Model-based parameter optimization to improve bias magnetic field immunity of NMR sensors

Nuclear magnetic resonance (NMR) sensors enable compact angular velocity sensing via noble-gas spin precession. Embedded alkali-metal magnetometers provide critical orientation references, yet their vulnerability to bias magnetic field fluctuations causes persistent drift despite phase-based calibration schemes. This work systematically investigates the sensitivity of the measured angular velocity to bias magnetic field variations in NMR sensors operating with phase-calibrated magnetometer. A signal propagation model reveals the coupling effects of alkali-metal relaxation time, nuclear spin relaxation time, and magnetic moment on the sensitivity of the measured angular velocity to bias magnetic field variations. We propose a parameter optimization strategy to suppress this sensitivity by adjusting drive field amplitude. Experimental results confirm the theoretical framework, demonstrating enhanced rejection to bias magnetic field perturbations. The system achieved a 28.0% reduction in the minimum value of the Allan deviation, with the sensitivity of the measured angular velocity to bias magnetic field variations reduced by approximately 40% within a controlled offset range of 10 nT. The findings provide critical insights for magnetic control requirements in NMR sensors and establish a practical approach for suppressing bias magnetic field variation-induced angular velocity measurement errors without additional hardware.