Modeling and Compensation of Axial Magnetic Field Error in Nuclear Magnetic Resonance Sensor Based on Bloch Equation

Nuclear Magnetic Resonance (NMR) sensors, with their potential advantages of miniaturization and high precision, have become one of the best choices for angular velocity measurement sensors in future Inertial Navigation Systems (INS). Under the limitations of magnetic field control technology and external magnetic field disturbances, current technology is difficult to satisfy the magnetic field precision requirements of NMR sensors to attain navigation-level measurements. Existing methods typically reduce the sensor's dependence on the axial magnetic field accuracy by closed-loop control of the carrier frequency. However, because of the limitations of the model and control accuracy, the effect of main magnetic field variations on the sensor performance cannot be overlooked. To address this problem, this paper proposes an innovative a method for modeling and compensation the axial magnetic field error of NMR sensors. First, the mechanism influencing of the axial magnetic field change on the system demodulation process is examined, and a physical model describing the axial magnetic field variation and sensor error is established using the Bloch equation; then, the model is simplified based on the principle of ignoring small quantities and function approximation; finally, a compensation experiment of the axial magnetic field error is carried out. Experimental results show that compared with the existing methods, the proposed method achieves a 19.5% improvement in frequency error stability under the condition of axial magnetic field changes. This work provides effective guidance for future sensor magnetic error compensation.