Figure:Correlation structure for TLS and GNSS observations: a parallel

An improved stochastic model for TLS observations is of main importance, particularly when the observations are used in least-squares adjustment. Indeed, the best unbiased estimates of unknown parameters in linear models have the smallest expected meansquared errors as long as the residuals are weighted with their true variance covariance matrix.

During 2018, we have started investigating the stochastic model of TLS point clouds with a focus on the correlation structure and its impact of surface and curve modelization with B-splines. Since TLS raw measurements are made of range and angles, both mathematical and physical correlations have to be accounted for. Mathematical correlations comes from the transformation from polar to Cartesian coordinates in the determination of control points for B-splines approximation with least-squares. Physical correlations can be spatial or temporal, i.e. depends on the time when the measurements were taken and on the object on which the laser was reflected. They need to be modelled more accurately to get trustworthy test statistics in case of deformation analysis with e.g. the congruency test. Because GNSS phase observations shares the same concept as TLS range measurements, we made a parallel betwen the two stochastic models and made first proposal how a correlation model for TLS range measurements would look like. Additionally, we proposed a simplification of the intensity model for a use in regression B-splines approximation.

First promising results were obtained by using TLS observations from the historic masonry arch bridge over the river Aller near Verden in Germany, particularly to assess the impact of mathematical correlations on test statistics.