Uncertainty analysis for accurate ground truth trajectories with robotic total stations

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.