Tuning Frequency Extraction of Free Induction Decay Signal Leveraging Higher Order Singular Value Tensor Decomposition and Fourier Synchrosqueezing Transform

The frequency of the free induction decay (FID) signal output from an Overhauser magnetometer sensor is proportional to the magnetic field to be measured. Due to the low initial signal-to-noise ratio (SNR), sensor tuning is necessary to suppress the noise and thus improve the frequency estimation accuracy. To improve the tuning performance in complex strong-disturbance environments, this article introduces a novel method using higher order singular value tensor decomposition (HOSVTD) and Fourier synchrosqueezing transform (FSST), namely, SVDFT. First, multiple FID signals are obtained using an equal delay multichannel acquisition strategy to establish a deeper, more intrinsic correlation attribute. Second, matrix segmentation is used to organize the signals into a higher order tensor to compute singular values, and tensor canonical polyadic (CP) decomposition is incorporated to derive a low-noise FID signal. Subsequently, the FSST is used to analyze the low-noise signal to extract the time-frequency ridges to capture the tuning frequency. Finally, the SVDFT is contrasted with three techniques: autocorrelation and fast Fourier transform (AC-FFT), singular value decomposition (SVD) combined with short-time Fourier transform (STFT) (ST-SVD), and the HOSVTD and synchroextracting transform (SET), namely, SVDET. The experimental results demonstrate that under the presence of spike noise and the SNR is less than −20 dB, the frequency tuning deviations of the commonly used methods are up to 100 Hz, while that of the SVDFT is within 5 Hz, which verifies that the SVDFT can significantly enhance the sensor tuning accuracy in complex strong-disturbance conditions and has a strong ability for environmental adaptation.