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This brief paper presents an observer-based control approach for the acceleration control of tail-controlled skid-to-turn (STT) missiles. The proposed approach provides a solution to overcoming the drawbacks of existing nonlinear missile controllers that it is needed to know the values of wind angles (angle of attack and sideslip angle). A nonlinear observer for wind angles is designed using a parametric affine missile model developed by the authors, where the coupling term between the lateral and longitudinal motion is also considered. Using the wind angle estimate, we can design the observer-based controller to show the desired acceleration tracking performance. The performance and stability of the resulting overall missile system are analyzed by taking into account the effects of the wind angle estimator. Simulation results are also included to show that the proposed approach provides satisfactory performance for missile dynamics.