Artificial intelligence for determining systematic effects of laser scanners
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(2019) 10:3
ORIGINAL PAPER
Artificial intelligence for determining systematic effects of laser scanners Karl-Rudolf Koch1
· Jan Martin Brockmann1
Received: 6 November 2018 / Accepted: 13 November 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract Artificial intelligence is interpreted by a machine learning algorithm. Its realization is applied for a two-dimensional grid of points and depends on six parameters which determine the limits of loops. The outer loop defines the width of the grid, the most inner loop the number of scans, which result from the three-dimensional coordinate system for the xi -, yi -, z i -coordinates of a laser scanner. The yi -coordinates approximate the distances measured by the laser scanner. The minimal standard deviations of the measurements distorted by systematic effects for the yi -coordinates are computed by the Monte Carlo estimate of Sect. 6. The minimum of these minimal standard deviations is found in the grid of points by the machine learning algorithm and used to judge the outcome. Two results are given in Sect. 7. They differ by the widths of the grid and show that only for precise applications the systematic effects of the laser scanner have to be taken care of. Instead of assuming a standard deviation for the systematic effects from prior information as mentioned in Sect. 1, the xi -, yi -, z i coordinates are repeatedly measured by the laser scanner. However, there are too few repetitions to fulfill the conditions of the multivariate model of Sect. 2 for all measured coordinates. The variances of the measurements plus systematic effects computed by the Monte Carlo estimate of Sect. 6 can therefore be obtained for a restricted number of points only. This number is computed by random variates. For two numbers, the variations of the standard deviations of the yi -coordinates, the variations of the standard deviations of the xi -, yi -, z i -coordinates from the multivariate model, the variations of the standard deviations of the systematic effects and the variations of the confidence intervals are presented. The repeated measurements define time series whose autoand cross-correlation functions are applied as correlations for the systematic effects of the measurements. The ergodicity of the time series is shown. Keywords Machine learning algorithm · Repeated measurement · Confidence interval · Autocovariance and cross-covariance function · Probability density function · Monte Carlo method Mathematics Subject Classification 60-04
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GEM - International Journal on Geomathematics
(2019) 10:3
1 Introduction Artificial intelligence is understood here as machine learning which is presented in Sect. 3 on the machine learning algorithm, cf. Williams et al. (2006). Systematic effects have to be expected in the measurements of the three-dimensional coordinates by a laser scanner despite a calibration. Systematic effects are neither random, since
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