Ultra Wideband (UWB) is widely used to mitigate drift in visual-inertial odometry (VIO) systems. Consistency is crucial for ensuring the estimation accuracy of a UWBaided VIO system. An inconsistent estimator can degrade localization performance, where the inconsistency primarily arises from two main factors: (1) the estimator fails to preserve the correct system observability, and (2) UWB anchor positions are assumed to be known, leading to improper neglect of calibration uncertainty. In this paper, we propose a consistent and tightly-coupled visual-inertial-ranging odometry (CVIRO) system based on the Lie group. Our method incorporates the UWB anchor state into the system state, explicitly accounting for UWB calibration uncertainty and enabling the joint and consistent estimation of both robot and anchor states. Furthermore, observability consistency is ensured by leveraging the invariant error properties of the Lie group. We analytically prove that the CVIRO algorithm naturally maintains the system's correct unobservable subspace, thereby preserving estimation consistency. Extensive simulations and experiments demonstrate that CVIRO achieves superior localization accuracy and consistency compared to existing methods.

翻译：超宽带（UWB）技术被广泛应用于抑制视觉-惯性里程计（VIO）系统的漂移。一致性对于保证UWB辅助VIO系统的估计精度至关重要。不一致的估计器会降低定位性能，其不一致性主要源于两个因素：（1）估计器未能保持正确的系统可观测性；（2）假设UWB锚点位置已知，导致校准不确定性被不当忽略。本文提出一种基于李群的一致紧耦合视觉-惯性-测距里程计（CVIRO）系统。该方法将UWB锚点状态纳入系统状态，显式处理UWB校准不确定性，实现对机器人状态与锚点状态的联合一致估计。此外，通过利用李群的不变性误差特性确保可观测性一致。我们通过理论分析证明，CVIRO算法能自然保持系统正确的不可观测子空间，从而维持估计一致性。大量仿真与实验表明，相较于现有方法，CVIRO在定位精度与一致性方面均表现出显著优势。