## 5 Performance Evaluation
### Localization Accuracy  
The underwater environment presents unique challenges to accurate localization [15]. Accuracy is defined by the mean error ratio, which is the average of the difference between the estimated location and the actual location of a node for location estimation [2]. RLS is a projection-based localization method while the location of detector sensors should be projected by receiver anchors on the water surface.  
There are some major sources of error in the localization process. By assuming the positions of anchor nodes are accurate enough, we can focus on the error sources between beacons and ordinary nodes. The localization error may arise from three sources [50]:  
* Time stamping uncertainty: it is expected that the timestamp field is generated just before the sending and as soon as the packet is received, but some delays may affect the accuracy of calculated range based on timestamps [51].
* Projection accuracy: in other existing projection-based localization schemes like USP [15], the position of anchor nodes are transferred by ordinary sensor nodes in the plane of node residence in the depth of the ocean, while this occurs with anchors in RLS. Each receiver anchor node employs the simple geometric relationship based on Equation (6) to project the location of detector sensor into the water surface. It is obvious that both ranging errors and depth errors negatively affect the accuracy of RLS as far as projection accuracy is concerned.
* Underwater multipath fading: any underwater location detection system will be greatly influenced by underwater multipath channel fading [22]. Some major factors influencing underwater multipath fading include water temperature and clarity, motion behavior of receiver and underwater objects, and transmission range.
* Node Movement: some external factors, such as temperature variations, wind, and ocean currents and so on, may cause underwater objects to move slowly [44]. The influence of this motion on localization introduces some errors due to the continuously changing position during message exchanges. Fortunately, current underwater sensor nodes can control passive mobility well and limit the relative speeds between sensor nodes to less than 0.1 m/s [52].  
Figure 8 illustrates the relationship between the mean error ratio and the number of sensor nodes. It is observed that with the increase of the nodes number, the accuracy of our scheme increases, but this increment is very limited, so the errors in RLS do not depend much on the node density. RLS works accurately for both sparse and dense underwater networks. Figure 8 also shows that the mean error ratio will decrease observably with the anchor ratio. For example, with 250 sensor nodes, when the anchor percentage is 3%, the localization error is around 0.07R. But when the anchor percentage is enlarged to 12%, it reduces to approximately 0.03. Thus, more anchor nodes can translate into smaller mean error ratios. This is because with the increase of anchor ratio, more anchors are available to receive the localization request messages from detector sensors, so the nodes have more anchors in their communication range to choose from.