Ground plane perception is of vital importance to human mobility. In order to develop a stereo-based mobility aid for the partially sighted, we model the ground plane based on disparity and analyze its uncertainty. Because the mobility aid is to be mounted on a person, the cameras will be moving around while the person is walking. By calibrating the ground plane at each frame, we show that a partial pose estimate can be recovered. Moreover, by keeping track of how the ground plane changes and analyzing the ground plane, we show that obstacles and curbs are detected. Detailed error analysis has been carried out as reliability is of utmost importance for human applications.