Two-Step Nonlinear Calibration of LTS SQUID-based Full Tensor Magnetic Gradient System

The full tensor magnetic gradient (FTMG) system based on low-temperature superconducting quantum interference device (SQUID) planar gradiometers is susceptible to measurement errors, including imbalance errors, angular misalignment, scale factor deviations, and offset errors. To mitigate these effects, a two-step calibration method is proposed. In the first step, a three-dimensional Helmholtz coil generates a known magnetic field to correct imbalance and offset errors. In the second step, the FTMGmodule is rotated within a Maxwell coil to obtain outputs from all gradiometers. By minimizing the objective function between modeled and measured responses, the estimated error parameters can be obtained using the Trust-Region Reflective algorithm. Simulation results show that the mean absolute percentage error (MAPE) between the estimated and true parameters remains below 10%. Experimental validation further confirms the reliability of the method, as the residual magnetic gradient components for the six calibrated gradiometers are reduced from 688.16, 1017.32, 341.18, 532.45, 874.24, and 268.07 nT/m to 0.52, 0.30, 0.57, 0.35, 0.39, and 0.36 nT/m, respectively. These results demonstrate that the proposed approach significantly enhances the accuracy and stability of FTMG measurements.