A Likelihood-Based Triangulation Method for Uncertainties in Through-Water Depth Mapping

Coastal environments, which are crucial for economic and strategic reasons, heavily rely on accurate bathymetry for safe navigation and resource monitoring. Recent advancements in through-water photogrammetry have shown promise in mapping shallow waters efficiently. However, robust uncertainty modeling methods for these techniques, especially in challenging coastal environments, are lacking. This study introduces a novel likelihood-based approach for through-water photogrammetry, focusing on uncertainties associated with camera pose—a key factor affecting depth mapping accuracy. Our methodology incorporates probabilistic modeling and stereo-photogrammetric triangulation to provide realistic estimates of uncertainty in Water Column Depth (WCD) and Water–Air Interface (WAI) height. Using simulated scenarios for both drone and airborne surveys, we demonstrate that viewing geometry and camera pose quality significantly influence resulting uncertainties, often overshadowing the impact of depth itself. Our results reveal the superior performance of the likelihood ratio statistic in scenarios involving high attitude noise, high flight altitude, and complex viewing geometries. Notably, drone-based applications show particular promise, achieving decimeter-level WCD precision and WAI height estimations comparable to high-quality GNSS measurements when using large samples. These findings highlight the potential of drone-based surveys in producing more accurate bathymetric charts for shallow coastal waters. This research contributes to the refinement of uncertainty quantification in bathymetric charting and sets a foundation for future advancements in through-water surveying methodologies.