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

TL;DR

This paper introduces a two-stage weighted projection method (TS-WPM) for TDOA-based localization that improves accuracy under challenging conditions, supports cooperative localization with TW-TOA, and is validated through a comprehensive 3GPP-compliant framework.

Contribution

The paper presents TS-WPM, a novel iterative localization algorithm that enhances accuracy and robustness, extends it for cooperative scenarios, and provides a detailed analytical and simulation evaluation framework.

Findings

TS-WPM achieves near-CRLB performance in high GDOP and low SNR conditions.

Cooperative localization with TS-WPM improves accuracy with limited anchors.

The method offers a balanced trade-off between computational complexity and localization precision.

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\'er-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.