Frequency Estimation Enhancement for Industrial Free Induction Decay Signals Under Low SNR via Hankelization and Modified Covariance
Bibliographic record
Abstract
The frequency of a free induction decay (FID) signal from an industrial proton precession magnetometer (PPM) is proportional to the magnetic field strength. To achieve high-precision frequency estimation for an FID signal with a low signal-to-noise ratio (SNR), a long estimation period is always required, which limits the application scenarios of the PPMs, such as aeromagnetic detection. To break through the contradiction between frequency estimation precision and time, this article proposes an enhanced frequency estimation method via Hankelization and modified covariance, dubbed EFE-HMC. First, the collected 1-D FID signal is constructed as a third-order tensor through Hankelization, and then the noise tensors are removed by multilinear singular value decomposition (MLSVD) to improve the SNR; second, the preprocessed third-order tensor is inverted into a 1-D signal, and the modified covariance is employed to estimate the corresponding signal frequency; and third, an experimental test platform is constructed to compare the proposed EFE-HMC with three state-of-the-art methods including carry chain, equal precision, and Dn-ResUnet. The results demonstrate that when the SNR is lower than −10 dB and the estimation time varies from 50 to 200 ms, the frequency estimation precision is improved by 60% on average. Moreover, the frequency estimation time is reduced by about 150 ms when the frequency estimation precision is better than 0.03 Hz.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".