Beamforming using subspace estimation from a diagonally averaged sample covariance
Bibliographic record
Abstract
The potential benefit of a large-aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming. This paper introduces a Toeplitz-constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far-field targets embedded in background isotropic noise. The estimator is obtained by averaging along subdiagonals of the sample covariance matrix, followed by covariance extrapolation using the method of maximum entropy. The sample covariance is computed from limited data snapshots, a situation commonly encountered with large-aperture arrays in environments characterized by short periods of local stationarity. Eigenvectors computed from the Toeplitz-constrained covariance are used to construct signal-subspace projector matrices, which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming. Monte Carlo simulations corresponding to increasing array aperture suggest convergence of the proposed projector to the clairvoyant signal projector, thereby outperforming the classic projector obtained from the sample eigenvectors. Beamforming performance of the proposed method is analyzed using simulated data, as well as experimental data from the Shallow Water Array Performance experiment.
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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 | 0.001 | 0.002 |
| 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 | 0.002 | 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".