Robust Optimization Localization via Ellipsoidal Uncertainty Sets for NLOS Errors Learned From CIR-Based Range Error Prediction

In wireless localization, non-line-of-sight (NLOS) propagation in complex environments significantly degrades the time-of-arrival (TOA) positioning accuracy of ultra-wideband (UWB) systems. However, existing robust optimization methods mainly rely on interval uncertainty set modeling for NLOS errors, which inherently neglects the non-uniformity and correlation of NLOS errors, with these interval set bounds often being conservatively predefined. To address these issues, this paper proposes replacing interval sets with ellipsoidal uncertainty sets for a more accurate characterization of the statistical properties of NLOS errors. In particular, the ellipsoidal uncertainty set is constructed based on the mean vector and covariance matrix of NLOS errors predicted by a deep learning model. Since ellip-soidal uncertainty sets inherently lead to nonconvex formulations, we introduce auxiliary variables for reparameterization and apply the S-lemma, thereby reformulating the original problem into a tractable convex optimization problem. Simulation and experimental results demonstrate that, compared with existing methods, our ellipsoidal set-based approach, which accounts for the non-uniformity and correlation of NLOS errors, significantly improves localization accuracy and robustness across various complex environments.