Robust Regression Method for NLoS Identification and Localization in Ultra-Dense Networks

The dense distribution of access nodes in next-generation networks enables ultra-high-precision localization using time of arrival (ToA) measurements. However, in complex environments, some ToA measurements may originate from non-line-of-sight (NLoS) paths, degrading localization accuracy. Traditional robust methods for mitigating NLoS errors typically rely on high-complexity convex optimization or extensive data collection, imposing large localization overhead for ultra-dense networks. This paper proposes a novel robust method for joint NLoS identification and localization, which requires only a limited number of ToA measurements and scales efficiently to ultra-dense network deployments. To select an appropriate subset of ToAs for localization, we formulate a robust least-squares regression problem from a combinatorial optimization perspective. We design a solution algorithm with a computational complexity of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}(N\log N)$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> is the number of ToAs. This complexity is lower than most robust localization methods. Our algorithm iteratively refines the localization result using a coarse-to-fine positioning step and an adaptive ToA selection step. We provide theoretical error analysis to ensure the convergence of NLoS identification and localization results toward the optimal solution under mild conditions. Simulation results show that even with up to 32% of ToAs being NLoS, the proposed algorithm achieves an NLoS identification accuracy exceeding 85% and a localization error below 1 m.