Integrated calibration and magnetic disturbance compensation of three-axis magnetometers

•The influence of hard-iron and soft-iron material is analyzed.•The proposed method has good compensation performance in all situations.•Compared with ellipsoid-fitting method, it is not necessary to compute pseudo-linear parameters.•Compared with several traditional methods, the proposed method has better integrated compensation performance.•The method can be used for integrated compensation in underwater vehicles or aircrafts.