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.

翻译：本通讯从两个互补方向扩展了精确稀疏高斯变分推断（ESGVI）算法在状态估计中的应用。首先，将ESGVI推广至在矩阵李群上操作，从而能够估计包含方向分量的状态，同时尊重底层的群结构。其次，引入了能够适应重尾和偏斜噪声分布的因子，这在超宽带（UWB）定位中因非视距（NLOS）和多径效应而普遍存在。研究表明，这两项扩展均能自然地融入ESGVI框架，同时保持其稀疏和无导数的结构。所提方法在一个包含大量NLOS测量的UWB定位实验中得到了验证，显示出更高的精度和相当的一致性。最后，基于因子图的估计框架内的Python实现已开源（https://github.com/decargroup/gvi_ws），以支持更广泛的研究使用。