Heteroscedastic Bias-Robust Projected Gradient Descent for UWB Localization in Complex Indoor Environments.

Ultra-wideband (UWB) localization is widely used in indoor positioning because it provides high temporal resolution and direct geometric range constraints. In complex indoor environments, however, UWB ranging is affected by non-line-of-sight propagation, multipath reflection, heterogeneous measurement quality, and link-dependent persistent bias, producing long-tailed errors and trajectory drift. This paper proposes HBR-PGD, a heteroscedastic bias-robust projected gradient descent framework for UWB-only indoor localization. Its central idea is a role-separated error-source formulation that assigns packet-level quality degradation, anchor-channel persistent bias, and sparse instantaneous NLOS anomalies to different roles in a unified constrained residual model. Packet-level quality features are mapped to heteroscedastic uncertainty scales, robust loss shape parameters, and non-negative NLOS correction priors; anchor-channel soft gating limits residual-correction freedom; and target trajectories and bounded structural bias states are jointly estimated in overlapping sliding windows. Experiments on a public indoor UWB dataset show that HBR-PGD achieves RMSE values of 0.107 m, 0.068 m, and 0.204 m in residential-apartment, small-apartment, and workshop/industrial environments, respectively. Compared with WLS, MCC-VC-TOA, SR-MCC, and AR-PNN, HBR-PGD consistently improves overall accuracy and high-percentile robustness, with the largest gain in the workshop/industrial environment. Ablation results verify the contributions of heteroscedastic weighting, structural-bias estimation, gated correction, and information-weighted fusion. These results suggest that HBR-PGD is a practical UWB-only localization framework for complex indoor environments with heterogeneous measurement quality, persistent link bias, and sparse NLOS anomalies.