A Risk-Aware Safety Framework for UWB-Localized Quadrotors: Geometry-Aware Error Compensation and Belief-Space Collision Avoidance

Ultra-wideband (UWB) positioning provides cost-effective localization for quadrotors in global navigation satellite system (GNSS)-denied environments, but geometry-dependent, heavy-tailed errors challenge state estimation and safety-critical control. This paper presents a risk-aware framework linking geometry-aware error quantification with belief-space collision avoidance under a fixed four-anchor UWB configuration. Specifically, horizontal dilution of precision (HDOP) and nearest-anchor distance are used as spatial features in a Student’s-t process regression (STPR) model to predict UWB positioning errors and quantify the associated uncertainty. The compensated UWB measurements are then fused with inertial data through a Kalman filter to obtain a Gaussian belief state. A belief control barrier function (BCBF) maps ellipsoidal collision regions to a unit sphere, approximates them using tangent half-spaces, and is embedded in nonlinear model predictive control (NMPC). In outdoor flight experiments, the positioning RMSE is reduced to 0.071 m by the proposed STPR-KF method, compared with 0.299 m for raw UWB and 0.292 m for conventional KF. Feasible risk-aware obstacle avoidance and adjustable safety clearance are further demonstrated through numerical simulations. The feasibility of linking geometry-aware UWB error characterization with belief-space safety constraints for UWB-localized quadrotor navigation is therefore indicated.