Extended Kalman smoothing of free spin precession signals for precise magnetic field determination
Authors
- Mertenskötter, Lutz
ORCID: 0000-0001-5074-2721 - Riebesehl, Jasper
- Stannat, Wilhelm
- Pohlandt, Wiebke
- Kilian, Wolfgang
2020 Mathematics Subject Classification
- 62M10 68U20 37M10,94A08
Keywords
- Bayesian methods, extended Kalman smoother, Rauch-Tung-Striebel smoother, expectation maximization, magnetometry, free precession decay, free spin precession, 3-Helium, metastability exchange optical pumping (MEOP), optical magnetic gradiometer, optically pumped magnetometer (OPM).
DOI
Abstract
We present a novel application of the Extended Kalman Smoother (EKS) for high-precision frequency estimation from free spin precession signals of polarized 3^He. Traditional approaches often rely on nonlinear least-squares fitting, which can suffer from limited robustness to signal decay and time-dependent frequency shifts. By contrast, our EKS-based method captures both amplitude and frequency variations with minimal tuning, adapting automatically to fluctuations via an expectation-maximization algorithm. We benchmark the technique in extensive simulations that emulate realistic spin precession signals with exponentially decaying amplitudes and noisy frequency drifts. Compared to least- squares fits with fixed block lengths, EKS systematically reduces estimation errors, particularly when frequencies evolve or signal-to-noise ratios are moderate to high. We further validate these findings with experimental data from a free-precession decay 3^He magnetometer. Our results indicate that EKS-based analysis can substantially improve precision in nuclear magnetic resonance-based magnetometry, where accurate frequency estimation underpins abso- lute field determinations. This versatile approach promises to enhance the stability and accuracy of future high-precision measurements
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