In situ calibration of triaxial coils of a vector optically pumped magnetometers based on a particle swarm optimization algorithm

A novel in situ method has been demonstrated for calibrating parameters (coil constants and nonorthogonal angles) of triaxial coils of a three-axis optically pumped magnetometer (OPM). In total, 12 error sources including nonorthogonal errors, proportional coefficient errors and zero-offset errors have been considered into the calibration model. We utilize a particle swarm optimization (PSO) algorithm to estimate the errors, and compare it with a regular Levenberg-Marquardt (LM) algorithm. The results demonstrate that the PSO algorithm has higher accuracy, better convergence stability, faster convergence rate and less calibration uncertainty. The calibration realizes the simultaneous measurement of the coil parameters and the correction of the 12 error sources. The coil constants are (88.93 ± 0.22) nT/mA, (88.78 ± 0.12) nT/mA, and (197.64 ± 0.29) nT/mA which deviate 1.2–1.4 % from the theoretical values, respectively. The nonorthogonal angles are (89.50 ± 0.06) °, (89.46 ± 0.04) ° and (89.40 ± 0.02) ° which correct the errors to 19.6–30.7 % of the original values, respectively. This study realizes in situ coil calibration without auxiliary devices and can be applied to most types of three-axis OPMs including the miniature magnetometers with higher accuracy.