Artificial intelligence for determining systematic effects of laser scanners
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 \(x_i\)-, \(y_i\)-, \(z_i\)-coordinates of a laser scanner. The \(y_i\)-coordinates approximate the distances measured by the laser scanner. The minimal standard deviations of the measurements distorted by systematic effects for the \(y_i\)-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 \(x_i\)-, \(y_i\)-, \(z_i\)-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 \(y_i\)-coordinates, the variations of the standard deviations of the \(x_i\)-, \(y_i\)-, \(z_i\)-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 auto- and cross-correlation functions are applied as correlations for the systematic effects of the measurements. The ergodicity of the time series is shown.
KeywordsMachine learning algorithm Repeated measurement Confidence interval Autocovariance and cross-covariance function Probability density function Monte Carlo method
Mathematics Subject Classification60-04
The authors are indebted to Ernst-Martin Blome for taking care of the measurements and to Boris Kargoll for his valuable comments.
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