Whether it be in air defense applications or for air traffic control it is highly desirable to be able to assess in real time the type of aircraft one is dealing with. This task may prove useful when the object refuses to cooperate or to confront the transmitted information with the observed trajectory. In the present paper we advocate an approach based on position (radar) measurements only, for versatility. Besides, we propose to focus on rotation-invariant kinematic trajectory features such as absolute velocity, curvature, torsion and parameters alike, as relevant distinctive features to automatically classify aircraft trajectories in real time. Those features are fed into convolutional neural networks that are state of the art for time series classification. Notably they seamlessly handle trajectories of variable length and hence may be used in real time. The constructed classifiers are trained with real data collected from publicly available information transmitted by the aircrafts. This allows for benchmarking of the proposed learning algorithms, as well as discussion on the best possible achievable accuracy.