Wireless positioning in Non-Line-of-Sight (NLoS) scenarios presents significant challenges due to multipath effects that lead to biased measurements and reduced positioning accuracy. This paper revisits electromagnetic field theory related to diffraction and in the context of wireless positioning and proposes a novel positioning technique that greatly improves accuracy in NLoS environments dominated by diffraction. The method is applied to a critical public safety use case: precisely locating at-risk individuals within buildings, with a particular focus on improving 3D positioning and z-axis accuracy. By leveraging the Geometrical Theory of Diffraction (GTD), the approach introduces an innovative NLoS path length model and a new NLOS positioning technique. Using Fisher information analysis, we establish the conditions required for 3D positioning and derive lower bounds on positioning performance for both 3D and z-axis estimates for the proposed NLOS positioning technique. Additionally, we propose an algorithmic implementation of the proposed NLoS positioning method using non-linear least squares estimation, which we term D-NLS. The positioning performance of our proposed NLOs positioning technique is validated using an extensive ray-tracing simulation. The numerical results highlight the superiority of our approach in outdoor-to-indoor environments, which directly estimates NLoS path lengths and delivers significant performance enhancements over existing methods for both 3D and z-axis positioning scenarios.
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