Two-step calibration method for three-axis magnetic sensor error based on particle swarm optimization

The three-axis magnetic sensors are mostly calibrated by scalar method such as ellipsoid fitting and so on, but these methods cannot completely determine the 12 parameters of the error model. A two-stage calibration method based on particle swarm optimization (TSC-PSO) is proposed, which makes full use of the amplitude invariance and direction invariance of Earth’s magnetic field vector.

The TSC-PSO designs two-stage fitness function. Stage 1: design a fitness function of the particle swarm by the amplitude invariance of the Earth’s magnetic field to obtain a preliminary error matrix G and the bias error B. Stage 2: further design the fitness function of the particle swarm by the invariance of the Earth’s magnetic field to obtain a rotation matrix R, thereby determining the error matrix uniquely.

The proposed TSC-PSO can completely determine 12 unknown parameters in error model and further decrease the maximum fluctuation error of the Earth’s magnetic field amplitude and the absolute error of heading.

The proposed TSC-PSO provides an effective solution for three-axis magnetic sensor error compensation, which can greatly reduce the price of magnetic sensors and be used in the fields of Earth’s magnetic survey, drilling and Earth’s magnetic integrated navigation.

The proposed TSC-PSO has significantly improved the magnetic field amplitude and heading accuracy and does not require additional heading reference. In addition, the method is insensitive to noise and initialization conditions, has good robustness and can converge to a global optimum.