In the presence of ground reflections, the traditional methods for aircraft noise direction of arrival estimation based on the time differences between the microphones of a compact array lose accuracy in the vertical angle. This paper studies the benefits of using a tetrahedral array geometry of first order directional microphones instead of omnidirectional ones to reduce this error. It shows that the ground reflections introduce a systematic error in the time delay estimates, which is considerably reduced by using directional microphones, and that the selection of the optimum directivity pattern depends on the height of the array over the ground. The mean square estimation errors of the proposed approach are compared to the Cramer-Rao bound of those of a minimum variance estimator for a tetrahedral array of omnidirectional microphones in free field. Finally, computer simulations using real jet and propeller signals are used to assess the performance of the proposed method in the presence of microphone self noise and wind induced noise.