Calibration of a Magnetic Gradient Tensor System in Non-Uniform Magnetic Fields

This paper investigates the calibration problem of an 8-magnetometer magnetic gradient tensor system (MGTS) based on a cubic structure in non-uniform magnetic fields. Existing calibration methods are mostly designed for uniform fields, which show obvious limitations under complex magnetic field conditions, leading to the decrease of measurement accuracy. Therefore, we propose a calibration method suitable for non-uniform magnetic fields. Specifically, the method constructs a multi-objective cost function using 6 invariants that remain constant during the rotation of the MGTS, and employs the sequential quadratic programming (SQP) algorithm for the optimization, which has better global convergence performance and wider suitability. Finally, the proposed method is validated by simulation experiments. The results show that under the condition that the standard deviation of the environmental noise is 1nT, the root-mean-square error of the tensor contraction of the MGTS center calibrated by our method is reduced by 97.10% and 81.16% compared with the two benchmark methods (FCM and RCM), which fully proves the validity and high efficiency of the method.