This paper addresses the design of a secure and fault-tolerant air transportation system in the presence of attempts to disrupt the system through the satellite-based navigation system. Adversarial aircraft are assumed to transmit incorrect position and intent information, potentially leading to violations of separation requirements among aircraft. We propose a framework for the identification of adversaries and malicious aircraft, and then for air traffic control in the presence of such deliberately erroneous data. The framework consists of three mechanisms that allow each aircraft to detect attacks and to resolve conflicts: fault detection and defense techniques to improve Global Positioning System (GPS)/inertial navigation, detection and defense techniques using the Doppler/received signal strength, and a fault-tolerant control algorithm. A Kalman filter is used to fuse high frequency inertial sensor information with low frequency GPS data. To verify aircraft position through GPS/inertial navigation, we propose a technique for aircraft localization utilizing the Doppler effect and received signal strength from neighboring aircraft. The control algorithm is designed to minimize flight times while meeting safety constraints. Additional separation is introduced to compensate for the uncertainty of surveillance information in the presence of adversaries. We evaluate the effect of air traffic surveillance attacks on system performance through simulations. The results show that the proposed mechanism robustly detects and corrects faults generated by the injection of malicious data. Moreover, the proposed control algorithm continuously adapts operations in order to mitigate the effects these faults. The ability of the proposed approaches to defend against attacks enables reliable air traffic operations even in highly adversarial surveillance conditions.