Robust Algorithm for 5G NLOS Localization and Synchronization With Single Anchor Uncertainties

In 5G non-line-of-sight (NLOS) positioning and synchronization, uncertain anchor position and orientation significantly affect the performance of localization algorithms. In this letter, we propose a robust closed-form NLOS localization method that addresses these uncertainties by integrating time of arrival (TOA), angle of departure (AOD), and angle of arrival (AOA) measurements using a single base station (BS). Our approach features a closed-form weighted least squares (WLS) solution that jointly accounts for both position and orientation uncertainties of the anchor, modeling their effects as bias terms. By exploiting the geometric symmetry of NLOS paths, we directly estimate and mitigate these anchor uncertainty-induced biases. Supported by the Cramer-Rao lower bound (CRLB), comparative simulations show that the proposed algorithm not only achieves theoretical accuracy limits, but also significantly outperforms existing methods.