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This paper proposes a method that uses an aircraft with a single-antenna GPS receiver and Pitot tube to estimate wind speed and direction and to calibrate the airspeed. This sensor combination alone does not determine the true attitude of the aircraft, so the wind parameters cannot be obtained directly from the measurements. However, if the aircraft flies at different headings, such as in banking turns or circle maneuvers, the wind magnitude and direction can be estimated from the geometrical relation between the wind and the measurements. An extended Kalman filter (EKF) is applied to estimate wind parameters. The EKF can also estimate the scaling factor used to convert dynamic pressure to airspeed. This is useful for the operation of small unmanned aerial vehicles (UAVs) because of difficulty in determining the airspeed scaling factor of a low-cost UAV. Simulations are performed for a constant 2-D wind. To test the effectiveness of the proposed method, flight tests of a small UAV are conducted. Simulations and flight test results show that the proposed method is effective.