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

• URL: http://arxiv.org/abs/2507.17602v1
• Date: Wed, 23 Jul 2025 15:32:26 GMT
• Title: Extended Kalman Smoothing of Free Spin Precession Signals for Precise Magnetic Field Determination
• Abstract summary: We present a novel application of the Extended Kalman Smoother (EKS) for high-precision frequency estimation from free spin precession signals.<n>Our results indicate that EKS-based analysis can substantially improve precision in nuclear magnetic resonance-based magnetometry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 absolute field determinations. This versatile approach promises to enhance the stability and accuracy of future high-precision measurements.

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