The orthogonalization of magnetic systems

The construction of an orthogonal reference frame based on a set of three s kew 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 th e magnetic axes as a dual set of axes that are linked to the system. Theref ore, one orthogonal reference frame can be identified from the coil axes an d another from the magnetic axes. Although this representation is not uniqu e, it is the most intuitive visual representation as it is shown. The param etrizations based on the operation of the fluxgate transducer for the magne tic sensors compact spherical coil (CSC) (Orsted satellite) and compact det ector coil (CDC) (Astrid-2 satellite) are analyzed and identified. In princ iple, only the transformation matrix that orthogonalizes the sensor is need ed, but it is customary to express this matrix as a function of some non-or thogonal angles. Therefore, most relevant conventions from the literature a re presented for comparison. All the representations agree for the case of small angle approximation, which is valid for most sensors. (C) 2001 Elsevi er Science B.V. All rights reserved.