}(i.e.\ communication\ range)\) and another equation (26) is
obtained-
\begin{equation}
LE=\left\{\begin{matrix}1.1429\ R\ +\ 16.21056\ Hop_{\text{count}}\ -\ 60.4726;for\ DV-Hop\\
0.08077\ R\ +\ 4.77295\ Hop_{\text{count}}\ -\ 3.97544;for\ IDV\\
\ -0.43927R\ +\ 0.03471\ Hop_{\text{count}}+\ 20.55158;for\ ODR\\
\end{matrix}(26)\right.\ \nonumber \\
\end{equation}The equation (26) along with Table 5 exposes the cause behind the
reduction in localization error due to the increase in the communication
range. Table 5 demonstrates an interesting trend that with the rise in
communication range the hop counts start falling. Therefore \({}^{\prime}R^{\prime}\) and\(\text{Ho}p_{\text{count}}\) are inversely proportional to each other.
Further all the three prepositions of the equation (26) state that the
effect of \(\text{Ho}p_{\text{count}}\) is many more times than the\({}^{\prime}R^{{}^{\prime}}.\) Hence if at any stage \({}^{\prime}R^{\prime}\) is enhanced, the drop in\(\text{Ho}p_{\text{count}}\) becomes strongly prominent to pull back
the localization error several times.
Further, the investigation of the equation (26) shows that the ODR is
more and more dependent upon \({}^{\prime}R^{\prime}\) rather than\(\text{Ho}p_{\text{count}}\), which establishes its efficiency to
exploit the antenna capabilities of a sensor more than the DV-Hop and
IDV, because in DV-Hop and IDV the prominent factor is\(\text{Ho}p_{\text{count}}\) rather than \({}^{\prime}R^{\prime}\). Even the equation
(26) shows that the localization error will remain quite low in contrast
with DV-Hop and IDV.