A Likelihood-Based Triangulation Method for Uncertainties in Through-Water Depth Mapping
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".