## 5 Performance Evaluation
### Simulation Results
The x-axis represents the average energy consumption of the whole network at each localization interval, which was calculated by summing up the energy consumption of all the nodes at each localization interval, and averaging the result over time (excluding the first localization intervals, in order to eliminate the initialization effects) and over the 5000 simulations. The y-axis represents the distance estimation accuracy at the furthest neighbor, which was calculated from the average number of received packets at the furthest neighbors. This value was obtained by taking, at each localization interval, the furthest neighbor for each node of the network, and averaging the number of packets received by these nodes. Then the results were averaged over time (excluding the first localization intervals) and over the 5000 simulations. From the number of received packets, the accuracy of the distance estimation was calculated according to the expressions of the TOA-based and RSS-based distance estimations which are derived in Appendix A and B. In the TOA case, the estimated distance is a Gaussian random variable given by Equation (24) with mean equal to the real distance and standard deviation given by Equation (25) for one-way TOA measurements or by Equation (26) for two-way TOA measurements. Figure 10 represents the accuracy as the ratio between the standard deviation of the distance estimation (\(\sigma\)) and the factor \(c\cdot\sigma_{t}\), which is the standard deviation corresponding to one one-way TOA measurement. Therefore, the accuracy in this figure should be read as relative to the accuracy of one TOA measurement. In the RSS case, the estimated distance is a log-normal random variable with variance given by Equation (32). Figure 11 represents the accuracy as the ratio between the standard deviation of the distance estimation (\(\Delta d\)) and the real distance \(d\), where the distance estimation variance was calculated for a channel with \(\sigma_{RSS}=2\) dB (for other values of \(\sigma_{RSS}\) the particular values of the relative accuracy change: they get bigger for bigger values of \(\sigma_{RSS}\), but the relation between the three strategies remains the same). Therefore, the accuracy in this figure should be read as a relative error in the distance (a percentage of the real distance). From these figures, it can be clearly noticed that the proposed method has a better performance regarding both the energy consumption and the accuracy of the distance estimations. The gain with respect to the other strategies is especially noticeable for short localization packets, which is the usual situation, as these packets do not carry any data information. Finally, we have evaluated the performance of the proposed strategy for a case in which the power consumption is not equal to the transmitted power (which is usually the  
It can be seen in Figure 12 that the proposed strategy is again the only one that guarantees the desired accuracy (\(n=5\)), but in this case its energy consumption (Figure 12) is a little bit higher than for strategy #2 (which does not guarantee the desired accuracy). To better understand this behavior, we show in Figure 13 the relation between the average energy consumption and the accuracy of the distance estimations for the different strategies. Figure 11: Relation between the average energy consumption per localization and the RSS-based distance estimation accuracy for the three strategies. (**a**) l = 4 bytes; (**b**) l = 40 bytes. Figure 10: Relation between the average energy consumption per localization and the TOA-based distance estimation accuracy for the three strategies. (**a**) l = 4 bytes; (**b**) l = 40 bytes. As it can be noticed, for a given energy consumption, the proposed strategy achieves better accuracy than strategy #2, and for a given accuracy, the proposed strategy has lower energy consumption. Our proposed method shows still a gain, but of lower entity with respect to the ideal case shown in Figures 10 and 11.