On Convexification of Range Measurement Based Sensor and Source\n Localization Problems
Bibliographic record
Abstract
This manuscript is a preliminary pre-print version of a journal submission by\nthe authors, revisiting the problem of range measurement based localization of\na signal source or a sensor. The major geometric difficulty of the problem\ncomes from the non-convex structure of optimization tasks associated with range\nmeasurements, noting that the set of source locations corresponding to a\ncertain distance measurement by a fixed point sensor is non-convex both in two\nand three dimensions. Differently from various recent approaches to this\nlocalization problem, all starting with a non-convex geometric minimization\nproblem and attempting to devise methods to compensate the non-convexity\neffects, we suggest a geometric strategy to compose a convex minimization\nproblem first, that is equivalent to the initial non-convex problem, at least\nin noise-free measurement cases. Once the convex equivalent problem is formed,\na wide variety of convex minimization algorithms can be applied. The paper also\nsuggests a gradient based localization algorithm utilizing the introduced\nconvex cost function for localization. Furthermore, the effects of measurement\nnoises are briefly discussed. The design, analysis, and discussions are\nsupported by a set of numerical simulations.\n
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".