Spatial Harmonic Expansion for Use With Magnetic Sensor Arrays

In order to reduce the effects of external magnetic fields on the accuracy of magnetic sensor measurements used for the reconstruction of ac electric currents flowing in massive parallel conductors, we use a spatial circular harmonic expansion of the magnetic scalar potential. Thanks to the linearity of the magnetic field problem with respect to the sources, we can then apply the least squares inversion and obtain the set of currents from the knowledge of the magnetic field data collected by the sensor array in the vicinity of the current carrying conductors. Furthermore, we can optimize the positions and the orientations of the magnetic sensors using D-optimality theory and particle swarm optimization.