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

TL;DR

This paper introduces an Extended Kalman Smoother method for precise frequency estimation of free spin precession signals, improving robustness and accuracy over traditional fitting techniques in magnetic field measurements.

Contribution

The paper presents a novel EKS-based approach that adaptively estimates amplitude and frequency variations in spin precession signals, outperforming fixed-parameter least-squares methods.

Findings

EKS reduces estimation errors in simulations with decaying signals.

EKS outperforms least-squares fitting in noisy, evolving frequency scenarios.

Experimental validation confirms improved magnetic field measurement accuracy.

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.