## 5 Performance Evaluation
### Localization Success  
Localization success is defined as the ratio of nodes in the entire network that could be localized successfully [2; 28]. RLS is an event-driven localization scheme, so the ratio of localized nodes should be evaluated as detector sensors (the sensors that receive an event). In simulation, all sensor nodes will detect the event, at least once. The average localization success is defined as:  
\[Avg_{LS}=\frac{\sum_{i=0}^{n}\frac{N_{t}\times N_{t}}{N_{d}}}{n} \tag{11}\]  
where \(Avg_{LS}\) shows the average localization success and \(N_{t}\) is the total number of sensor nodes deployed in the 3D space. The number of localized nodes and the number of detector sensors are shown by \(N_{t}\) and \(N_{d}\), respectively. We average the sensor location estimation over 100 trials, so \(n\) is the number of instances, which set to 100. Figure 7: Average localization success. (**a**) Beacon nodes with random distribution; (**b**) Versus Grid deployment in water surface. Figure 6: (**a**) Random distribution; (**b**) Grid anchor deployment. High average localization success is desired by RLS due to its targets for surveillance applications and disaster preventions. Consequently, a detector sensor is a should-do-localized sensor node in RLS localization scheme. This metric is illustrated in Figure 7.  
As can be seen, the localization success of RLS increases with increasing percentage of anchor nodes, while the ratio of localized nodes does not change much when we deploy more sensor nodes in the volume. Compared to SLMP [8], RLS can achieve a high level of localization ratio (approximately near 100%) with only 8% anchor nodes, while SLMP strictly depends on the node density to achieve around 95% of coverage with 10% anchor nodes [8]. It is shown in [47,48,49] that range-based distributed localization schemes have relatively high requirements on the node density of the network. This represents an advantage of RLS which is independent of the node density. Our proposed method can achieve a high localization ratio, as it is shown in Figure 7(a), without any requirement on the node density. The reason is that our scheme does not depend on communication between sensor nodes. It depends on communication with surface anchors. It means that this method is appropriate for both dense and sparse deployments. Figure 7(a) shows us that the localization ratio increases slightly with the number of sensor nodes, which is the result of the increase in anchors based on the node number percentage. Hence, we can infer that the more the anchor percentages, the higher the localization success. As illustrated in Figure 7(b), anchors with grid deployment help provide a higher localization ratio compared to random anchor deployment seen in Figure 7(a). The issue of anchor node's placement should not be neglected [30]. Anchor node's effective placement can greatly improve the localization ratio. In grid deployment, the localization ratio can reach to its highest level with 100% localization success with 150 sensor nodes and an anchor rate 12%, while in anchor random deployment, we should increase the number of sensor nodes up to 300 and the anchor rate to 12% to achieve the same amount of localization ratio. The reason is that in the anchor node deployment in grid manner, many more help transmit the messages to the anchors. In fact, this deployment guarantees the presence of at least three anchor nodes in communication range of each ordinary sensor node. Hence, the localization ratio will be increased. It is obvious that an anchor node's effective placement cannot use some localization schemes like SLMP [8], where anchors are floated among ordinary sensor nodes in the network. Based on th comparison between RLS and LSL and DNRL in [2] with the same assumptions, it is obvious that our scheme outperforms both LSL and DNRL in terms of localization ratio. To reach around 80% of localization ratio, DNRL and LSL with 250 sensor nodes, require 10% beacon coverage.