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-Cram\'er--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.