A three-dimensional alternating current electromagnetic field tracking system for determining the position and orientation of an object, wherein the system comprises: - an electromagnetic field transmitter comprising three coils (22, 22', 22") configured to generate three magnetic fields (H x, H y, H z) and - one or more electromagnetic field receivers each comprising three measurement coils, - a control unit wherein the electromagnetic field transmitter comprises at least one offset coil (8, 8', 8") arranged to generate an addition magnetic field (H add), wherein the offset coil (8, 8', 8") is offset relative to the coils (22, 22', 22") of the electromagnetic field transmitter, wherein the control unit is configured to calibrate the system on the basis of the addition magnetic field (H add), wherein the at least one offset coil (8, 8', 8") is arranged and configured to generate the additional magnetic field passively by induction, characterised in that the tracking system is configured to carry out a digital modulation process and hereby determine one or more parameters needed to accomplish the calibration process by means of said digital modulation process, wherein the digital modulation process is a phase-shift keying, PSK, modulation process modulating the phase of a constant frequency carrier wave, wherein the system is configured to determine if the carrier wave and the modulated signal are in phase or 180° out of phase at time T=0 and hereby determine the operational sign of the carrier wave and thus the orientation of the one or more electromagnetic field receivers. - an electromagnetic field transmitter comprising three coils (22, 22', 22") configured to generate three magnetic fields (H x, H y, H z) and - one or more electromagnetic field receivers each comprising three measurement coils, - a control unit wherein the electromagnetic field transmitter comprises at least one offset coil (8, 8', 8") arranged to generate an addition magnetic field (H add), wherein the offset coil (8, 8', 8") is offset relative to the coils (22, 22', 22") of the electromagnetic field transmitter, wherein the control unit is configured to calibrate the system on the basis of the addition magnetic field (H add), wherein the at least one offset coil (8, 8', 8") is arranged and configured to generate the additional magnetic field passively by induction, characterised in that the tracking system is configured to carry out a digital modulation process and hereby determine one or more parameters needed to accomplish the calibration process by means of said digital modulation process, wherein the digital modulation process is a phase-shift keying, PSK, modulation process modulating the phase of a constant frequency carrier wave, wherein the system is configured to determine if the carrier wave and the modulated signal are in phase or 180° out of phase at time T=0 and hereby determine the operational sign of the carrier wave and thus the orientation of the one or more electromagnetic field receivers. wherein the electromagnetic field transmitter comprises at least one offset coil (8, 8', 8") arranged to generate an addition magnetic field (H add), wherein the offset coil (8, 8', 8") is offset relative to the coils (22, 22', 22") of the electromagnetic field transmitter, wherein the control unit is configured to calibrate the system on the basis of the addition magnetic field (H add), wherein the at least one offset coil (8, 8', 8") is arranged and configured to generate the additional magnetic field passively by induction, characterised in that the tracking system is configured to carry out a digital modulation process and hereby determine one or more parameters needed to accomplish the calibration process by means of said digital modulation process, wherein the digital modulation process is a phase-shift keying, PSK, modulation process modulating the phase of a constant frequency carrier wave, wherein the system is configured to determine if the carrier wave and the modulated signal are in phase or 180° out of phase at time T=0 and hereby determine the operational sign of the carrier wave and thus the orientation of the one or more electromagnetic field receivers.