Gaussian Variational Inference with Non-Gaussian Factors for State Estimation: A UWB Localization Case Study
Andrew Stirling, Mykola Lukashchuk, Dmitry Bagaev, Wouter Kouw, James Richard Forbes
AI summary
Problem
Standard batch state estimation methods assume Gaussian noise and Euclidean states, making them sensitive to outliers and geometric inconsistencies in real-world robotics, particularly in UWB localization plagued by NLOS/multipath effects and orientation constraints.
Approach
The authors extend the Exactly Sparse Gaussian Variational Inference (ESGVI) algorithm to operate on matrix Lie groups for proper orientation handling and integrate non-Gaussian measurement factors (like Skew-Laplace) to model heavy-tailed, skewed noise distributions.
Key results
- Generalized ESGVI to matrix Lie group states for manifold-consistent estimation.
- Integrated non-Gaussian (Skew-Laplace) measurement factors into the variational framework.
- Demonstrated improved accuracy and comparable consistency in real-world NLOS-rich UWB localization experiments.
- Released an open-source Python implementation within a factor-graph framework.
Why it matters
Provides robotics researchers and practitioners with a robust, derivative-free variational inference tool that handles real-world sensor noise and geometric constraints without sacrificing scalability.
Abstract
This letter extends the exactly sparse Gaussian vari- ational 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 orienta- tion 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 to support broader research use.