Interval-based Uncertainty Bounding for Terrestrial Laser Scanning Observations

One of the main fields of engineering geodesy is deformation monitoring of natural and man-made structures. Infrastructure objects such as bridges, dams, and tunnels are of special interest because their operational safety must be ensured at all times. Area-based deformation analysis can be effectively conducted using terrestrial laser scanners (TLS). Unlike the limited, pre-selected, and point-based measurements used in traditional approaches, TLS samples the environment with millions of points without the need to signal the points. Point clouds data from TLS are influenced by remaining systematic errors as well as random noise. These sources of uncertainty are frequently handled using probabilistic approaches, which may provide an inadequate or overoptimistic representation of the overall uncertainty in point cloud data. In this contribution, an alternative approach based on interval mathematics is proposed to bound the uncertainty due to remaining systematic errors. To this end, a sensitivity analysis of TLS observation correction models is performed, and typical variability of the input parameters, such as temperature, pressure, humidity, and temperature gradients, as well as instrument misalignment, is assessed. Subsequently, error bands for the polar measurement elements in the form of intervals are obtained. While variance propagation follows a quadratic form, interval-based techniques enable linear uncertainty propagation, which is more effective for describing residual systematic uncertainty and worst-case scenarios. The methodology will be explained in detail, and typical values for the obtained intervals will be discussed and highlighted in a simulation study.