## 4 Performance Evaluations
### Simulation Results
#### 4.2.2 Random Deployment  
Sometimes, in the case of random deployment networks, some nodes cannot be connected to their neighbors due to the fact that the geometric distance between them may be beyond their communication range. This may cause a localization method to fail to estimate the locations of these isolated nodes, so we appropriately improve the total number of nodes and the communication radius to avoid this. Approximately 350 nodes (including anchor nodes and sensor nodes) are randomly distributed in an area of 1000 m \(\times\) 1000 m. Table 5 shows the ALE results of the six methods when the total number of anchor nodes is 70 (20%) and the communication radius R varies from 100 m to 300 m.  
We can see from the simulation results in Table 5 that, in the case of random deployment, our proposed LSRR-LA method achieves the best positioning accuracy. For example, when the node communication radius \(R=200\) m and anchors number \(M=20\%\), the LSRR-LA method presents an ALE of 38.9, which is much better than the others. As shown in Table 6, similar to regular deployment, five different anchor populations are also considered in random deployment. Here, we just show the ALE results of the C-shaped network when the communication radius \(R=150\) m and the number of anchors \(M\) is 65, 75, 85, 95, and 105, respectively. All of the competing methods demonstrate a performance improvement as the network becomes denser; however, these methods do not exhibit satisfactory improvements. Taking the LSRR-LA method for instance, we notice that its ALE is 38.9 with \(M=65\) while its ALE is only decreased to 34.8 with \(M=105\), which proves that anchor populations have just a little impact on positioning accuracy in random deployment networks, since it is not the same in the case of regular deployment networks (refer to Table 4). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(R=100\) m/10\% & \(R=150\) m/15\% & \(R=200\) m/20\% & \(R=250\) m/25\% & \(R=300\) m/30\% \\ \hline  & & \multicolumn{3}{c}{**Number of Anchors \(M=70\)/20\%**} \\ \hline DV-hop & 266.4/79.9\% & 156.3/71.6\% & 112.6/65.4\% & 87.4/61.3\% & 71.5/54.8\% \\ Amorphous & 516.2/89.6\% & 306.5/85.5\% & 215.5/81.9\% & 164.9/79.5\% & 125.6/74.3\% \\ MDS-MAP & 333.2/83.9\% & 224.2/80.2\% & 169.9 /77.1\% & 143.5/76.4\% & 117.3/72.5\% \\ PDM & 76.5/29.2\% & 56.8/21.9\% & 45.4/14.1\% & 37.9/10.7\% & 32.7/1.3\% \\ LSVR & 110.4/51.5\% & 71.9/38.3\% & 53.5/27.2\% & 42.8/21.0\% & 36.4/11.2\% \\ LSRR-LA & 53.5 & 44.4 & 38.9 & 33.8 & 32.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of ALE under different radio ranges in the random deployment network. Figure 5: Comparison of the 3D Localization results (\(R=100\) m, \(M=20\%\)). Figure 6 shows us the overall summarization of Tables 5 and 6. Accordingly, Figure 5(a) depicts the ALE results of the six algorithms in random deployed networks, when the communication radius varies from 100 m to 300 m. The positioning accuracy of DV-Hop, Amophos, and MDS-MAP algorithm is very poor when the communication radius \(R\) is small (\(R\) = 100 m). Our LSRR-LA always maintains the highest positioning accuracy regardless of whether \(R\) is smaller (\(R\) = 100 m) or \(R\) is larger (\(R\) = 300 m). Figure 6(b) shows the ALE results of the six algorithms when the number of anchor nodes is increased from 65 to 105. We can see that LSRR-LA is still the best in these algorithms. Similar to Figure 3, Figure 7 also shows an overall summarization of the six competing methods in random deployment networks, when the communication radius \(R\) is 150 m and the anchor node \(M\) is 70. It can be seen from the figure that our LSRR-LA demonstrates the best positioning performance. Figure 8 gives the localization results of the six algorithms when the communication radius \(R\) is 150 m and the number of anchors \(M\) is 70. Compared with Figure 4, LSRR-LA presents a rather stable