  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.
