Enhanced UAV Localization and Outlier Detection Using SVD-Enhanced UWB for Bridge Inspections

This study presents an improved Ultra-Wideband (UWB) positioning algorithm for Unmanned Aerial Vehicles (UAV) performing bridge inspections. The algorithm uses a two-stage singular value decomposition (SVD) to reduce positioning errors caused by tilted anchor configurations. By evaluating the condition number of the anchor configuration during initial placement, the root-mean-squares error (RMSE) is reduced to one-eighth of the value for the original method at nearly 10-degree tilt. Optimal anchor placement strategies were further explored, analyzing both non-coplanar and coplanar arrangements. While non-coplanar configurations can enhance accuracy when anchor heights are large, coplanar layouts generally provide greater stability, and square arrangements provide better positioning accuracy. Finally, the SVD-based outlier detection method is also introduced in coplanar configurations. Unlike traditional dilution of precision (DoP) methods, where different positioning algorithms produce different DoP values, the proposed method requires only anchor coordinates and measured distances, thereby achieving more accurate outlier detection and robust performance in bridge inspection environments.