The phase error suppression method based on the reference frequency modification in NMR angular velocity sensor

The nuclear magnetic resonance (NMR) angular velocity sensors utilizing dual-isotope Xe (¹²⁹Xe and ¹³¹Xe) systems offer the advantages of high precision in compact size. These sensors derive angular velocity from dual-isotope Xe precession frequencies, typically extracted by phase-locked loop techniques. The phase errors originating from the in situ Rb magnetometer inaccuracies represent a critical error source. Conventional phase error suppression methods typically employ a reference signal to suppress phase errors, with the reference frequency set to the intermediate value between dual-isotope Xe precession frequencies to avoid the Xe resonance region. However, these approaches remain inadequate for dual-isotope configurations owing to the distinct frequencies involved. Based on the phase-frequency characteristic analysis, the phase errors coupling mechanism in the dual-isotope Xe system is investigated, and an error suppression method based on reference frequency modification is proposed by integrating with phase-locked loop technology and angular velocity measurement principle. This approach reveals the intrinsic relationship between reference frequency selection and dual-isotope Xe phase error interference. By modifying the reference frequency to a theoretically derived feature value that aligns with the dual-isotope Xe frequency discrepancy, the dual-isotope Xe phase errors can be canceled. Experimental validation demonstrates that the bias instability of the dual-isotope Xe precession frequency error is reduced by 19.9 %, directly enhancing long-term reliability in precession frequency detection. This method is beneficial for enhancing the stability of angular velocity measurements and optimizing the operational accuracy of in situ Rb magnetometers, rendering it suitable for multi-isotope NMR sensors and multi-frequency atomic magnetometers.