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arXiv · 2507.17602

Extended Kalman Smoothing of Free Spin Precession Signals for Accurate Magnetic Field Determination

Jasper Riebesehl·Lutz Mertenskötter·Wiebke Pohlandt·Wilhelm Stannat·Wolfgang Kilian
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Abstract

We present a novel application of the Extended Kalman Smoother (EKS) for highly accurate 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 absolute field determinations. This versatile approach promises to enhance the stability and accuracy of future highly accurate measurements.

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Jasper Riebesehl, Lutz Mertenskötter, Wiebke Pohlandt, Wilhelm Stannat, Wolfgang Kilian. 2025-07-23. Extended Kalman Smoothing of Free Spin Precession Signals for Accurate Magnetic Field Determination. https://doi.org/10.1088/1367-2630%2Fae4fe9

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