Spectral-Entropic Guidance, Navigation, and Control: A Fault-Tolerant Architecture for Autonomous Landing in Sensor-Denied and High-Turbulence Environments

We present a novel dual-layer supervisory control architecture for autonomous aircraft landing in adverse conditions characterized by sensor degradation and severe atmospheric disturbances. Traditional PID and Kalman filter approaches often fail when sensor noise becomes non-Gaussian or when "Zero-Day" wind shear events occur. The proposed Spectral-Entropic Guidance, Navigation, and Control (SE-GNC) framework integrates algebraic graph theory and information-theoretic predictive analytics to achieve fault-tolerant glideslope tracking with provable stability guarantees. The outer supervisory layer operates in two hierarchical modes: (1) a Spectral Graph Supervisor employing the Fiedler eigenvector of the sensor Laplacian matrix to detect and veto spatially correlated anomalies via topological analysis, and (2) an Entropic Disturbance Predictor utilizing Approximate Entropy (ApEn) metrics on real-time airflow measurements to anticipate turbulence onset before it impacts the airframe dynamics. Hardware-in-the-loop simulations demonstrate a 40% reduction in glideslope deviation and a 99.9% successful landing rate under conditions that destabilize conventional autopilots.