High-precision UWB localization with progressive beacon selection for inspection robots

Accurate ultra-wideband (UWB) localization for ground inspection robots is challenging in cluttered industrial environments due to multipath/non-line-of-sight (NLOS) effects and varying beacon geometry. This paper proposes a two-dimensional ( 2 D)-consistent localization pipeline that projects three-dimensional ( 3 D) UWB ranges onto the horizontal plane by removing the known height component, thereby constructing planar localization circles. An auxiliary-point localization model is then developed: for each beacon pair, an auxiliary point is generated according to the geometric relation of the two circles (intersection, tangency, or separation), and the robot position is obtained by fusing all auxiliary points via centroid estimation. To enhance reliability under unfavorable beacon layouts and abnormal ranging, a two-stage validation is introduced, including position dilution of precision (PDoP) verification for geometric strength and a residual consistency test for range agreement. Finally, a progressive beacon-combination strategy ranks beacons by projected ranges, forms nested candidate groups, and selects the best group using a size-penalized residual score. Simulation and real-world fixed-point experiments show that the resulting method provides a lightweight yet robust localization solution suitable for inspection robots operating in complex indoor and industrial scenarios.