The paper pertains to the reduction of measurement errors in gyroscopes used for tracking the position of walking persons. Such tracking systems commonly use inertial or other means to measure distance travelled, and one or more gyros to measure changes in heading. MEMS-type gyros or IMUs are best suited for this task because of their small size and low weight. However, these gyros have large drift rates and can be sensitive to accelerations. The Heuristic Drift Reduction (HDR) method presented in this paper estimates the drift component and eliminates it, reducing heading errors by almost one order of magnitude.