Apparatus, having a frame encompassing a volume. The apparatus includes three pairs of separated planar conductive coils, the separated coils of each pair having a common axis of symmetry, the three pairs being attached to the frame so that the common axes of symmetry are mutually orthogonal, and so that the coils surround the volume. An alternating current power supply is coupled to drive the separated coils of each pair in anti-phase so as to generate a magnetic field having a preset spatial variance over the volume. The apparatus also includes a probe that is configured to enter the volume and that has a sensor coupled to generate a signal responsive to a temporal rate of change of the magnetic field and to the preset spatial variance thereof. A processor is configured to receive the signal and in response formulates a position of the probe within the volume.