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Optimal and efficient inference tools for field tracking with precessing spins

Klaudia Dilcher1,*, Piotr Bania2,3,†, Diana Méndez-Avalos4, Aleksandra Sierant4, Morgan W. Mitchell4,5, and Jan Kołodyński3,1,‡

  • *Contact author: k.dilcher@cent.edu.pl
  • †Contact author: pba@agh.edu.pl
  • ‡Contact author: jankolo@ifpan.edu.pl
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Phys. Rev. Applied 26, 024062 – Published 25 August, 2026

DOI: https://doi.org/10.1103/jfhj-kr1j

Abstract

Precise, real-time monitoring of magnetic field evolution is significant in applications including magnetic navigation and searches for physics beyond the standard model. One main field-monitoring technique, the spin-precession magnetometer (SPM), observes electron, nucleus, color center, or muon spins as they precess in response to their local magnetic field. Here, we study Bayesian signal-recovery methods for SPMs in the free-induction decay mode. In particular, we study tracking of field changes well within the coherence time of the spin system and thus well beyond the response bandwidth, as in [R. Jiménez-Martínez et al. Phys. Rev. Lett. 120, 040503 (2018)]. We derive the Bayesian Cramér-Rao bound that dictates the ultimate precision in estimating the Larmor frequency, which we show is attained by the computationally expensive prediction error method. Relative to this benchmark, we show that the extended Kalman filter (EKF) and cubature Kalman filter offer near-optimal tracking that is also computationally efficient, with the use of the latter giving better results only for a large spin number. Focusing thus on the EKF, we show that it is sufficient to accurately track fluctuating and unknown transient signals. Our methods can be easily adapted to other types of sensors undergoing nonlinear dissipative dynamics and experiencing intrinsic Gaussian-like stochastic noises.

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Phys. Rev. Applied 26, 024062– Published 25 August, 2026
  • Received 1 December 2025
  • Revised 18 May 2026
  • Accepted 8 July 2026
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