## 4 Simulation
### Numerical Results  
Figure 5 shows the traveling distances of the mobile anchor with different numbers of unknown nodes. In this experiment, the communication range R is 100 m, and we calculated the traveling distance of the mobile anchor when the mobile anchor locates all unknown nodes. The average traveling distances of the mobile anchor when using the SCAN, SCAN-ET, SLMAT, and NHexCurve methods do not explicitly increase or decrease with an increasing number of unknown nodes, because the mobile anchor in these methods follows a prescheduled route. The traveling distance when using the NHexCurve method is the worst, because its movement trajectory creates a larger radio signal overlap area to improve the positioning. SLMAT also creates a larger radio signal overlap area than the SCAN method to solve the collinear problem when positioning an unknown node. The traveling distance of the mobile anchor when using SCAN-ET is better than when using the SCAN method when there are fewer unknown nodes. This is because the mobile anchor moves to the vertices of the triangle in a zone that can immediately position the unknown nodes. This makes it possible to reduce the total traveling distance in the next line segment used by the SCAN method to find the third point to solve the collinear problem. However, the SCAN-ET becomes slightly worse than the SCAN method when the number of unknown nodes is higher than 55, because the mobile anchor has a greater opportunity to move to the vertices of the triangle in each zone. By applying the ISP algorithm, the mobile anchor's average traveling distances when using the i-SCAN and MARS methods decreases with increasing numbers of unknown nodes. When using the i-SCAN method, the mobile anchor obtains more available reference points from neighboring-positioned nodes, such that the traveling distance decreases with increasing numbers of unknown nodes. The traveling distance of the mobile anchor is decreased by about 200 m to 1500 m when using i-SCAN compared with when using the original SCAN method. MARS uses the projection mechanism to prevent the mobile anchor from regularly following the traveling trajectories of the SCAN method, enabling the mobile anchor to further reduce its traveling distance by 400 m to 600 m compared to when using i-SCAN. In the following, we will show that the mobile anchor using MARS is able to exhibit shorter traveling distances when the unknown nodes are densely deployed. Figure 6 shows the traveling distances of all of the evaluated methods with different communication ranges. The number of unknown nodes in this experiment is 40. The mobile anchor is able to cover a greater area when using a long communication range. This also implies that the mobile anchor needs to travel less distance to be able to cover the entire deployment area. Therefore, the traveling distances of all methods decrease with increasing communication range. Figure 5: Traveling distances with different numbers of unknown nodes (R = 100 m). Because the moving trajectories of the mobile anchor in the SLMAT and NHexCurve methods generate more overlapping of coverage, their mobile anchor's traveling distances are still longer than that when using the SCAN method. The mobile anchor when using NHexCurve has a shorter traveling distance than that when using SLMAT when the communication range is 150 m. The mobile anchor when using NHexCurve is able to achieve a reduction in the number of horizontal scans when using a long communication range R. The mobile anchor's traveling distances when using SCAN-ET and SCAN are very close. SCAN-ET exhibits clearly better results than SCAN when using a short communication range. The reason for this is that the mobile anchor is able to immediately position the unknown nodes after visiting the triangle's vertices in a given zone. Therefore, the traveling distance of the mobile anchor can be reduced for the next line segment used by the SCAN method to find the third non-collinear reference point.