One-step calibration of magnetic gradient tensor system with nonlinear least square method

•All of the error parameters are contained in the nonlinear equations.•Error parameters are estimated by the nonlinear least square algorithm.•One-step calibration of magnetic gradient tensor system is achieved.•Effectiveness and practicality of the proposed method is validated using experiments.

Due to technological limitations, the accuracy of magnetic gradient tensor system is tightly affected by different scale factors, bias of each axis, non-orthogonality between axes and misalignment errors between magnetometers. In order to obtain precise measurement, calibration of the magnetic gradient tensor system is quite essential. A mathematical model containing error parameters of magnetic gradient tensor system is established, and one-step calibration method based on nonlinear least square method is proposed. The effectiveness and convergence of the proposed algorithm is proved by simulation and experiments. In experiments, a tri-axial nonmagnetic rotation platform, a proton magnetometer and a cross magnetic gradient tensor system containing four three-axis fluxgate magnetometers are used. Experimental results show that the proposed method can decrease the measurement errors of magnetic gradient tensor system greatly.