The average value is calculated after each setup during an experiment
illustrates localization error (LE) as defined by the equation (21).
\begin{equation}
\begin{matrix}\left.\ \begin{matrix}LE=\frac{\sum\text{Distance\ between\ estimated\ localized\ poition\ and\ actual\ position}}{R\ \times\ total\ number\ of\ unknown\ nodes}\ \times\ 100\%\\
=\ \frac{\sum_{i=1}^{U_{n}}\sqrt{\left(x_{\text{ai}}-x_{\text{ei}}\right)^{2}+\left(y_{\text{ai}}-y_{\text{ei}}\right)^{2}}}{RU_{n}}\ \times\ 100\%;\\
\end{matrix}\right\}&(21)\\
\end{matrix}\nonumber \\
\end{equation}where\(\left(x_{\text{ai}},\ y_{\text{ai}}\right)\ and\ (x_{\text{ei}},y_{\text{ei}})\)are the actual and estimated coordinates respectively of the unknown
node \({}^{\prime}i^{\prime}\).
The localization error definition, from equation (21), can show its
relationship with the communication range. Therefore a substantial value
of the communication range may improve the localization accuracy
dramatically. But in real life, the communication range is never able to
cover a region uniformly in all the directions as shown in Fig. 2 also.
So it is inappropriate to analyze the performance of any model based on
a regular-shaped coverage area. Rather the communication range should
bear a random effect of attenuation during simulation experiments. To
exhibit the effect of random attenuation of communication range on
localization accuracy, the concept of ranging error is introduced in the
simulation environment. The experiments performed show the performance
of DV-Hop, IDV, and ODR under the environment when there is no ranging
error as well as when the network is affected by ranging error. The
ranging error is considered under three different slabs i.e. 0- 10%, 0-
20%, and 0- 30% of the communication range. The communication range
got attenuated by taking value from the ranging error slabs in a random
fashion during an experiment.
After the communication range; the number of unknown nodes is another
term that affects the performance of the localization error as shown by
the equation (21). Hence it is a need to perform experiments for the
analysis of the proposed model ODR along with the referenced model (i.e.
DV-Hop and IDV) based on two variables, where one variable is the
unknown nodes’ percentage and the other variable is communication range.
Therefore to cover all possibilities three experiments are simulated. In
Experiment 1, the relationship between anchor nodes and localization
error is discussed. The second, Experiment 2, marks the effect of
communication range on the localization error. The last simulation setup
studies the localization error due to some variations in the total
number of nodes, in Experiment 3.