Extended Kalman Smoothing of Free Spin Precession Signals for Accurate Magnetic Field Determination
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914166293397504 |
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| author | Riebesehl, Jasper Mertenskötter, Lutz Pohlandt, Wiebke Stannat, Wilhelm Kilian, Wolfgang |
| author_facet | Riebesehl, Jasper Mertenskötter, Lutz Pohlandt, Wiebke Stannat, Wilhelm Kilian, Wolfgang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended Kalman Smoothing of Free Spin Precession Signals for Accurate Magnetic Field Determination Riebesehl, Jasper Mertenskötter, Lutz Pohlandt, Wiebke Stannat, Wilhelm Kilian, Wolfgang Quantum Physics 62M10, 68U20, 37M10, 94A08 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. |
| title | Extended Kalman Smoothing of Free Spin Precession Signals for Accurate Magnetic Field Determination |
| topic | Quantum Physics 62M10, 68U20, 37M10, 94A08 |
| url | https://arxiv.org/abs/2507.17602 |