Uncertainty and quality of multi-sensor systems

By default multi-sensor systems, the combination of different sensors, are used in static (e.g. monitoring) and dynamic (e.g. kinematic data acquisition) environments for engineering geodesy and surveying. This covers sensors combined in one instrument (e.g. in terrestrial laser scanners or total stations) as well as measurement systems combining different sensors or instruments for integrated solutions (e.g. Static GNSS Monitoring Arrays or Mobile Mapping). At the FIG Working Week 2023 in Orlando, USA, the FIG Commission 6 ‘Engineering Surveying’ and the German Geodetic Commission jointly organized a scientific workshop on ‘Uncertainty and Quality of Multi-Sensor Systems’. On 27th–28th May 2023 an intensive scientific program ranging from ‘High Frequent Strain Measurements’ to ‘High Definition Mapping for Autonomous Driving’ was taking place. Together with the Editors-in-Chief of the Journal of Applied Geodesy (JAG) it was decided to give the interested presenters the opportunity to publish a peer-reviewed contribution in the JAG. In this issue four papers are put together to give the geodetic scientific community the chance to read the contents of the scientific workshop.

The first contribution is ‘Improving the approximation quality of tensor product B-spline surfaces by local parameterization’ by Corinna Harmening and Ramon Butzer [1]. This contribution deals with the modelling of Terrestrial Laser Scanning (TLS) point clouds using B-spline surfaces. The approximation quality of classical tensor product B-spline surfaces is improved by means of local parameterization. This covers the goodness-of-fit, correctness and stability of classical TP B-spline surfaces. The advantage is a smaller number of control points, finally delivering a less complex parametrization. The optimized B-spline surfaces were used to model four data sets (simulated and measured) with different characteristics, and the results were compared to nominal surfaces as well as to the results achieved by means of classical TP B-spline surfaces.

The second contribution ‘Development of GPS time-based reference trajectories for quality assessment of multi-sensor systems’ by Sören Vogel and Frederic Hake [2] deals with reliable reference information of superior accuracy serving as ground truth to validate multi-sensor systems. One important issue is reliable and accurate synchronization to GPS time, especially for kinematic multi-sensor systems. However, this global time information is not provided for high-accuracy tracking sensors such as robotic total stations (RTSs) or laser trackers (LTs). Linking UTC timestamps to raw observations from an RTS is generally possible using ‘Measure & Stream’ for supported Leica Geosystems instruments or using a precise trigger signal for laser trackers. The authors investigate how often the determination of the time offset is required to obtain a reliable and accurate estimation of the time drift. This depends on the instrument used, the expected tracking speed, and the required accuracy level.

In ‘PointNet-based modeling of systematic distance deviations for improved TLS accuracy’ by Jan Hartmann, Dominik Ernst, Ingo Neumann and Hamza Alkhatib [3] systematic deviations in TLS distance measurements are investigated. A calibration approach by applying a deep learning model based on PointNet to predict and correct these systematic distance deviations is developed. A data set collected under controlled environmental conditions, containing various objects of different materials, served as the basis for training and validation the PointNet based model. The analysis shows the model’s capability to accurately model systematic distance deviations. By defining test data sets, excluded from the training process, it could be shown that the accuracy of the TLS point cloud could be improved.

Finally, the contribution ‘Empirical uncertainty evaluation for the pose of a kinematic LiDAR-based multi-sensor system’ by Dominik Ernst, Sören Vogel, Ingo Neumann and Hamza Alkhatib [4] deals with the accuracy of trajectories of kinematic multi-sensor systems including low-cost LiDARs. These LiDARs deviate from other geodetic sensors in their uncertainty modelling. This paper demonstrates the uncertainty evaluation of a LiDAR-based MSS localizing itself using an inertial measurement unit (IMU) and matching LiDAR observations to a known map. Sensor data fusion is realized in a novel Error State Kalman filter, considering the influences of the sensor uncertainties and their combinations. The results provide new insights into the impact of random and systematic deviations resulting from parameters and their uncertainties established in prior calibrations.