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

arXiv: https://arxiv.org/abs/2512.19855 · HTML: https://mlsanity.com/paper/2512.19855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Omni-swarm: A Decentralized Omnidirectional Visual-Inertial-UWB State Estimation System for Aerial Swarms](https://mlsanity.com/paper/2103.04131/) (2021)
- [Exactly Sparse Gaussian Variational Inference with Application to Derivative-Free Batch Nonlinear State Estimation](https://mlsanity.com/paper/1911.08333/) (2019)
- [Advancing Mixture Models for Least Squares Optimization](https://mlsanity.com/paper/2103.02472/) (2021)
- [VIR-SLAM: Visual, Inertial, and Ranging SLAM for single and multi-robot systems](https://mlsanity.com/paper/2006.00420/) (2020)
- [Uncertainty-aware Gaussian Mixture Model for UWB Time Difference of Arrival Localization in Cluttered Environments](https://mlsanity.com/paper/2307.16848/) (2023)
- [Variational Inference with Parameter Learning Applied to Vehicle Trajectory Estimation](https://mlsanity.com/paper/2003.09736/) (2020)
- [Multi-Agent Relative Pose Estimation with UWB and Constrained Communications](https://mlsanity.com/paper/2203.11004/) (2022)
- [Calibration and Uncertainty Characterization for Ultra-Wideband Two-Way-Ranging Measurements](https://mlsanity.com/paper/2210.05888/) (2022)
- [MURP: Multi-Agent Ultra-Wideband Relative Pose Estimation with Constrained Communications in 3D Environments](https://mlsanity.com/paper/2312.17731/) (2023)

## Abstract (arXiv)

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.