Probabilistic Localization With Gateway Location Errors and Multiple Transmissions
Bibliographic record
Abstract
This article investigates the effect of uncertainty in the positions of a set of spatially separated receivers (gateways) that are used to localize a device (target) that transmits a burst signal intermittently. Such systems have applications in radar, sonar, and wireless sensor networks, and have been extensively studied, at least in the context of point estimation. This article extends the limited work on region estimation to include the effect of uncertainty in the locations of the gateways on the probability that the target is in a specified region. Specifically, this article extends previous work that found the a posteriori probability density function (pdf) of the target’s coordinates from estimates of the times the transmitted message arrives at the receivers [Time of Arrivals (ToA)] under the assumption the positions of the gateways were known exactly. The expression for the a posteriori pdf is redeveloped to include the uncertainty in the measurement of the receivers’ positions. Three practical scenarios are considered: 1) the target transmits a single message and the gateways measure the ToAs as well as their own positions; 2) the target transmits multiple messages and the gateways measure the ToAs as well as their own positions upon each reception; and 3) the target transmits multiple messages and the gateways measure the ToAs upon each reception, but the positions of the gateways are measured once, at the time of installation. Various numerical examples are given to corroborate, provide insights, and illustrate the utility of the obtained results.
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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".