Two-Stage Weighted Projection for Reliable Low-Complexity Cooperative and Non-Cooperative Localization

2025-02-26

AI Summary

This paper addresses the accuracy and robustness bottlenecks of TDOA/TW-TOA localization under high geometric dilution of precision (GDOP), low signal-to-noise ratio (SNR), and sparse anchor deployment. To this end, we propose a two-stage weighted projection method (TS-WPM). TS-WPM introduces a novel dynamic dual-stage iterative projection framework, integrating error covariance weighting with SNR-aware non-line-of-sight (NLOS) bias modeling, and establishes a 3GPP-compliant multipath Cramér–Rao lower bound (CRLB) analysis model. Theoretical analysis and simulations demonstrate that TS-WPM significantly outperforms weighted least squares (WNLS) under high-GDOP and low-SNR conditions; remarkably, it achieves near-CRLB accuracy with only two anchors via cooperative localization. Moreover, TS-WPM features low computational complexity and real-time feasibility, supporting both cooperative and non-cooperative scenarios.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In this paper, we propose a two-stage weighted projection method (TS-WPM) for time-difference-of-arrival (TDOA)-based localization, providing provable improvements in positioning accuracy, particularly under high geometric dilution of precision (GDOP) and low signal-to-noise ratio (SNR) conditions. TS-WPM employs a two-stage iterative refinement approach that dynamically updates both range and position estimates, effectively mitigating residual errors while maintaining computational efficiency. Additionally, we extend TS-WPM to support cooperative localization by leveraging two-way time-of-arrival (TW-TOA) measurements, which enhances positioning accuracy in scenarios with limited anchor availability. To analyze TS-WPM, we derive its error covariance matrix and mean squared error (MSE), establishing conditions for its optimality and robustness. To facilitate rigorous evaluation, we develop a 3rd Generation Partnership Project (3GPP)-compliant analytical framework, incorporating 5G New Radio (NR) physical layer aspects as well as large-scale and small-scale fading. As part of this, we derive a generalized Cram{'e}r-Rao lower bound (CRLB) for multipath propagation and introduce a novel non-line-of-sight (NLOS) bias model that accounts for propagation conditions and SNR variations. Our evaluations demonstrate that TS-WPM achieves near-CRLB performance and consistently outperforms state-of-the-art weighted nonlinear least squares (WNLS) in high GDOP and low SNR scenarios. Moreover, cooperative localization with TS-WPM significantly enhances accuracy, especially when an insufficient number of anchors (such as 2) are visible. Finally, we analyze the computational complexity of TS-WPM, showing its balanced trade-off between accuracy and efficiency, making it a scalable solution for real-time localization in next-generation networks.

Problem

• Improves TDOA-based localization accuracy
• Supports cooperative localization with TW-TOA
• Ensures computational efficiency in real-time networks

Innovation

• Two-stage weighted projection method
• Dynamic range and position updates
• Cooperative localization with TW-TOA