Adaptive Nonlinear Scalar Calibration Method for Triaxial Magnetic Sensors Across a Wide Magnetic Field Range

Achieving high-precision magnetic field measurements in weak-field environments has become increasingly critical with the rapid advancement of quantum magnetometry. However, most existing calibration methods rely on geomagnetic-level references and fail to capture the nonlinear response and cross-range inconsistencies that arise across a broad magnetic-field range, resulting in severe accuracy degradation under weak-field conditions. This article proposes an adaptive nonlinear scalar calibration method (AN-SCM) to address the nonlinear calibration problem of triaxial magnetometers across a wide magnetic-field range. The method models the scale factors of each axis as polynomial functions of the measured field, providing a semiphysical and interpretable alternative to traditional linear and black-box approaches. A residual-based adaptive strategy is employed to automatically determine the optimal polynomial order, achieving a balanced trade-off between model complexity and generalization capability. To obtain a traceable weak-field reference, a scalar-magnetometer-based Helmholtz-coil inverse calibration procedure is developed, enabling accurate magnetic-field generation at the nanotesla (nT) level. Experimental results over the 30μ T-30 nT range demonstrate the necessity of nonlinear modeling, showing that AN-SCM reduces the magnetic-magnitude error (MME) at 30 nT by 28.7% compared with traditional methods. A high-to-low field transfer evaluation further shows that calibration parameters obtained under microtesla-level fields fail to reliably describe sensor behavior in the nT regime, whereas AN-SCM maintains stable performance under weak-field conditions. These results indicate that nonlinear effects dominate in weak-field environments and must be explicitly modeled to enable reliable wide-range precision magnetic-field measurement.