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Heteroscedastic Bias-Robust Projected Gradient Descent for UWB Localization in Complex Indoor Environments
Zhongyang Yu1, Qinghua Liu1, Yong Qian2
1School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China.
Sensors (Basel, Switzerland)
|July 28, 2026
Summary
This study introduces HBR-PGD, a novel framework for ultra-wideband (UWB) indoor localization. It enhances accuracy in complex environments by robustly handling measurement errors and biases for precise positioning.
Area of Science:
- Robotics and Automation
- Signal Processing
- Geodesy and Geomatics
Background:
- Ultra-wideband (UWB) localization offers high precision for indoor positioning.
- Complex indoor environments introduce challenges like non-line-of-sight (NLOS) propagation, multipath reflections, and heterogeneous measurement quality, leading to errors and trajectory drift.
Purpose of the Study:
- To develop a robust UWB-only indoor localization framework, HBR-PGD, that addresses heterogeneous measurement quality and persistent biases.
- To improve the accuracy and reliability of UWB localization in challenging indoor settings.
Main Methods:
- Proposes HBR-PGD (heteroscedastic bias-robust projected gradient descent) framework.
- Employs a role-separated error-source formulation within a unified constrained residual model.
- Integrates packet-level quality features for uncertainty scaling, robust loss parameters, and NLOS correction priors.
- Utilizes anchor-channel soft gating and joint estimation of trajectories with bounded structural bias states in sliding windows.
Main Results:
- HBR-PGD achieved Root Mean Square Errors (RMSE) of 0.107 m, 0.068 m, and 0.204 m in residential-apartment, small-apartment, and workshop/industrial environments, respectively.
- Demonstrated consistent improvement in overall accuracy and high-percentile robustness compared to existing methods (WLS, MCC-VC-TOA, SR-MCC, AR-PNN).
- Ablation studies confirmed the effectiveness of heteroscedastic weighting, structural-bias estimation, gated correction, and information-weighted fusion.
Conclusions:
- HBR-PGD is a practical and effective framework for UWB-only indoor localization in complex environments.
- The method successfully mitigates issues arising from heterogeneous measurement quality, persistent link bias, and sparse NLOS anomalies.
- The proposed approach offers enhanced accuracy and robustness for real-world indoor positioning applications.
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