This paper proposes a new method that estimates the three-dimensional stochastic wind velocity for an aircraft equipped with a Pitot-static tube and airflow vanes. Since the performance of most state estimators, e.g., the extended Rauch-Tung-Striebel smoother, relies on the process and measurement noise covariance settings, the proposed method employs the expectation-maximization approach to estimate the noise covariance matrices to improve the estimation accuracy. Numerical simulations demonstrated that the proposed method can successfully estimate the noise covariance matrices, especially for the noise covariance of the wind velocity, using the measurement data and reconstruct the wind velocity offline. Additionally, the smoothed true airspeed, angle of attack, and angle of sideslip data are more accurate compared to the direct measurements. This feature is also beneficial for other applications such as the aerodynamic model identifications of aircraft.@en