## 4 Simulation
### Numerical Results
This simulation only uses the deployment results that satisfy the requirements of sparse and dense deployment. Figure 8a presents the results obtained for the dense deployment scenario. Without obtaining the information from the position-aware neighbor nodes, the traveling distances of the mobile anchor when using the SCAN, SLMAT, NHexCurve, and SCAN-ET methods slightly increase with increasing numbers of unknown nodes. The mobile anchor still has a greater traveling distance when using both SLMAT and NHexCurve than when using the other methods, because they regularly follow the prescheduled trajectory, which is longer than that of the SCAN method. SCAN-ET exhibits better results than the others because it smartly determines whether the mobile anchor needs to visit the vertices of a triangle in a given zone. Conversely, the traveling distances of the mobile anchor when using i-SCAN and MARS decrease with an increasing number of unknown nodes. The ISP algorithm uses the positioned nodes to reduce the number of unknown nodes that need to be located by  
Figure 7: The percentage of positioned unknown nodes with limited traveling distance. the mobile anchor. i-SCAN receives the advantages of the ISP algorithm, and as such, the traveling distance of the mobile anchor is better than that obtained when using the other SCAN-like methods. The traveling distance is only about 68% to 84% of that obtained when using the SCAN method. MARS uses the ISP algorithm and smartly determines whether to change the prescheduled scan trajectory employed by the SCAN method. Therefore, MARS exhibits outstanding results compared to the other methods. The traveling distance of the mobile anchor is only about 45% to 70% of that obtained when using the SCAN method. Figure 8(b) presents the results for the sparse deployment scenario. The mobile anchor scans almost the whole deployment area following its prescheduled trajectory in the SCAN, SLMAT, and NHexCurve methods, because the unknown nodes are scattered everywhere. Similarly, the ISP algorithm also cannot leverage its advantages here. This is evidenced by the almost identical traveling distances of the mobile anchor when using the SCAN and i-SCAN methods. The traveling distance of the mobile anchor when using the SCAN-ET method depends on whether the mobile anchor detects unknown nodes in a zone. Therefore, its results are better than those obtained with SCAN and i-SCAN. The traveling  
Figure 8: The traveling distance in the dense and sparse deployment scenarios. (**a**) Dense deployment scenario, which is the scenario favorable for the ISP algorithm. The topology of the deployed unknown nodes is a strongly connected graph. Each unknown node can be connected to any other node. (**b**) Sparse deployment scenario, which is the scenario unfavorable for the ISP algorithm. The unknown nodes are not able to find any neighbor nodes within their communication range. distance of the mobile anchor is about 10% to 3.7% of that when using the SCAN method. MARS still achieves better results than other methods, even though the advantage of the ISP algorithm is not applicable. MARS uses the projection mechanism to determine whether the mobile anchor can skip the next line segment of the movement trajectory employed by the SCAN method in order to help the mobile anchor shorten its traveling distance. The traveling distance of the mobile anchor is about 15% to 21% of that when using the SCAN method. Table 1 shows the positioning size of the positioning area for the non-ideal signal scenario. The maximum communication range in this simulation is 100 m, and the number of unknown nodes is 40. The error ratio increases with increasing size. The positioning area of the SCAN, SLMAT, NHexCurve, and SCAN-ET methods are about 17 m\({}^{2}\)-20 m\({}^{2}\), 14.72 m\({}^{2}\)-19.26 m\({}^{2}\), 15.35 m\({}^{2}\)-19.38 m\({}^{2}\), and 14.45 m\({}^{2}\)-19.4 m\({}^{2}\), respectively. These methods use the triangulation method to locate unknown nodes.