This paper pertains to the reduction of the effects of measurement errors in rate gyros used for tracking, recording, or monitoring the position of persons walking indoors. In such applications, bias drift and other gyro errors can degrade accuracy within minutes. To overcome this problem we developed the Heuristic Drift Elimination (HDE) method, that effectively corrects bias drift and other slow-changing errors. HDE works by making assumptions about walking in structured, indoor environments. The paper explains the heuristic assumptions and the HDE method, and shows experimental results. In typical applications, HDE maintains near-zero heading errors in walks of unlimited duration.