改进高斯变分推断，提升超宽带定位在非视距环境下的精度与鲁棒性。
Gaussian Variational Inference with Non-Gaussian Factors for State Estimation: A UWB Localization Case Study
- 在矩阵李群上扩展算法，支持方向状态估计并保持结构一致性。
- 引入非高斯因子，有效应对超宽带定位中的重尾和偏斜噪声。
- 开源实现支持研究复现，适合做高精度定位与不确定性建模的开发者。
本文将精确稀疏高斯变分推断（ESGVI）算法拓展至两个互补方向：首先，将算法推广至矩阵李群，实现含方向分量的状态估计，同时保留底层群结构特性；其次，引入非高斯因子以处理超宽带（UWB）定位中常见的非视距（NLOS）与多径效应带来的重尾及偏斜噪声分布。两项扩展均自然融入原ESGVI框架，保持其稀疏性与无导数特性。通过富含非视距测量的UWB定位实验验证，新方法在精度上优于传统方法，且一致性相当。相关代码已基于因子图框架开源（https://github.com/decargroup/gvi_ws），便于学术与工程应用。
原文摘要 · Abstract (English)
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.
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