A Novel Positioning Framework: Two-Stage Weighted Projection with NLOS Bias Modeling

Traditionally, parallel projection methods (PPMs) have been primarily applied to time-of-arrival (TOA)-based localization. In this paper, we present a series of advancements to PPMs that significantly extend their capabilities and improve positioning accuracy. Specifically, we introduce: 1) a reformulated iterative PPM (IPPM) tailored for time-difference-of-arrival (TDOA)-based localization, and 2) a novel weighted PPM (WPPM), where a two-stage refining approach enhances positioning accuracy, particularly in challenging conditions such as low signal-to-noise ratio (SNR) or high geometric dilution of precision (GDOP). To rigorously evaluate the performance of these enhancements, we develop a comprehensive system-level analytical framework compliant with the 3rd Generation Partnership Project (3GPP) standards. This framework incorporates key 5G new radio (NR) physical layer aspects alongside large-scale and small-scale fading effects. As part of our analysis, we derive a generalized Cramér-Rao lower bound (CRLB) to characterize ranging and positioning error bounds in the presence of additive white Gaussian noise (AWGN) and multipath propagation. Additionally, we propose a novel method to model non-line-of-sight (NLOS) bias induced by multipath, incorporating underlying radio propagation characteristics and SNR. The derived ranging errors are utilized to conduct Monte-Carlo simulations to evaluate the performance of the proposed enhancements and benchmark them against CRLB. Our results demonstrate that the novel WPPM consistently outperforms the weighted non-linear least squares (WNLS) method under non-ideal conditions such as low SNR or high GDOP.