# Three-Dimensional Localization of Underwater Nodes Using Airborne Visible Light Beams
## 5 Results and Discussion
### Mobile Node  
To evaluate the localization performance for mobile underwater nodes, we have implemented the random waypoint (RWP) mobility model [40] to simulate the relatively complex movement of the mobile underwater node. In this mobility model, the underwater node moves at a constant speed, beginning its journey from a randomly chosen point within a 3D space. It then travels in a randomly selected direction within the defined region. After a randomly determined duration in the range of 10 to 30 s, the mobile underwater node changes direction, selecting a new random path. Notably, there is no pause time when the mobile underwater node alters its direction. Figure 9 shows the average localization performance for varying transmission power for 100 iterations where a node receives the required number of transmissions to localize itself.  
For the mobile node, the comparison between OMNI and 3D-LUNA follows a similar trend to the static node, with 3D-LUNA consistently outperforming OMNI by producing lower localization errors across all power levels. At low power levels (100 mW-1 W), OMNI shows significantly higher errors, reaching approximately 12 m at 100 mW, while 3D-LUNA reduces it to around 10 m. The error remains noticeably higher for OMNI at 500 mW and 1 W, but both methods show a clear improvement as power increases. In the mid-power range (5 W-10 W), OMNI's error remains significantly higher than 3D-LUNA, though the gap starts to shrink. At higher power levels (50 W-100 W), both methods converge to a similar accuracy level with minimal error, demonstrating that at very high power, the method selection becomes less critical. Overall, 3D-LUNA is a better choice, particularly at lower and mid-power levels, as it ensures greater accuracy without requiring excessive power.  
The error rate between consecutive power levels varies for OMNI and 3D-LUNA, but it displays a similar trend to static nodes, with 3D-LUNA consistently outperforming OMNI at lower power levels (100 mW-10 W) due to its more efficient signal distribution. The most significant reduction occurs between 1 W and 5 W, where 3D-LUNA achieves nearly 50% error reduction compared to OMNI's 30-40%, highlighting its superior power utilization. As power increases to 10 W, the gap narrows, with OMNI beginning to catch up, though 3D-LUNA still maintains a slight advantage (~5-10% more error reduction). Beyond 10 W, and especially from 50 W to 100 W, both methods experience a similar trend, with error reduction rates converging as the power of transmission becomes the dominant factor. This trend suggests that while power distribution optimization is critical at lower power levels, at higher power, the influence of transmission power makes OMNI and 3D-LUNA nearly equivalent in performance.  
When comparing static and mobile nodes, the mobile node generally exhibits higher errors across all power levels, indicating that mobility introduces additional localization challenges. At low power levels, the error for mobile nodes is higher than that of static nodes, suggesting that movement increases uncertainty in localization. However, the error reduction pattern remains similar, where higher power levels improve accuracy for both cases, and 3D-LUNA consistently outperforms OMNI. Notably, at high power (50 W and 100 W), the errors in both static and mobile cases converge, showing minimal difference between OMNI and 3D-LUNA, reinforcing the conclusion that transmission power dominates over method selection at these levels. In summary, while both cases benefit from higher power, 3D-LUNA is the superior choice, especially in mobile scenarios where errors tend to be more pronounced.