Fundamental Limits of Doppler Shift-Based, ToA-Based, and TDoA-Based Underwater Localization
Bibliographic record
Abstract
Dear Editor, This paper is concerned with the underwater localization based on acoustic signals. Specifically, we will focus on the search of an underwater target that can constantly broadcast a beacon signal, such as a black box. Common measurements for localization are Doppler shift [1], time of arrival (ToA) [2]–[4], time difference of arrival (TDoA) [5], [6], angle of arrival (AoA) [7], etc. In this paper we will investigate the fundamental limits of Doppler shift-Based, ToA-Based, TDoA-based underwater localization. Note that AoA is not covered, because Doppler shift can be viewed as one type of AoA. The discussion will focus on short-baseline positioning with a mobile anchor, i.e., an autonomous underwater vehicle (AUV). Due to the large distance and the limited battery life of the AUV, the target is quite likely to lie outside the convex hull of the AUV's trajectory. In such cases, we will show that accurate localization is almost impossible by exclusively dependent on a single type of measurements. However, system performance will be significantly improved by combing Doppler shift with ToA or TDoA measurements. The reason for such improvement will be unveiled theoretically and numerically in this letter.
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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 | 0.004 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".