Application of particle swarm optimization to non-orthogonal error correction in SAFEM total magnetic intensity measurements

In the semi-airborne frequency-domain electromagnetic (SAFEM) method, the total magnetic intensity (TMI) is derived from the vector synthesis of triaxial inductive magnetic sensors. However, non-orthogonal errors in the sensors introduce measurement inaccuracies. Traditional calibration techniques are unsuitable for induction magnetic sensors because they require either static magnetic field measurements or complex alternating current reference fields. We propose a novel, high-precision calibration method based on an improved particle swarm optimization (IPSO) algorithm that circumvents the need for an external physical reference to address this challenge. This method establishes a mathematical model of the non-orthogonal error, transforming the calibration into an optimization problem that aims to minimize the root mean square error (RMSE) of the TMI. Simulation results demonstrate that the proposed IPSO algorithm exhibits higher convergence accuracy and stronger noise immunity compared with the standard PSO. Experiments with a physical measurement system further validated the method's efficacy: after calibration, the maximum absolute error and the RMSE of the TMI were significantly reduced by 82.84% and 87.64%, respectively. This study provides a critical technical solution for the complex, multi-parameter error calibration of alternating current vector magnetometers, ensuring the acquisition of high-precision TMI data for SAFEM systems.