Uncertainty-Aware 3D UAV Tracking Using Single-Anchor UWB Measurements

In this letter, we present an uncertainty-aware single-anchor Ultra-Wideband (UWB)-based 3D tracking framework. Specifically, a mobile Unmanned Aerial Vehicle (UAV) maintains a desired standoff distance to a moving target using range and 3D bearing measurements from a multi-antenna UWB anchor rigidly mounted on the UAV. To enhance the stability and safety under measurement degradation and motion uncertainty, we jointly design a robust factor-graph-based target localization method and a covariance-aware control Lyapunov function–control barrier function (CLF–CBF) tracking controller. This controller adaptively adjusts distance bounds and safety margins based on the posterior target covariance provided by the factor graph. The proposed system is evaluated through numerical simulations and real-world experiments carried out in a narrow indoor corridor environment.

💡 Research Summary

This paper presents an uncertainty‑aware framework for three‑dimensional tracking of a moving target by an unmanned aerial vehicle (UAV) equipped with a single ultra‑wideband (UWB) anchor that contains a multi‑antenna array. The anchor simultaneously measures the range and the 3‑D bearing (azimuth and elevation) of a UWB tag attached to the target. To cope with measurement degradation (e.g., multipath, NLoS) and motion uncertainty, the authors jointly develop a robust factor‑graph‑based state estimator and a covariance‑aware controller that combines Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs).

System model. The UAV and the target are modeled as discrete‑time double integrators with bounded acceleration inputs. The UWB anchor provides a scalar range measurement and a pair of angular measurements. The angular data are converted into unit direction vectors on the unit sphere S², enabling a geometrically consistent residual definition.

Robust factor graph. Four factor types are defined: (i) a prior factor on the initial target state, (ii) a dynamic factor encoding the target’s motion model, (iii) a range factor using a Gaussian noise model, and (iv) a robust bearing factor. The bearing factor projects the geodesic error onto the tangent space of S² and applies a Cauchy loss to suppress large outliers caused by multipath or NLoS. The full MAP problem is solved incrementally with iSAM2, yielding at each time step a MAP estimate of the target trajectory and an associated Gaussian posterior covariance.

Uncertainty quantification. From the posterior covariance, the position block Σₚ,T,k is extracted. A scalar confidence radius Rₖ is computed as the square‑root of the largest eigenvalue scaled by the χ²‑distribution quantile, guaranteeing that the true position lies inside a sphere of radius Rₖ with probability 1‑α. This radius quantifies the estimator’s confidence and is fed directly into the controller.

Covariance‑aware CLF‑CBF controller. The controller works with the estimated relative distance dₖ and unit line‑of‑sight vector nₖ. A CLF term drives dₖ toward a desired stand‑off distance d*. A set of CBF constraints enforces physical near/far distance limits. Importantly, the limits are tightened by the confidence radius Rₖ, creating an adaptive “confidence‑tube” around the desired distance. An uncertainty‑induced deadzone of size Rₖ is also introduced around d* to avoid aggressive control actions when the estimator is uncertain. The resulting quadratic program respects actuator saturation and velocity limits while guaranteeing safety and convergence.

Results. Monte‑Carlo simulations demonstrate that the estimator remains accurate and the controller respects safety constraints even when a substantial fraction of bearing measurements are corrupted. Real‑world experiments in a narrow indoor corridor show the UAV maintaining a 1.5 m distance from a moving target while automatically widening the safety envelope when the estimator’s covariance spikes (e.g., during sudden target accelerations or temporary occlusions). The system successfully avoids collisions with doors that appear abruptly and returns to the nominal distance once confidence is restored.

Contributions. 1) A single‑anchor UWB scheme that fuses range and 3‑D bearing via a robust factor graph, including a Cauchy‑loss bearing factor for outlier resilience. 2) A novel CLF‑CBF controller that explicitly incorporates posterior covariance, yielding adaptive distance bounds and deadzones. 3) An end‑to‑end real‑time implementation validated in both simulation and hardware, demonstrating that low‑cost single‑anchor hardware can achieve reliable 3‑D target tracking in cluttered indoor environments.