Spatial Harmonic Expansion for Use with Magnetic Sensor Arrays

External magnetic fields affect the accuracy of magnetic sensor measurements used for the reconstruction of ac electric currents flowing in massive parallel conductors. In order to reduce the impact of external magnetic fields, a spatial circular harmonic expansion of the magnetic scalar potential is carried out. Thanks to the linearity of the magnetic field problem with respect to the sources, the least squares inversion can be applied and the set of currents can be obtained from the knowledge of the magnetic field data collected by the sensor array in the vicinity of the current carrying conductors. Furthermore, the positions and the orientations of the magnetic sensors are optimized using D-optimality theory and particle swarm optimization.