The Orthogonalization of Magnetic Systems

The construction of an orthogonal reference frame based on a set of three skew axes for a magnetic coil system and a magnetic sensor is discussed and presented. For a skew system, it is possible to define the coil axes and the magnetic axes as a dual set of axes that are linked to the system. Therefore, one orthogonal reference frame can be identified from the coil axes and another from the magnetic axes. Although this representation is not unique, it is the most intuitive visual representation as it is shown. The parametrizations based on the operation of the fluxgate transducer for the magnetic sensors compact spherical coil (CSC) (Orsted satellite) and compact detector coil (CDC) (Astrid-2 satellite) are analyzed and identified. In principle, only the transformation matrix that orthogonalizes the sensor is needed, but it is customary to express this matrix as a function of some non-orthogonal angles. Therefore, most relevant conventions from the literature are presented for comparison. All the representations agree for the case of small angle approximation, which is valid for most sensors.