Abstract: Magnetic compasses may be affected by local disturbances in the magnetic field in their vicinity. These disturbances may be caused by the addition or removal of a metal article concerned with a vehicle in which the compass is mounted, and may also be due to local variations in the Earth's magnetic field. The system described herein compensates for such disturbances in the magnetic field to maintain the accuracy of the magnetic compass by transforming an ellipsoidal locus to a spherical locus at a different orientation in space. For example, a one-shot algorithm is employed in which data collected during a setting maneuver of the vehicle is processed to fit a generalized reduced quadric equation having six or less coefficients rather than the nine calibration points required in the prior art for fitting a generalized quadric equation for an ellipsoid. The present invention thus significantly reduces the processing power required.