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

TL;DR

This paper extends Gaussian variational inference for state estimation to handle non-Gaussian noise and orientation states on Lie groups, validated through UWB localization experiments showing improved accuracy.

Contribution

It introduces a generalized ESGVI algorithm for matrix Lie groups and heavy-tailed noise, maintaining sparsity and derivative-free properties.

Findings

Improved localization accuracy in NLOS-rich UWB measurements

Maintains computational efficiency with sparse, derivative-free structure

Open-source Python implementation available for research use

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.