Influence of Beacon Geometry and Camera Pose on the Height Limits of Uav Localization

This paper investigates the effects of ground-based visual beacon geometry, camera pose, and single-beacon loss on the accuracy-based height limits of UAV localization. Regular configurations with 3–6 peripheral beacons and variants with a central beacon are considered. Monte Carlo simulations of PnP/P3P localization cover beacon-field radii of 10–50 m, projection errors of 0.5–5.0 pixels, horizontal camera offsets up to 1.5 field radii, and optical-axis tilts up to 40°. The geometric height limit is determined using a mean 3D localization error criterion of no more than 1 m and a successful-trial rate of at least 0.99. At a 30 m radius and 2-pixel error, increasing peripheral beacons from four to six raises the height limit from 63.4 to 67.3 m. Peripheral-beacon loss reduces it by 12.0% for the square, 7.0% for the pentagon, and 3.8% for the hexagon with a central beacon. At an offset of 1.5 field radii and 40° tilt, the geometric height limit for configurations with 4–6 peripheral beacons and their central-beacon variants exceeds the nominal value by 28–35%, whereas the optical height limit is defined for only 17–21% of directions. Power-law approximations with coefficients of determination above 0.999 enable beacon-field geometry selection considering the height limit and fault tolerance.