Generalized Likelihood Ratio Test for Detection of Gaussian Rank-One Signals in Gaussian Noise With Unknown Statistics
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider the classical radar problem of detecting a target in Gaussian noise with unknown covariance matrix. In contrast to the usual assumption of deterministic target amplitudes, we assume here that the latter are drawn from a Gaussian distribution. The generalized likelihood ratio test (GLRT) is derived based on multiple primary data and a set of secondary data containing noise only. The new GLRT is shown to be the product of Kelly's GLRT and a corrective, data dependent term. We also investigate two-step approaches where the GLRT for a known disturbance covariance matrix is first derived. In order to come up with detectors that provide a good tradeoff between detection of matched signals and rejection of mismatched signals, we also investigate the two-step GLRT when a fictitious signal is included in the null hypothesis. The constant false alarm rate properties of the detectors are analyzed. Numerical simulations are presented, which show that for small sample sizes the newly-proposed GLRT can outperform Kelly's GLRT and, in addition, that detectors including a fictitious signal are very powerful, at least for low-to-intermediate clutter to noise ratio values.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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 it