Determining uncertainties of correlated measurements by Monte Carlo simulations applied to laserscanning

Karl-Rudolf Koch 1
  • 1 Theoretical Geodesy, Institute of Geodesy and Geoinformation, University of Bonn, Nussallee 17, 53115 Bonn, Germany. E-mail:


The determination of uncertainties according to the “Guide to the Expression of Uncertainty in Measurement (GUM)” is extended to correlated measurements. The correlations are estimated by repeated observations. Uniform, trapezoidal and triangular distributions recommended by GUM are generalized to multivariate distributions by Monte Carlo simulations. To introduce the Type B component of uncertainty of GUM, which expresses uncertainty based on experience, two methods are discussed. The first one introduces individual corrections to the measurements with identical variances, the second one an identical correction with the same variance to each observation. Correlations are caused by the latter method. The correlations of the coordinates of points measured by the laserscanner Leica HDS 3000 are estimated from repeated observations. Except for the correlations of the three coordinates of the same points, the correlations turn out to be small. Nevertheless, they should be considered for the uncertainties of distances derived from the coordinates, especially if an addition constant for the measured distances of the laserscanner is introduced.

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This journal is a forum for research articles in the area of application of geodesy to engineering and other natural sciences. It publishes innovative contributions on sensor developments, multi-sensor systems and sensor data fusion focusing on the capture of georeferenced data. The scope covers various other topics related to applied geodesy, such as optical and microwave 3-D measurement techniques and other sensors for geotechnical measurements.