Method for calibrating a magnetometer

A method for calibrating a magnetometer including the following steps:

• the magnetometer travels through a set of path positions, said path positions being distinguished from each other by a location of the magnetometer and/or by an orientation of the magnetometer;
• acquisition by the magnetometer at acquisition times of a plurality of measurements of a magnetic field when the magnetometer travels through said set of path positions and determination of a magnetic field gradient for said acquisition times;
• provision of trajectory information representative of the location and the orientation of a point integral with the magnetometer at a plurality of travel times while the magnetometer travels through the set of path positions,
• for each of a plurality of determination times determined from the acquisition times and the travel times, matching up of the measurements of the magnetic field with the trajectory information by associating and synchronizing measurements of the magnetic field and trajectory information in order to have, for each one of said plurality of determination times, a measurement of the magnetic field, a magnetic field gradient, and trajectory information representative of the location and the orientation of a point integral with the magnetometer at said determination time,
• determination of calibration parameters of the magnetometer by minimisation of a cost function involving, for a plurality of determination times, at least said calibration parameters, a measurement of the magnetic field at said determination time, and a relation which links change in the magnetic field with change in the location and in the orientation of the magnetometer derived from the trajectory information at said determination times,
• wherein the cost function is based on comparisons between a theoretical estimation of the measurement of the magnetic field at a determination time and a measurement of the magnetic field at said determination time, and wherein the theoretical estimation of the magnetic field is determined from the relation linking the change in a magnetic field with the change in the location and in the orientation of the magnetometer derived from the trajectory information, the theoretical estimation of the magnetic field being also determined from the magnetic field gradient at a preceding determination time,
• wherein the relation locally expresses, at each determination time, an equation of a particular derivative of the magnetic field:
• {right arrow over ({dot over (B)})}=∇{right arrow over (B)}·{right arrow over (v)}+Ω×{right arrow over (B)}
• with {right arrow over (B)} a magnetic field vector, ∇{right arrow over (B)} a gradient vector of the magnetic field, {right arrow over ({dot over (B)})} a vector of a time derivative of the magnetic field, {right arrow over (v)} a velocity vector representative of a modification of the location of the magnetometer and Ω a rotation matrix representative of a modification of the orientation of the magnetometer.