# Three-Dimensional Localization of Underwater Nodes Using Airborne Visible Light Beams
## 5 Results and Discussion
### Stationary Node  
For stationary underwater nodes, 30 nodes are placed underwater in random locations. We then compare the performance of both OMNI and 3D-LUNA. Figure 8 shows the localization error for both methods under varying transmission power. The results reflect the average of 100 iterations.  
As indicated by the results, 3D-LUNA consistently outperforms Omni by maintaining a lower localization error across all power levels. At low power levels (100 mW-1 W), Omni's error is significantly higher compared to 3D-LUNA, with the gap remaining noticeable at 500 mW and 1 W. In the mid-power range (5 W-10 W), Omni still exhibits nearly double the error of 3D-LUNA at 5 W, though the difference starts to shrink at 10 W. However, at higher power levels (50 W and 100 W), both methods achieve similar accuracy, with error becoming minimal, indicating that at very high power, transmission strength dominates over method choice. When analyzing the error rate change relative to power levels, 3D-LUNA clearly stands out as it consistently demonstrates a higher reduction rate at lower power levels, particularly between 100 mW and 5 W. Initially, between 100 mW and 500 mW, 3D-LUNA achieves an error reduction rate of approximately 15-20%, whereas OMNI reduces error by only 10-15%. As power increases to 1 W, the gap widens, with 3D-LUNA achieving up to 30-35% reduction compared to OMNI's 20-25%. The most significant divergence occurs between 1 W and 5 W, where 3D-LUNA reaches a peak reduction of 50-55%, nearly 10-15% higher than OMNI's 30-40%. This indicates that 3D-LUNA  
Figure 8: Localization performance comparison between 3D-LUNA and OMNI for static nodes. The error bars represent 95% confidence intervals.  
adapts more efficiently in the mid-power range. However, beyond 10 W, both methods experience a sharp decline in rate change, with OMNI dropping to 25-30% and 3D-LUNA maintaining a slight lead at 35-40%. At 50 W and 100 W, both methods exhibit minimal rate change, converging at 5-10%, showing diminishing returns. Overall, the gap in rate change between the two methods is most prominent in the lower-to-mid power range, whereas at high power levels, their performance stabilizes, indicating that 3D-LUNA is most beneficial in power-constrained environments, while both methods perform similarly at high power.  
Both OMNI and 3D-LUNA are highly dependent on the transmission power and how the signal intensity is distributed. At lower power levels (100 mW to 5 W), the error is significantly higher for both methods due to weaker signals, which are more susceptible to attenuation and environmental noise. However, the error in OMNI remains consistently larger compared to 3D-LUNA because OMNI distributes power uniformly in all directions, leading to greater signal dispersion and reduced signal strength at the receiver. In contrast, 3D-LUNA appears to use a more concentrated and efficient power distribution, ensuring stronger signal reception and reduced localization error. When power increases beyond 5 W, the stronger transmission mitigates attenuation effects. However, beyond 10 W, both methods approach a point where increasing power has minimal impact on localization error. By 50 W and 100 W, both OMNI and 3D-LUNA reach similar low-error performance, indicating that at these high power levels, the effectiveness of signal distribution becomes less critical as the primary constraints shift to environmental factors. This suggests that while transmission power plays a key role in reducing localization error, the way the power is distributed is crucial at lower power levels, where a more focused transmission like 3D-LUNA provides a significant advantage.  
Overall, 3D-LUNA proves to be the superior approach, especially at lower and mid-power levels, offering better accuracy without requiring excessive power, making it a more efficient option in scenarios where power consumption matters.