This paper describes the use of maximum likelihood parameter estimation to estimate unknown aerodynamic coefficients from flight data. The filter error method as a maximum likelihood method uses the model with process noise and measurement noise and this makes the filter error method more general than the output error method which considers measurement noise only. In this paper, the basic concepts of the filter error method are examined and applied to the extraction of aerodynamic parameters for the simulated vehicle motions. The computational aspects of the filter error method including the optimization of a likelihood function and the tuning of the Kalman filter are also discussed in some detail.