A method for estimating aerodynamic angles in the absence of appropriate sensors is proposed, using measurements of three projections of flight speed carried out by the navigation system and the values of the orientation angles. The relevance of the problem being solved is determined by the fact that on unmanned aerial vehicles (UAVs) sensors of aerodynamic angles, that is, angles of attack and slip, are often not installed due to restrictions on dimensions and mass. The proposed method is based on the joint use of mathematical models of aircraft motion, known from flight dynamics, and the theory of parametric identification of dynamic systems. The key factor ensuring the accuracy of the proposed method is the use of very accurate measurements of three UAV velocity projections performed by a satellite navigation system or an inertial navigation system with satellite correction. To account for the influence of wind, parametric identification of three projections of wind speed is provided. Another feature of the method is that instead of the missing aerodynamic angle sensors, it is proposed to use information about the aerodynamic coefficients of the lifting and lateral forces of the UAV. If these coefficients are known with errors, their values are also specified by identification methods. The dimension of the identification problem turns out to be low in the range of small and medium angles of attack when the aerodynamic dependencies are linear. The results of testing the proposed method based on simulation data on the flight test bench of a modern training aircraft for nine different flight modes under conditions of simulating random errors of onboard measurements corresponding to the flight experiment are presented.