A novel estimation technique for bias magnetic field in NMR Gyroscope based on nonlinear disturbance observer

Nuclear Magnetic Resonance Gyroscopes (NMRGs), a subclass of atomic gyroscopes, offer a promising solution for next-generation high-precision inertial sensors due to their compact size and low drift. The performance of NMRGs depends critically on the precise control of the bias magnetic field, and further research is required on how to accurately estimate the bias magnetic field. The inherent unobservability of instantaneous differential parameters and transient coupling dynamics compels conventional methods to employ equilibrium approximations in bias field estimation, inevitably induces systematic errors due to neglected time-varying dynamics. To address this limitation, a nonlinear disturbance observer (NDO)-based estimation framework is proposed. A nuclear spin dynamics model was developed to analyze the relationship between phase-locked loop (PLL) detected frequency and bias magnetic field. Theoretical analysis reveals that the dynamic response process of nuclear spin in the system and the tracking error of the PLL were overlooked in previous estimation methods. These overlooked terms can be effectively accounted for through a specifically designed disturbance observer, and further estimation accuracy is achieved via model-based adjustments. Additionally, the use of feedback linearization guarantees rapid convergence and an overshoot-free estimation process. To enable practical implementation on existing systems, the control law and observer were approximated utilizing a proportional–integral (PI) scheme. The simulation results validate effectiveness of the method, while experimental validation demonstrates that the proposed estimation technique accelerates the estimation process, and maintains an overshoot-free response.