In the context of robotics, accurate ground truth positioning is essential for the development of Simultaneous Localization and Mapping (SLAM) and control algorithms. Robotic Total Stations (RTSs) provide accurate and precise reference positions in different types of outdoor environments, especially when compared to the limited accuracy of Global Navigation Satellite System (GNSS) in cluttered areas. Three RTSs give the possibility to obtain the six-Degrees Of Freedom (DOF) reference pose of a robotic platform. However, the uncertainty of every pose is rarely computed for trajectory evaluation. As evaluation algorithms are getting increasingly precise, it becomes crucial to take into account this uncertainty. We propose a method to compute this six-DOF uncertainty from the fusion of three RTSs based on Monte Carlo (MC) methods. This solution relies on point-to-point minimization to propagate the noise of RTSs on the pose of the robotic platform. Five main noise sources are identified to model this uncertainty: noise inherent to the instrument, tilt noise, atmospheric factors, time synchronization noise, and extrinsic calibration noise. Based on extensive experimental work, we compare the impact of each noise source on the prism uncertainty and the final estimated pose. Tested on more than 50 km of trajectories, our comparison highlighted the importance of the calibration noise and the measurement distance, which should be ideally under 75 m. Moreover, it has been noted that the uncertainty on the pose of the robot is not prominently affected by one particular noise source, compared to the others.

翻译：在机器人领域，精确的地面真值定位对于同步定位与建图（SLAM）及控制算法的开发至关重要。机器人全站仪（RTS）能在各类户外环境中提供高精度的参考位置，尤其是在全球导航卫星系统（GNSS）因环境遮挡而精度受限的区域更具优势。通过三台RTS协同工作，可获得机器人平台的六自由度（DOF）参考位姿。然而，在轨迹评估中，各姿态的不确定性鲜少被计算。随着评估算法精度日益提升，考虑这种不确定性变得至关重要。我们提出一种基于蒙特卡洛（MC）方法的三台RTS融合六自由度不确定性计算方法。该方案通过点对点最小化技术，将RTS噪声传播至机器人平台位姿。为建模该不确定性，我们识别了五类主要噪声源：仪器固有噪声、倾斜噪声、大气因素、时间同步噪声及外参标定噪声。通过大量实验，我们比较了各类噪声源对棱镜不确定性和最终估计位姿的影响。在超过50公里轨迹的测试中，对比结果凸显了标定噪声与测量距离的重要性——理想情况下测量距离应控制在75米以内。此外，研究发现机器人位姿不确定性并非由单一噪声源主导，而是受多源噪声协同作用。