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Sensors 2018, 18(9), 2964; https://doi.org/10.3390/s18092964

On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation

Geodetic Institute, Leibniz Universität Hannover, Nienburger Str. 1, 30167 Hannover, Germany
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Received: 12 July 2018 / Revised: 28 August 2018 / Accepted: 3 September 2018 / Published: 5 September 2018
(This article belongs to the Special Issue Terrestrial Laser Scanning)
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Abstract

For a trustworthy least-squares (LS) solution, a good description of the stochastic properties of the measurements is indispensable. For a terrestrial laser scanner (TLS), the range variance can be described by a power law function with respect to the intensity of the reflected signal. The power and scaling factors depend on the laser scanner under consideration, and could be accurately determined by means of calibrations in 1d mode or residual analysis of LS adjustment. However, such procedures complicate significantly the use of empirical intensity models (IM). The extent to which a point-wise weighting is suitable when the derived variance covariance matrix (VCM) is further used in a LS adjustment remains moreover questionable. Thanks to closed loop simulations, where both the true geometry and stochastic model are under control, we investigate how variations of the parameters of the IM affect the results of a LS adjustment. As a case study, we consider the determination of the Cartesian coordinates of the control points (CP) from a B-splines curve. We show that a constant variance can be assessed to all the points of an object having homogeneous properties, without affecting the a posteriori variance factor or the loss of efficiency of the LS solution. The results from a real case scenario highlight that the conclusions of the simulations stay valid even for more challenging geometries. A procedure to determine the range variance is proposed to simplify the computation of the VCM. View Full-Text
Keywords: terrestrial laser scanner; stochastic model; B-spline approximation; control point; intensity-based model terrestrial laser scanner; stochastic model; B-spline approximation; control point; intensity-based model
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kermarrec, G.; Alkhatib, H.; Neumann, I. On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation. Sensors 2018, 18, 2964.

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