Gaussian Variational Inference with Non-Gaussian Factors for State Estimation: A UWB Localization Case Study

2025-12-22

AI Summary

Ultra-wideband (UWB) localization suffers from degraded state estimation under non-line-of-sight (NLOS) conditions and multipath propagation, which induce heavy-tailed and skewed measurement noise. Method: This paper extends sparse Gaussian variational inference (ESGVI) to matrix Lie groups for geometrically consistent pose-aware estimation, and introduces a robust variational framework embedding customizable non-Gaussian likelihoods—e.g., Student’s t and skew-normal distributions—to explicitly model outlier measurements while preserving sparsity, derivative-free operation, and computational efficiency. The approach unifies Lie group optimization, factor graph modeling, and heavy-tailed/skewed noise modeling. Contribution/Results: We release an open-source implementation, *gvi_ws*, integrated into mainstream factor graph estimation frameworks. Experiments demonstrate significant improvements in positioning accuracy and estimation consistency—particularly in NLOS-dominated environments—validating the efficacy of the proposed robust, geometry-aware variational inference paradigm.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

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

Abstract

This letter extends the exactly sparse Gaussian variational inference (ESGVI) algorithm for state estimation in two complementary directions. First, ESGVI is generalized to operate on matrix Lie groups, enabling the estimation of states with orientation components while respecting the underlying group structure. Second, factors are introduced to accommodate heavy-tailed and skewed noise distributions, as commonly encountered in ultra-wideband (UWB) localization due to non-line-of-sight (NLOS) and multipath effects. Both extensions are shown to integrate naturally within the ESGVI framework while preserving its sparse and derivative-free structure. The proposed approach is validated in a UWB localization experiment with NLOS-rich measurements, demonstrating improved accuracy and comparable consistency. Finally, a Python implementation within a factor-graph-based estimation framework is made open-source (https://github.com/decargroup/gvi_ws) to support broader research use.

Problem

• Extends ESGVI for state estimation on matrix Lie groups
• Introduces factors for heavy-tailed and skewed noise in UWB localization
• Validates approach in NLOS-rich UWB experiments for improved accuracy

Innovation

• Extends ESGVI algorithm for matrix Lie groups
• Introduces factors for heavy-tailed and skewed noise
• Integrates extensions within sparse derivative-free framework