Frequency Estimation Enhancement for Industrial Free Induction Decay Signals Under Low SNR via Hankelization and Modified Covariance

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.