The least squares estimation of time delay and its use in signal detection
Bibliographic record
Abstract
This paper examines the use of two spatially separated receivers to determine the presence of a distant signal source and its relative bearing. Ideally, the phase shift between the receivers' output is proportional to the frequency, with the time delay between outputs equal to the proportionality constant. Because of noise, the plot of phase against frequency is scattered along a straight line whose slope is the time delay. A least squares estimator of the slope turns out to be equivalent to the maximum likelihood estimator developed by Hamon and Hannan [1]. Since the goodness of fit of the least squares line is a function of the coherence between the receivers' output, the sum of the squared errors is used as a test statistic in detection. The proposed detector has a detection threshold that depends only on the probability of false alarm and not on the ambient noise level. It can also be simply extended to an array of receivers.
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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 | 0.001 |
| 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".