Two solutions to the localization using time difference of arrival problem
Bibliographic record
Abstract
In this paper, two new solutions to the localization of an emitter using time difference of arrival (TDOA) measurements are proposed. The maximum likelihood estimation for this problem will result in a nonlinear and nonconvex optimization problem, which is very difficult to solve. The solutions presented in this paper consider an alternate formulation, which is based on the sensor-emitter geometry. This formulation results in quadratic (however, nonconvex) optimization problem. The first solution relaxes the original optimization problem into a semidefinite program (SDP). Using the solution to this relaxed SDP, emitter is localized using a randomization technique. The second solution forms the Lagrangian dual of the original problem, and it is shown that the dual problem is an SDP. From the solution to the dual problem a solution to the original problem is found. It has to be noted that the solution obtained using the optimal dual variable, is optimal to the original problem only if strong duality holds. This has not been proven in this paper analytically. Extensive simulations performed suggests that the strong duality may hold for this problem.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".