The task of reconstructing the motion of an object by magnetic measurements

We examine the problem of determining the spatial position of a triaxial magnetometer onboard an artificial satellite by measuring the fields in orbit. Such a task is interesting from the point of view that to solve it, data on the satellite and the character of its motion in orbit are not used. We obtain explicit expressions for the Euler angles via the field components measured in orbit and taken from a field model, which is considered given.