Linear calibration method of magnetic gradient tensor system

•Mathematical model of error parameters is constructed for tri-axial fluxgate magnetometer.•Least square solution of single magnetometer error model is deduced by two non-linear conversions.•A least square estimation is proposed for the misalignment errors between different magnetometers.•Scale factors, biases and non-orthogonality angles are ascertained accurately.•Linear calibration of magnetic gradient tensor system is achieved.

Based on the detailed analysis of systematic errors, mathematical model of error parameters is constructed and linear calibration method is proposed for magnetic gradient tensor system. Firstly, nonlinear mathematical model of error parameters for single vector magnetometer is constructed based on scalar calibration, and least square solution is deduced by two nonlinear conversions without any mathematical simplification. Then outputs of four tri-axial magnetometers are calibrated to sensor’s orthogonal coordinate respectively. Secondly, a least square estimation is proposed for the misalignment errors between different magnetometers according to the rotation matrix comprising conversion of different orthogonal coordinate system. After calibration, outputs of tri-axial magnetometers are acquired along the ideally platform frame-orthogonal coordinate system and these enable calibration of magnetic gradient tensor system. Simulations and experiments show that the proposed linear calibration method can accurately solve the detailed error parameters and decrease measurement errors of magnetic gradient tensor system remarkably.