Alleviating Sensor Position Error in Source Localization Using Calibration Emitters at Inaccurate Locations
Bibliographic record
Abstract
A previous study shows that the use of a calibration emitter whose position is known exactly can significantly reduce the loss in time differences of arrival (TDOA) based source localization accuracy when the available sensor positions have random errors. This paper extends the previous work to a more practical scenario where the exact position of a calibration emitter is not known. By modeling the calibration position error as additive Gaussian noise, the amount of reduction in localization accuracy due to calibration position error is derived through CramÉr–Rao lower bound (CRLB) analysis. In addition, the analysis also affirms the previous studies on Bayesian sensor network localization that it remains possible to improve the localization accuracy even if the calibration position is completely unknown. Next, a performance analysis illustrates that the penalty could be very high if one simply pretends the calibration position is accurate and ignores its error. A closed-form solution is then developed by accounting for the calibration position error and it is proved analytically to reach the CRLB accuracy when the sensor and calibration position errors are small relative to the distance between the calibration emitter and the sensor. Finally, the results are generalized to the case where multiple calibration emitters are available. When deploying multiple calibration emitters, although their positions may not be known exactly, we show that it is possible to completely eliminate the sensor position error and recover the best localization accuracy that is limited by the measurement noise in TDOAs only. All the theoretical developments are corroborated by simulations.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| 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) | 0.001 | 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 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".