## 4 Performance Evaluation
### Simulation Results
As shown in Figure 11, we observe that the average energy  
Figure 10: Average localization time for different number of beacon nodes. Figure 9: Average estimated localization error for different communication ranges. consumption is increased if number of normal nodes is increased. Besides, the residual power decreases if communication range of the normal nodes increases. This is because of the more power consumption due to higher communication range. The comparison of the performance of our DIstributed Localization (DIL) algorithm is made with other similar localization algorithms CAB [5] and APIT [11]. The concentric anchor beacon (CAB) localization algorithm uses a small number of anchor nodes. Each anchor emits several beacon signals at different power levels, which are received by the sensors to calculate their location. We have considered CAB to compare with our simulation results, as we use three beacons that transmit signals to the normal nodes. The normal nodes calculate their location based on the RSSI values of the beacons. In APIT (Approximate Point In Triangle), a reference node sends location information periodically to the sensors. Then each sensor makes triangles based on the received location information of the reference nodes in order to calculate its own location. We compare APIT with our simulation results, as in our protocol,  
Figure 11: Average residual power for different number of beacon nodes. Figure 12: Comparison of average estimated localization error for different number of beacon nodes. the beacon node transmits the location information to each normal node, which ultimately calculates its location. As shown in Figure 12, the average localization error of our algorithm is compared with CAB and APIT for different number of beacon nodes. It is observed that the average localization error decreases if number of beacon nodes increases. If the number of beacon nodes is about 40, the average estimated localization error of our scheme can have up to 18.36 \(\%\) error, whereas CAB and APIT can have larger localization error, which is up to 22.82 \(\%\) and 32.17 \(\%\), respectively. Obviously, DIL can have better performance over CAB and APIT. Besides, CAB can have limited improvement in localization error if number of beacon nodes is increased, but we can get better localization accuracy of normal nodes if number of beacons are increased in our protocol. As shown in Figure 13, we simulate and compare with CAB and APIT to study the effect of different standard deviation (\(\sigma\)) on estimated localization error. It is noted that the standard deviation has slight effect on other two schemes, but have larger effect on our algorithm. It is reasonable in case of CAB and APIT as they do not use RSSI to find location of a node. Figure 14 shows the average estimated localization error with variation in communication range. Our algorithm as well as APIT scheme have better performance when the communication range increases. Since the communication range increases, it implies that more normal node can receive more beacon packets from different beacon nodes. Thus, the accuracy of localization is improved. However, CAB is not affected as the beacon nodes in CAB always transmit data with fixed power level. Beside, it is found that the average estimated localization error is decreased if the number of beacon nodes is increased. Figure 15 indicates the comparisons of localization time for different protocols, while different localization schemes are executed. The results show that DIL algorithm gives better performance on localization time, which is due to the limited transmission overheads. It is to be noted that, in our protocol, each anchor node and beacon nodes transmit packets to their neighbors only once. Figure 13: Comparison of average estimated localization error for different standard deviations.