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A magnetic compass requires a careful calibration procedure and complicated compensation algorithms before obtaining precise heading because of its vulnerability to several types of errors. Existing calibration approaches are not applicable for a 2-axis digital compass applied in pedestrian navigation, especially in order to eliminate predictable magnetic disturbances and tilt error without a tilt sensor or external information on the local magnetic field. This paper introduces an adaptive and unified error model for a 2-axis digital compass, which includes all predictable errors from the navigation platform and the pedestrian's walking behavior. An easy-to-use and computation-efficient calibration approach is proposed, utilizing the heading from GPS to estimate the parameters of this model in the calibration procedure. Several tests were conducted to validate this approach and evaluate its performance in upgrading the positioning accuracy. The results demonstrate that the approach suggested is applicable for decreasing the errors on a 2-axis compass from several tens of degrees to the extent that is adequate to guarantee the positioning accuracy of our self-developed low-cost pedestrian navigation system about 2% of the travelled distance; or below 8 m during 10 min of continuous walking - comparable to typical commercial dead reckoning modules or inexpensive inertial measurement units.