Modern commercial aircraft rely on hardware redundancy and median-voting logic to ensure air data system integrity, but these mechanisms remain critically vulnerable to Common-Cause Failures (CCFs). During common-cause events, whether environmental (icing, volcanic ash, bird strikes), physical (insect nesting, drain blockage), or systemic (maintenance errors, manufacturing defects), identical faults across multiple sensors can evade detection, feeding catastrophic misinformation to flight control laws. This paper presents the development and validation of a distributed analytical redundancy architecture for detecting and isolating CCFs when traditional hardware consensus fails. The proposed solution employs a Kinematic Double-Model Adaptive Estimation (DMAE) framework utilizing Unscented Kalman Filters (UKFs). To mitigate simultaneous faults, the architecture deploys three independent DMAE estimators in parallel across the Captain, First Officer, and Standby sensor channels, synthesizing a single, high-integrity flight reference via median-consolidation logic. The framework's performance is rigorously evaluated against a comprehensive spectrum of complex, Airbus-defined fault scenarios, including simultaneous blockages, signal freezes, and biases. Furthermore, the algorithm is successfully transitioned from offline environments to real-time Simulink models for validation within the high-fidelity Airbus SESAME simulation environment. Experimental results confirm that the distributed DMAE successfully isolates faults and reconstructs true airspeed and angle of attack trajectories even when all physical sensors are differently compromised, demonstrating its industrial viability against common-cause anomalies.