A New Location Estimator for Mixed LOS & NLOS scenarios

Time-of-arrival (TOA)-based localization in mixed line-of-sight (LOS) and non-line-of-sight (NLOS) environments is challenging because conventional Euclidean range models do not capture diffraction-dominated propagation. We show that the diffraction path-length model smoothly transitions between LOS and diffraction-dominated NLOS conditions, eliminating the need for explicit path classification. Although this model provides a unified geometric description of mixed LOS/NLOS propagation, the resulting 3D maximum-likelihood problem is nonconvex, and a direct Gauss–Newton estimator based on this model can converge to suboptimal local minima. This motivates the development of a class of structure-exploiting estimators. For known target height, the model induces a virtual-anchor representation of the reduced 2D problem, enabling estimators that exhibit a clear complexity–performance tradeoff: surrogate formulations provide structure and computational efficiency, while a semidefinite-relaxation formulation more faithfully preserves the original likelihood at higher cost. Building on this same structure, we develop 3D sample–polish–select estimators that reduce the global search to one dimension, solve the associated fixed-height 2D subproblems, and then apply local nonlinear refinement in 3D. The proposed estimators achieve near-Cramér–Rao lower bound (CRLB) performance with substantially lower complexity than multistart Gauss–Newton, while also being far more robust to initialization than a direct single-start Gauss–Newton estimator.