Reliable online autonomy is critical for quadrotor operation in urban airspaces, where global navigation satellite systems (GNSS) measurements suffer from multipath, blockage, and latency issues, introducing non-stationary, temporally correlated errors that degrade conventional GNSS-IMU fusion. This paper presents a belief-adaptive online autonomy framework that augments an extended Kalman filter (EKF) with explicit GNSS trust modelling, second-order online belief adaptation, and latency-aware out-of-sequence measurement handling. GNSS trust is represented as a latent belief state that modulates measurement weighting and multipath bias uncertainty, and is updated online using EKF consistency signals. Unlike reactive covariance tuning, the proposed approach enables proactive and stable sensor trust adaptation without prior environmental knowledge or offline training. Evaluation in simulated urban air mobility scenarios with correlated multipath, stochastic latency, and obstacle constraints demonstrates improved belief convergence, smoother trajectories, and reduced estimation and tracking errors compared to naive, adaptive, and first-order baselines. The framework preserves classical GNSS-IMU fusion structure and can be integrated directly into existing flight control pipelines, supporting robust online autonomy in GNSS degraded environments.

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