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.