We design a fault detection and isolation algorithm using the integrated navigation system approach for detecting and potentially isolating a single Pitot tube failure in the safety-critical air data system used in Unmanned Aerial System (UAS). The design requires two Pitot tubes, one Inertial Measurement Unit (IMU), and a GNSS receiver. The algorithm utilizes two identical synthetic air data systems (SADS) as the bases for estimation. Each SADS works independently with a Pitot tube while sharing the IMU and the Global Navigation Satellite Systems (GNSS) receiver. The detection capability is achieved using residual thresholding techniques, and the isolation functionality is obtained via simple decision logic. This air data fault detection algorithm is designed to meet the integrity and continuity requirements. Both innovation-based and residual-based test statistics using various sliding window sizes are compared to see their effectiveness. A mathematical derivation is presented to show the relationship between the residual-based test and the observability matrix. A new Minimal Detectable Error (MDE) of the airspeed Va is developed, and protection level calculations for the angle-of-attack a and sideslip ß are derived. A simulation is presented to showcase the air data fault detection and isolation algorithm. Specifically, the impact of the external disturbance, the motion of the dynamics and the airspeed fault on a and ß state errors, and the detection capability are discussed. Furthermore, the protection levels of a and ß are illustrated.