This paper presents a fault detection and diagnosis (FDD) algorithm for various faults in the primary air data sensors (PADS) of an aircraft in the presence of external disturbances such as atmospheric turbulence. Rapid wind variations due to turbulence induce excessive error in the externally fitted air data probe measurements, which may lead to loss of control and misinterpretations by the flight crew. In adverse environmental conditions, the FDD of air data prefers robust and adaptive air data estimates that use an analytical redundancy approach with fewer computations. The proposed method considers the kinematics of the aircraft instead of the dynamics used in the state-of-the-art algorithms. The advantage of using kinematics is that it can reduce modeling errors significantly, avoiding high false alarm rates in the FDD process. For the estimation of stable and accurate air data under external disturbance, the inertial navigation system and global positioning system (INS/GPS) output are considered instead of actual air data probe or sensor measurements. The proposed algorithm uses estimates of air data using an exponentially weighted adaptive extended Kalman filter (EW-AEKF) to detect and diagnose PADS faults, which can perform well even in the presence of uncertain noise due to atmospheric turbulence experienced during flight. The simulation was carried out to validate the algorithm with flight data obtained from the X-Plane flight simulator under moderate atmospheric turbulence. The simulation experiments were carried out using the MATLAB programming platform. The results show that the proposed method achieves satisfactory FDD performance with lower root mean square error (RMSE) and computation time than traditional EKF-based algorithms.