We develop an air data system for aerial robots executing high-speed outdoor missions subject to significant aerodynamic forces on their bodies. The system is based on a combination of Extended Kalman Filtering (EKF) and autoregressive feedforward Neural Networks, relying only on IMU sensors and GPS. This eliminates the need to instrument the vehicle with Pitot tubes and mechanical vanes, reducing associated cost, weight, maintenance requirements and likelihood of catastrophic mechanical failures. The system is trained to clone the behaviour of Pitot-tube measurements on thousands of instrumented simulated and real flights, and does not require a vehicle aerodynamics model. We demonstrate that safe guidance and navigation is possible in executing complex maneuvers in the presence of wind gusts without relying on airspeed sensors. We also demonstrate accuracy enhancements from successful “simulation-to-reality” transfer and dataset aggregation techniques to correct for training-test distribution mismatches when the air-data system and the control stack operate in closed loop.