A terrain matching algorithm has been developed for use in a passive aircraft navigation system. A sequence of aerial, optical images is matched to a reference digital map of the three-dimensional terrain. Stereo analysis of successive images results in the recovery of an elevation map of the observed terrain. A 'cliff map' is then used as a novel, compact representation of the terrain surface. The position and heading of the aircraft are determined via a terrain matching algorithm that locates the observed cliff map within the reference cliff map. Novel results using real terrain data and an implementation of a real stereo algorithm provide an important extension to previous results using simulated stereo.