## 4 Simulation Results and Analysis
### Three-Dimensional Simulation Parameters and Results  
The proposed algorithm was compared with 3D DV-Hop, 3D DV-Hop based on PSO, and 3D DV-Hop based on SSA. The default parameters for the simulations were set to 100 nodes, 20% beacon nodes, and a communication radius of 40 m. The normalized ALE in the 3D scenarios can be expressed by Equation (39)  
\[ALE_{\text{3D}}=\frac{\sum_{i=1}^{N}\sqrt{\left(x_{ist}-x_{i}\right)^{2}+\left(y _{ist}-y_{i}\right)^{2}+\left(z_{ist}-z_{i}\right)^{2}}}{N\cdot R} \tag{39}\]  
where \(\left(x_{ist},\ y_{ist},\ z_{ist}\right)\) represents the estimated coordinates of the unknown nodes. \(\left(x_{i},\ y_{i},\ z_{i}\right)\) represents the true location of unknown nodes. The simulation parameters in 3D scenarios were set as shown in Table 3.  
The simulation scenarios included a 100 m \(\times\) 100 m \(\times\) 100 m 3D cubic terrain and a 3D anisotropic network distribution area consisting of rugged, hilly, and valley terrains. Figure 9 illustrates the node topology distributions in the 3D scenarios. The proportion of beacon nodes increased from 10% to 40%, and the simulation results of each algorithm are shown in Figure 10. The proposed algorithm outperformed the others across various beacon node ratios, with the localization error gradually decreasing as the number of beacons increased. The total number of nodes increased from 50 to 150, and the simulation results of each algorithm are shown in Figure 11. The communication radius increased from 40 m to 80 m, and the comparative effects of each algorithm under various topological distributions are shown in Figure 12.  
As the network size increases, the localization error of the proposed algorithm initially decreases and then levels off. This algorithm consistently outperforms the others in all scenarios, demonstrating stable localization accuracy that is less affected by network size. As the communication radius increases, the localization accuracy of all algorithms improves to varying extents. However, the proposed algorithm continues to maintain high localization accuracy even with a large communication radius. Figure 8: Comparison of localization error under different DOIs in 2D scenarios. (**a**) Two-dimensional variable ratio of beacon. (**b**) Two-dimensional variable communication radius. \begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameters** & **Value** \\ \hline Scenario size & 100 m \(\times\) 100 m \(\times\) 100 m \\ Communication radius & 40–80 m \\ Ratio of beacon & 10–40\% \\ Number of nodes & 50–150 \\ DOI & 0–0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Three-Dimensional simulation parameters. Figure 10: Comparison of localization errors under different beacon ratios in 3D scenarios. (**a**) Cubic terrain. (**b**) Rugged terrain. (**c**) Hilly terrain. (**d**) Valley terrain. Figure 9: Node distribution maps in 3D scenarios. (**a**) Cubic terrain. (**b**) Rugged terrain. (**c**) Hilly terrain. (**d**) Valley terrain. Figure 11: Comparison of localization errors under different numbers of nodes in 3D scenarios. (a) Cubic terrain. (b) Rugged terrain. (c) Hilly terrain. (d) Valley terrain. Figure 12: Comparison of localization errors under different communication radii in 3D scenarios. (a) Cubic terrain. (b) Rugged terrain. (c) Hilly terrain. (d) Valley terrain. The computational complexity of the proposed algorithm in 3D scenarios was analyzed and compared. The default parameter values were used in the simulation tests, with the specific results presented in Table 4.  
Figure 13 shows the comparison of the localization error at DOI values of 0, 0.05, and 0.1. Figure 13a shows the effect of increasing the proportion of beacon nodes from 10% to 40%, while Figure 13b demonstrates the impact of increasing the communication radius from 40 m to 80 m.  
The results indicated that localization errors increase with the DOI for all algorithms. However, the classical DV-Hop algorithm is more significantly affected.