# Three-Dimensional Localization of Underwater Nodes Using Airborne Visible Light Beams
## 1 Introduction  
The relentless advancement of communication technologies has dramatically transformed our capacity to interact with and understand the world around us. A significant contributor to this transformation is the Internet of Things (IoT), which envisions a seamlessly connected network of devices operating across diverse environments, including terrestrial, aerial, and aquatic domains. As we move towards the next generation of wireless technology with the emergence of 6G, the integration of underwater networks has become increasingly important. These networks hold the key to a multitude of critical applications such as monitoring marine life, assessing environmental pollutants, conducting oceanographic research, and executing high-priority operations like search-and-rescue missions or clandestine military surveillance. A fundamental challenge in deploying underwater networks is the precise localization of submerged nodes. Accurate positioning is essential not only for contextualizing the collected data but also for optimizing the network topology and boosting the efficiency of communication protocols. Traditional localization methods have predominantly utilized acoustic signaling [1, 2], relying on surface vessels or anchored nodes with GPS coordinates to translate relative positions into global coordinates. However, in scenarios where operational stealth is required--such as in covert naval operations--the presence of surface or tethered markers can compromise the mission by revealing the presence of the underwaternetwork [3; 4]. In addition, deploying markers could constitute a logistical challenge in applications that serve emerging events such as search and rescue and naval combat. To overcome these limitations, this paper proposes the use of VLC across the air-water interface as an innovative solution for underwater node localization. VLC stands out as an effective means due to its ability to transmit high-bandwidth data through both air and water, and hence it does not need the deployment of relaying nodes on the water surface. Unlike photoacoustic techniques [4], which often suffer from logistical complexities and limited data rates, VLC offers a more efficient and scalable approach. VLC eliminates the need for surface-deployed infrastructure such as buoys, anchored relays, or pressure-based markers. This not only reduces logistical burden but also removes visual and physical traces of the network from the water surface. The result is a system that is inherently well-suited for covert, rapidly deployable, and infrastructure-free localization, further enhanced by the high directionality and rapid attenuation of light in water [5], which localizes the transmission footprint and minimizes the risk of detection by unintended observers. By measuring received light intensities and applying trilateration algorithms, we demonstrate that underwater nodes can be accurately localized without the need for surface-based reference points. This method not only enhances the feasibility of deploying underwater networks in sensitive operations but also enables the introduction of new applications, e.g., studying the effect of climate change. In our preliminary investigation [6; 7; 8], we have assumed that the underwater node is equipped with a pressure sensor to measure its depth, effectively reducing the scope of the localization problem to 2D. However, in practice, the node may not have a pressure sensor due to constraints like power consumption, node size, or cost. This paper overcomes such a limitation and proposes 3D-LUNA, a novel method for 3D localization of underwater nodes using airborne visible light beams. This novel framework enables underwater node localization using airborne VLC without relying on pressure sensors or anchored nodes. The method reconstructs 3D positions by correlating light intensity measurements with modeled beam propagation across depth layers. To address the challenge of unknown depth, we introduce an optimization approach that identifies the most likely depth by minimizing errors.