Research on frequency estimated algorithms for FID atomic magnetometers

Free-Induction-Decay (FID) atomic magnetometers are widely used in precision magnetic field measurement applications. However, achieving precise frequency measurements within extremely short observation windows remains challenging, making accurate frequency estimation crucial for their performance. To address this issue, we propose a frequency estimation framework based on the Levenberg–Marquardt (LM) optimization method and systematically investigate the influence of sampling rate, signal-to-noise ratio (SNR), and relaxation time on estimation accuracy. The results demonstrate that higher sampling rates, improved SNR, and longer relaxation times significantly reduce estimation errors, with our algorithm achieving a magnetic field root mean square error (RMSE) of 0.0187 nT under conditions of 2 MHz sampling frequency, 50 dB SNR, and 0.5 ms sampling duration. Furthermore, we demonstrate reliable reconstruction of continuously varying time-domain FID waveforms, achieving average reconstruction errors below 40 pT. Our work improves the frequency measurement accuracy of FID signals, thereby advancing the precision of magnetic field estimation. By systematically examining the factors that influence the estimation process, this study lays the groundwork for the broader application of FID-based magnetometers in high-sensitivity and real-time measurement scenarios.