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This paper discusses the motion estimation of a general aviation airplane using the optical flow observed by a downward-looking body-fixed camera. The estimation is based on the so-called "subspace constraint," which arises when points stationary on the environment are tracked on the image plane. The constraint can be combined with the aircraft dynamics, giving rise to a nonlinear estimation problem that is solved using an implicit extended Kalman filter. The suggested algorithm was implemented in a simulation. A Monte-Carlo analysis showed that the estimation was unbiased. Furthermore, the standard deviations of the estimation errors converged to reasonable values after a relatively small time interval. An important feature of the method is that good performance was achieved even when tracking a relatively small number of feature points, implying modest real-time computational needs. The algorithm is more efficient than previously published works, in the sense that it does not require pre-storage of a terrain profile or the use of a stabilized camera.