用归一化流增强消息传递，实现多机器人协同定位的高精度自适应估计。
Normalizing Flow-Enhanced Message Passing for Multirobot Collaborative Localization
- 融合高斯信念传播与均值场近似，兼顾状态依赖与噪声估计。
- 引入基于归一化流的可学习采样梯度器，提升非线性测量下的定位精度。
- 适用于含旋转的状态空间，实测在自主水面艇上表现优异。
精确、鲁棒且自适应的定位对各类机器人任务至关重要。本文提出一种新型分布式消息传递（MP）算法，用于实现多机器人协同定位。该算法统一了高斯信念传播（GBP）与均值场（MF）近似：GBP保留机器人状态间的依赖关系，MF支持噪声统计估计。为有效处理非共轭项（来自非线性测量模型），算法采用参数化形式，通过梯度估计器处理这些项。除线性化与采样外，进一步设计基于归一化流（NF）的梯度估计器，实现可学习采样。端到端训练根据MP行为调整NF参数，提升整体估计性能。为支持包含旋转的实际机器人状态，方法扩展至李群状态空间。最终应用于融合里程计、全球导航卫星系统（GNSS）及机器人间超宽带（UWB）测距的多机器人定位任务。仿真与自主水面艇（ASVs）实验表明，该方法在精度、鲁棒性和适应性方面均有显著提升。
原文摘要 · Abstract (English)
Accurate, robust, and adaptive localization is essential for various robotic operations. This paper proposes a new message passing (MP) algorithm for realizing collaborative localization in a distributed manner. The algorithm unifies Gaussian belief propagation (GBP) and mean-field (MF) approximation, where GBP preserves dependencies among robot states, and MF enables estimation of noise statistics. To effectively handle non-conjugate terms from nonlinear measurement models, the algorithm adopts a parametric formulation in which these terms are treated by gradient estimators. Beyond linearization and sampling, we further design a normalizing flow (NF)-based gradient estimator, enabling learnable sampling. End-to-end training tunes NF parameters according to the behavior of MP, improving the overall estimation performance. To support estimation of practical robotic states that involve rotations, the method is then extended to Lie group state spaces. Finally, the method is applied to multirobot localization task fusing odometry, global navigation satellite system (GNSS) measurements, and inter-robot ultra wideband (UWB) ranging. Simulations and experiments on autonomous surface vehicles (ASVs) demonstrate its improved accuracy, robustness, and adaptability.
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