Abstract

Rigorous statistical testing of deformation using a terrestrial laser scanner (TLS) can avoid events such as structure collapses. Such a procedure necessitates an accurate description of the TLS measurements’ noise, which should include the correlations between angles. Unfortunately, these correlations are often unaccounted for due to a lack of knowledge. This contribution addresses this challenge. We combine (i) a least-square approximation to extract the geometry of the TLS point cloud with the aim to analyze the residuals of the fitting and (ii) a specific filtering coupled with a maximum likelihood estimation to quantify the amount of flicker noise versus white noise. This allows us to set up fully populated variance covariance matrices of the TLS noise as a result.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  • Author
  • Publication
  1. N. Pfeifer and C. Briese, “Laser scanning–principles and applications,” GeoSiberia 2007–International Exhibition and Scientific Congress. European Association of Geoscientists & Engineers (2007).
  2. S. Soudarissanane, R. Lindenbergh, M. Menenti, and P. Teunissen, “Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points,” ISPRS J. Photogramm. Remote Sens. 66(4), 389–399 (2011).
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    [Crossref]
  5. K. R. Koch, “Nurbs surface with changing shape,” Allg. Vermess. Nachr. 3, 83–89 (2010).
  6. G. Kermarrec, B. Kargoll, and H. Alkhatib, “On the impact of correlations on the congruence test: A bootstrap approach,” Acta Geod. Geophys. 55(3), 495–513 (2020).
    [Crossref]
  7. H. Pelzer, “Zur Analyse geodätischer Deformationsmessungen,” Dtsch. Geodät. Komm. Ser. C. 164 (1971).
  8. D. Wujanz, M. Burger, M. Mettenleiter, and F. Neitzel, “An intensity-based stochastic model for terrestrial laser scanners,” ISPRS J. Photogramm. Remote Sens. 125, 146–155 (2017).
    [Crossref]
  9. C. Holst and H. Kuhlmann, “Challenges and present fields of action at laser scanner based deformation analyses,” J. Appl. Geodesy 10(1), 17–25 (2016).
    [Crossref]
  10. G. Kermarrec, B. Kargoll, and H. Alkhatib, “Deformation analysis using B-spline surface with correlated terrestrial laser scanner observations – a bridge under load,” Remote Sens. 12(5), 829 (2020).
    [Crossref]
  11. K. R. Koch, Parameter Estimation and Hypothesis Testing in Linear Models (Springer International Publishing, 1999).
  12. J-M. Bardet, G. Lang, G. Oppenheim, A. Philippe, S. Stoev, and M. S. Taqqu, “Semi-parametric estimation of the long-range dependence parameter: A survey,” in Theory and Applications of Long-range Dependence (Birkhäuser, 2003), pp. 557–577.
  13. F. Neitzel, “Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation,” J. Geod. 84(12), 751–762 (2010).
    [Crossref]
  14. Y. Reshetyuk, Investigation and Calibration of Pulsed Time-of-flight Terrestrial Laser Scanners, (Trita-TEC-LIC, 2006).
  15. S. Alvarez-Rodríguez and N. Alcalá-Ochoa, “Low-cost encoder using a phase shifting algorithm utilizing polarization properties of light,” Appl. Opt. 55(33), 9450–9458 (2016).
    [Crossref]
  16. S. Alvarez-Rodríguez, F. G. Gerardo Peña-Lecona, M. Briones, M. Helguera, and N. Alcalá-Ochoa, “Low-cost non-concentric diffraction-based encoder,” Opt. Laser Technol. 138, 106836 (2021).
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  17. . Zoller + Fröhlich GmbH, “Z + F IMAGER 5016, 3d laser scanner data sheet” (2017), https://www.zf-laser.com/Z-F-IMAGER-R-5016.184.0.html.
  18. H. Austerlitz, “Analog signal transducers,” In Data Acquisition Techniques Using PCs, 2nd ed. (Academic Press, 2003), pp. 6–28.
  19. S. Alvarez-Rodrígue, N. Alcalá-Ochoa, J. Cruz-Salgado, and F. G. Peña Lecona, “Suppression of noise to obtain a high-performance low-cost optical encoder,” J. Sens. 2018, 1–10 (2018).
    [Crossref]
  20. L. Ward and P. Greenwood, “1/f noise,” Scholarpedia 2(12), 1537 (2007).
    [Crossref]
  21. F. F. Mazda, Telecommunications Engineer’s Reference Book (Butterworth-Heinemann, 1993).
  22. B. Levush, K. L. Jensen, and Y. Y. Lau, “A comparison of flicker noise and shot noise on a hot cathode,” IEEE Trans. Plasma Sci. 28(3), 794–797 (2000).
    [Crossref]
  23. G. A. Mihram, Simulation. Statistical Foundations and Methodology. Mathematics in Science and Engineering. (Academic Press, 1972).
  24. F. N. Hooge, “1/f noise sources,” IEEE Trans. Electron Devices 41(11), 1926–1935 (1994).
    [Crossref]
  25. B. Carter, “Op amp noise theory and applications,” in Op Amps for Everyone, 3rd ed. (Newnes/Elsevier, 2009), pp. 163–188.
  26. I. N. Bronshtein, H. Muehlig, G. Musiol, and K. A. Semendiaev, Handbook of Mathematics, 5th ed. (Springer, 2007).
  27. G. Kermarrec, M. Lösler, and J. Hartmann, “Analysis of the temporal correlations of TLS range observations from plane fitting residuals,” ISPRS J. Photogramm. Remote Sens. 171, 119–132 (2021).
    [Crossref]
  28. G. Kermarrec, “On estimating the Hurst parameter from least-squares residuals. Case study: Correlated terrestrial laser scanner range noise,” Mathematics 8(5), 674 (2020).
    [Crossref]
  29. S. Butterworth, “On the theory of filter amplifiers,” Wireless Eng. 7, 536–541 (1930).
  30. B. B. Mandelbrot, The Fractional Geometry of Nature (Birkhäuser, 1987).
  31. A. M. Sykulski, S. C. Olhede, A. P. Guillaumin, J. M. Lilly, and J. J. Early, “The debiased Whittle likelihood,” Biometrika 106(2), 251–266 (2019).
    [Crossref]
  32. P. Abry and D. Veitch, “Wavelet analysis of long-range-dependent traffic,” IEEE Trans. Inform. Theory 44(1), 2–15 (1998).
    [Crossref]
  33. P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, (Springer, 1991).
  34. P. Whittle, “Estimation and information in stationary time series,” Ark. Mat. 2(5), 423–434 (1953).
    [Crossref]
  35. M. S. Bos, J.-P. Montillet, S. D. Williams, and R. M. Fernandes, “Introduction to geodetic time series analysis,” arXiv: Other Statistics, 29–52 (2020).
  36. P. J. Rousseeuw, “Least median of squares regression,” J. Am. Stat. Assoc. 79(388), 871–880 (1984).
    [Crossref]
  37. W. F. Caspary, W. Haen, and H. Borutta, “Deformation Analysis by Statistical Methods,” Technometrics 32(1), 49–57 (1990).
    [Crossref]

2021 (2)

S. Alvarez-Rodríguez, F. G. Gerardo Peña-Lecona, M. Briones, M. Helguera, and N. Alcalá-Ochoa, “Low-cost non-concentric diffraction-based encoder,” Opt. Laser Technol. 138, 106836 (2021).
[Crossref]

G. Kermarrec, M. Lösler, and J. Hartmann, “Analysis of the temporal correlations of TLS range observations from plane fitting residuals,” ISPRS J. Photogramm. Remote Sens. 171, 119–132 (2021).
[Crossref]

2020 (3)

G. Kermarrec, “On estimating the Hurst parameter from least-squares residuals. Case study: Correlated terrestrial laser scanner range noise,” Mathematics 8(5), 674 (2020).
[Crossref]

G. Kermarrec, B. Kargoll, and H. Alkhatib, “On the impact of correlations on the congruence test: A bootstrap approach,” Acta Geod. Geophys. 55(3), 495–513 (2020).
[Crossref]

G. Kermarrec, B. Kargoll, and H. Alkhatib, “Deformation analysis using B-spline surface with correlated terrestrial laser scanner observations – a bridge under load,” Remote Sens. 12(5), 829 (2020).
[Crossref]

2019 (1)

A. M. Sykulski, S. C. Olhede, A. P. Guillaumin, J. M. Lilly, and J. J. Early, “The debiased Whittle likelihood,” Biometrika 106(2), 251–266 (2019).
[Crossref]

2018 (1)

S. Alvarez-Rodrígue, N. Alcalá-Ochoa, J. Cruz-Salgado, and F. G. Peña Lecona, “Suppression of noise to obtain a high-performance low-cost optical encoder,” J. Sens. 2018, 1–10 (2018).
[Crossref]

2017 (1)

D. Wujanz, M. Burger, M. Mettenleiter, and F. Neitzel, “An intensity-based stochastic model for terrestrial laser scanners,” ISPRS J. Photogramm. Remote Sens. 125, 146–155 (2017).
[Crossref]

2016 (2)

C. Holst and H. Kuhlmann, “Challenges and present fields of action at laser scanner based deformation analyses,” J. Appl. Geodesy 10(1), 17–25 (2016).
[Crossref]

S. Alvarez-Rodríguez and N. Alcalá-Ochoa, “Low-cost encoder using a phase shifting algorithm utilizing polarization properties of light,” Appl. Opt. 55(33), 9450–9458 (2016).
[Crossref]

2011 (1)

S. Soudarissanane, R. Lindenbergh, M. Menenti, and P. Teunissen, “Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points,” ISPRS J. Photogramm. Remote Sens. 66(4), 389–399 (2011).
[Crossref]

2010 (2)

K. R. Koch, “Nurbs surface with changing shape,” Allg. Vermess. Nachr. 3, 83–89 (2010).

F. Neitzel, “Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation,” J. Geod. 84(12), 751–762 (2010).
[Crossref]

2007 (1)

L. Ward and P. Greenwood, “1/f noise,” Scholarpedia 2(12), 1537 (2007).
[Crossref]

2006 (1)

D. D. Lichti and S. Jamtsho, “Angular resolution of terrestrial laser scanners,” Photogramm. Rec. 21(114), 141–160 (2006).
[Crossref]

2000 (1)

B. Levush, K. L. Jensen, and Y. Y. Lau, “A comparison of flicker noise and shot noise on a hot cathode,” IEEE Trans. Plasma Sci. 28(3), 794–797 (2000).
[Crossref]

1998 (1)

P. Abry and D. Veitch, “Wavelet analysis of long-range-dependent traffic,” IEEE Trans. Inform. Theory 44(1), 2–15 (1998).
[Crossref]

1994 (1)

F. N. Hooge, “1/f noise sources,” IEEE Trans. Electron Devices 41(11), 1926–1935 (1994).
[Crossref]

1990 (1)

W. F. Caspary, W. Haen, and H. Borutta, “Deformation Analysis by Statistical Methods,” Technometrics 32(1), 49–57 (1990).
[Crossref]

1984 (1)

P. J. Rousseeuw, “Least median of squares regression,” J. Am. Stat. Assoc. 79(388), 871–880 (1984).
[Crossref]

1953 (1)

P. Whittle, “Estimation and information in stationary time series,” Ark. Mat. 2(5), 423–434 (1953).
[Crossref]

1930 (1)

S. Butterworth, “On the theory of filter amplifiers,” Wireless Eng. 7, 536–541 (1930).

Abry, P.

P. Abry and D. Veitch, “Wavelet analysis of long-range-dependent traffic,” IEEE Trans. Inform. Theory 44(1), 2–15 (1998).
[Crossref]

Alcalá-Ochoa, N.

S. Alvarez-Rodríguez, F. G. Gerardo Peña-Lecona, M. Briones, M. Helguera, and N. Alcalá-Ochoa, “Low-cost non-concentric diffraction-based encoder,” Opt. Laser Technol. 138, 106836 (2021).
[Crossref]

S. Alvarez-Rodrígue, N. Alcalá-Ochoa, J. Cruz-Salgado, and F. G. Peña Lecona, “Suppression of noise to obtain a high-performance low-cost optical encoder,” J. Sens. 2018, 1–10 (2018).
[Crossref]

S. Alvarez-Rodríguez and N. Alcalá-Ochoa, “Low-cost encoder using a phase shifting algorithm utilizing polarization properties of light,” Appl. Opt. 55(33), 9450–9458 (2016).
[Crossref]

Alkhatib, H.

G. Kermarrec, B. Kargoll, and H. Alkhatib, “Deformation analysis using B-spline surface with correlated terrestrial laser scanner observations – a bridge under load,” Remote Sens. 12(5), 829 (2020).
[Crossref]

G. Kermarrec, B. Kargoll, and H. Alkhatib, “On the impact of correlations on the congruence test: A bootstrap approach,” Acta Geod. Geophys. 55(3), 495–513 (2020).
[Crossref]

Alvarez-Rodrígue, S.

S. Alvarez-Rodrígue, N. Alcalá-Ochoa, J. Cruz-Salgado, and F. G. Peña Lecona, “Suppression of noise to obtain a high-performance low-cost optical encoder,” J. Sens. 2018, 1–10 (2018).
[Crossref]

Alvarez-Rodríguez, S.

S. Alvarez-Rodríguez, F. G. Gerardo Peña-Lecona, M. Briones, M. Helguera, and N. Alcalá-Ochoa, “Low-cost non-concentric diffraction-based encoder,” Opt. Laser Technol. 138, 106836 (2021).
[Crossref]

S. Alvarez-Rodríguez and N. Alcalá-Ochoa, “Low-cost encoder using a phase shifting algorithm utilizing polarization properties of light,” Appl. Opt. 55(33), 9450–9458 (2016).
[Crossref]

Austerlitz, H.

H. Austerlitz, “Analog signal transducers,” In Data Acquisition Techniques Using PCs, 2nd ed. (Academic Press, 2003), pp. 6–28.

Bardet, J-M.

J-M. Bardet, G. Lang, G. Oppenheim, A. Philippe, S. Stoev, and M. S. Taqqu, “Semi-parametric estimation of the long-range dependence parameter: A survey,” in Theory and Applications of Long-range Dependence (Birkhäuser, 2003), pp. 557–577.

Borutta, H.

W. F. Caspary, W. Haen, and H. Borutta, “Deformation Analysis by Statistical Methods,” Technometrics 32(1), 49–57 (1990).
[Crossref]

Bos, M. S.

M. S. Bos, J.-P. Montillet, S. D. Williams, and R. M. Fernandes, “Introduction to geodetic time series analysis,” arXiv: Other Statistics, 29–52 (2020).

Briese, C.

N. Pfeifer and C. Briese, “Laser scanning–principles and applications,” GeoSiberia 2007–International Exhibition and Scientific Congress. European Association of Geoscientists & Engineers (2007).

Briones, M.

S. Alvarez-Rodríguez, F. G. Gerardo Peña-Lecona, M. Briones, M. Helguera, and N. Alcalá-Ochoa, “Low-cost non-concentric diffraction-based encoder,” Opt. Laser Technol. 138, 106836 (2021).
[Crossref]

Brockwell, P. J.

P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, (Springer, 1991).

Bronshtein, I. N.

I. N. Bronshtein, H. Muehlig, G. Musiol, and K. A. Semendiaev, Handbook of Mathematics, 5th ed. (Springer, 2007).

Burger, M.

D. Wujanz, M. Burger, M. Mettenleiter, and F. Neitzel, “An intensity-based stochastic model for terrestrial laser scanners,” ISPRS J. Photogramm. Remote Sens. 125, 146–155 (2017).
[Crossref]

Butterworth, S.

S. Butterworth, “On the theory of filter amplifiers,” Wireless Eng. 7, 536–541 (1930).

Carter, B.

B. Carter, “Op amp noise theory and applications,” in Op Amps for Everyone, 3rd ed. (Newnes/Elsevier, 2009), pp. 163–188.

Caspary, W. F.

W. F. Caspary, W. Haen, and H. Borutta, “Deformation Analysis by Statistical Methods,” Technometrics 32(1), 49–57 (1990).
[Crossref]

Cruz-Salgado, J.

S. Alvarez-Rodrígue, N. Alcalá-Ochoa, J. Cruz-Salgado, and F. G. Peña Lecona, “Suppression of noise to obtain a high-performance low-cost optical encoder,” J. Sens. 2018, 1–10 (2018).
[Crossref]

Davis, R. A.

P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, (Springer, 1991).

Early, J. J.

A. M. Sykulski, S. C. Olhede, A. P. Guillaumin, J. M. Lilly, and J. J. Early, “The debiased Whittle likelihood,” Biometrika 106(2), 251–266 (2019).
[Crossref]

Fernandes, R. M.

M. S. Bos, J.-P. Montillet, S. D. Williams, and R. M. Fernandes, “Introduction to geodetic time series analysis,” arXiv: Other Statistics, 29–52 (2020).

Gerardo Peña-Lecona, F. G.

S. Alvarez-Rodríguez, F. G. Gerardo Peña-Lecona, M. Briones, M. Helguera, and N. Alcalá-Ochoa, “Low-cost non-concentric diffraction-based encoder,” Opt. Laser Technol. 138, 106836 (2021).
[Crossref]

Greenwood, P.

L. Ward and P. Greenwood, “1/f noise,” Scholarpedia 2(12), 1537 (2007).
[Crossref]

Guillaumin, A. P.

A. M. Sykulski, S. C. Olhede, A. P. Guillaumin, J. M. Lilly, and J. J. Early, “The debiased Whittle likelihood,” Biometrika 106(2), 251–266 (2019).
[Crossref]

Haen, W.

W. F. Caspary, W. Haen, and H. Borutta, “Deformation Analysis by Statistical Methods,” Technometrics 32(1), 49–57 (1990).
[Crossref]

Hartmann, J.

G. Kermarrec, M. Lösler, and J. Hartmann, “Analysis of the temporal correlations of TLS range observations from plane fitting residuals,” ISPRS J. Photogramm. Remote Sens. 171, 119–132 (2021).
[Crossref]

Helguera, M.

S. Alvarez-Rodríguez, F. G. Gerardo Peña-Lecona, M. Briones, M. Helguera, and N. Alcalá-Ochoa, “Low-cost non-concentric diffraction-based encoder,” Opt. Laser Technol. 138, 106836 (2021).
[Crossref]

Holst, C.

C. Holst and H. Kuhlmann, “Challenges and present fields of action at laser scanner based deformation analyses,” J. Appl. Geodesy 10(1), 17–25 (2016).
[Crossref]

Hooge, F. N.

F. N. Hooge, “1/f noise sources,” IEEE Trans. Electron Devices 41(11), 1926–1935 (1994).
[Crossref]

Jamtsho, S.

D. D. Lichti and S. Jamtsho, “Angular resolution of terrestrial laser scanners,” Photogramm. Rec. 21(114), 141–160 (2006).
[Crossref]

Jensen, K. L.

B. Levush, K. L. Jensen, and Y. Y. Lau, “A comparison of flicker noise and shot noise on a hot cathode,” IEEE Trans. Plasma Sci. 28(3), 794–797 (2000).
[Crossref]

Kargoll, B.

G. Kermarrec, B. Kargoll, and H. Alkhatib, “On the impact of correlations on the congruence test: A bootstrap approach,” Acta Geod. Geophys. 55(3), 495–513 (2020).
[Crossref]

G. Kermarrec, B. Kargoll, and H. Alkhatib, “Deformation analysis using B-spline surface with correlated terrestrial laser scanner observations – a bridge under load,” Remote Sens. 12(5), 829 (2020).
[Crossref]

Kermarrec, G.

G. Kermarrec, M. Lösler, and J. Hartmann, “Analysis of the temporal correlations of TLS range observations from plane fitting residuals,” ISPRS J. Photogramm. Remote Sens. 171, 119–132 (2021).
[Crossref]

G. Kermarrec, “On estimating the Hurst parameter from least-squares residuals. Case study: Correlated terrestrial laser scanner range noise,” Mathematics 8(5), 674 (2020).
[Crossref]

G. Kermarrec, B. Kargoll, and H. Alkhatib, “Deformation analysis using B-spline surface with correlated terrestrial laser scanner observations – a bridge under load,” Remote Sens. 12(5), 829 (2020).
[Crossref]

G. Kermarrec, B. Kargoll, and H. Alkhatib, “On the impact of correlations on the congruence test: A bootstrap approach,” Acta Geod. Geophys. 55(3), 495–513 (2020).
[Crossref]

Koch, K. R.

K. R. Koch, “Nurbs surface with changing shape,” Allg. Vermess. Nachr. 3, 83–89 (2010).

K. R. Koch, Parameter Estimation and Hypothesis Testing in Linear Models (Springer International Publishing, 1999).

Kuhlmann, H.

C. Holst and H. Kuhlmann, “Challenges and present fields of action at laser scanner based deformation analyses,” J. Appl. Geodesy 10(1), 17–25 (2016).
[Crossref]

Lang, G.

J-M. Bardet, G. Lang, G. Oppenheim, A. Philippe, S. Stoev, and M. S. Taqqu, “Semi-parametric estimation of the long-range dependence parameter: A survey,” in Theory and Applications of Long-range Dependence (Birkhäuser, 2003), pp. 557–577.

Lau, Y. Y.

B. Levush, K. L. Jensen, and Y. Y. Lau, “A comparison of flicker noise and shot noise on a hot cathode,” IEEE Trans. Plasma Sci. 28(3), 794–797 (2000).
[Crossref]

Levush, B.

B. Levush, K. L. Jensen, and Y. Y. Lau, “A comparison of flicker noise and shot noise on a hot cathode,” IEEE Trans. Plasma Sci. 28(3), 794–797 (2000).
[Crossref]

Lichti, D. D.

D. D. Lichti and S. Jamtsho, “Angular resolution of terrestrial laser scanners,” Photogramm. Rec. 21(114), 141–160 (2006).
[Crossref]

Lilly, J. M.

A. M. Sykulski, S. C. Olhede, A. P. Guillaumin, J. M. Lilly, and J. J. Early, “The debiased Whittle likelihood,” Biometrika 106(2), 251–266 (2019).
[Crossref]

Lindenbergh, R.

S. Soudarissanane, R. Lindenbergh, M. Menenti, and P. Teunissen, “Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points,” ISPRS J. Photogramm. Remote Sens. 66(4), 389–399 (2011).
[Crossref]

Lösler, M.

G. Kermarrec, M. Lösler, and J. Hartmann, “Analysis of the temporal correlations of TLS range observations from plane fitting residuals,” ISPRS J. Photogramm. Remote Sens. 171, 119–132 (2021).
[Crossref]

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractional Geometry of Nature (Birkhäuser, 1987).

Mazda, F. F.

F. F. Mazda, Telecommunications Engineer’s Reference Book (Butterworth-Heinemann, 1993).

Menenti, M.

S. Soudarissanane, R. Lindenbergh, M. Menenti, and P. Teunissen, “Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points,” ISPRS J. Photogramm. Remote Sens. 66(4), 389–399 (2011).
[Crossref]

Mettenleiter, M.

D. Wujanz, M. Burger, M. Mettenleiter, and F. Neitzel, “An intensity-based stochastic model for terrestrial laser scanners,” ISPRS J. Photogramm. Remote Sens. 125, 146–155 (2017).
[Crossref]

Mihram, G. A.

G. A. Mihram, Simulation. Statistical Foundations and Methodology. Mathematics in Science and Engineering. (Academic Press, 1972).

Montillet, J.-P.

M. S. Bos, J.-P. Montillet, S. D. Williams, and R. M. Fernandes, “Introduction to geodetic time series analysis,” arXiv: Other Statistics, 29–52 (2020).

Muehlig, H.

I. N. Bronshtein, H. Muehlig, G. Musiol, and K. A. Semendiaev, Handbook of Mathematics, 5th ed. (Springer, 2007).

Musiol, G.

I. N. Bronshtein, H. Muehlig, G. Musiol, and K. A. Semendiaev, Handbook of Mathematics, 5th ed. (Springer, 2007).

Neitzel, F.

D. Wujanz, M. Burger, M. Mettenleiter, and F. Neitzel, “An intensity-based stochastic model for terrestrial laser scanners,” ISPRS J. Photogramm. Remote Sens. 125, 146–155 (2017).
[Crossref]

F. Neitzel, “Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation,” J. Geod. 84(12), 751–762 (2010).
[Crossref]

Olhede, S. C.

A. M. Sykulski, S. C. Olhede, A. P. Guillaumin, J. M. Lilly, and J. J. Early, “The debiased Whittle likelihood,” Biometrika 106(2), 251–266 (2019).
[Crossref]

Oppenheim, G.

J-M. Bardet, G. Lang, G. Oppenheim, A. Philippe, S. Stoev, and M. S. Taqqu, “Semi-parametric estimation of the long-range dependence parameter: A survey,” in Theory and Applications of Long-range Dependence (Birkhäuser, 2003), pp. 557–577.

Pelzer, H.

H. Pelzer, “Zur Analyse geodätischer Deformationsmessungen,” Dtsch. Geodät. Komm. Ser. C. 164 (1971).

Peña Lecona, F. G.

S. Alvarez-Rodrígue, N. Alcalá-Ochoa, J. Cruz-Salgado, and F. G. Peña Lecona, “Suppression of noise to obtain a high-performance low-cost optical encoder,” J. Sens. 2018, 1–10 (2018).
[Crossref]

Pfeifer, N.

N. Pfeifer and C. Briese, “Laser scanning–principles and applications,” GeoSiberia 2007–International Exhibition and Scientific Congress. European Association of Geoscientists & Engineers (2007).

Philippe, A.

J-M. Bardet, G. Lang, G. Oppenheim, A. Philippe, S. Stoev, and M. S. Taqqu, “Semi-parametric estimation of the long-range dependence parameter: A survey,” in Theory and Applications of Long-range Dependence (Birkhäuser, 2003), pp. 557–577.

Reshetyuk, Y.

Y. Reshetyuk, Investigation and Calibration of Pulsed Time-of-flight Terrestrial Laser Scanners, (Trita-TEC-LIC, 2006).

Rousseeuw, P. J.

P. J. Rousseeuw, “Least median of squares regression,” J. Am. Stat. Assoc. 79(388), 871–880 (1984).
[Crossref]

Semendiaev, K. A.

I. N. Bronshtein, H. Muehlig, G. Musiol, and K. A. Semendiaev, Handbook of Mathematics, 5th ed. (Springer, 2007).

Soudarissanane, S.

S. Soudarissanane, R. Lindenbergh, M. Menenti, and P. Teunissen, “Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points,” ISPRS J. Photogramm. Remote Sens. 66(4), 389–399 (2011).
[Crossref]

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Data availability

Data underlying the results presented in this paper are available on demand

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Figures (5)
Fig. 1.
Fig. 1. Principle of the TLS angle measurements by means of rotating mirrors.

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Fig. 2.
Fig. 2. The psd of the noise combination of the electronic device in log plot. The slopes of the psd for the WN (0) and the FN (−1) are given additionally in red and blue, respectively.

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Fig. 3.
Fig. 3. Vertical and horizontal angles $\phi $ and $\lambda $ , respectively, for the resolution extremely high (EH) for a plane (1 × 1 m) scanned at a distance of 5 m (no tilt).

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Fig. 4.
Fig. 4. Methodology to analyze the colored component noise from TLS angle measurements from the least-squares residuals.

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Fig. 5.
Fig. 5. (Left) psd of the residuals for the case 5 m (log plot). (Right) Butterworth cutoff frequency in MHz versus the laser measuring frequency (black axis) and correlation coefficient r_c between $\phi $ and $\lambda $ noise (red axis).

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Tables (2)

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Table 1. Laser measuring frequency [Hz] for different resolution settings for a Zoller + Fröhlich Imager 5016, quality high.

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Table 2. R F N / t o t in % using different resolutions.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

n T P i = d ,
P i = ( x y z ) i = ( r sin ⁡ ϕ cos ⁡ λ r sin ⁡ ϕ sin ⁡ λ r cos ⁡ ϕ ) i .
{ v ^ λ i = atan y i + v ^ y i x i + v ^ x i − atan y i x i v ^ ϕ i = atan ( x i + v ^ x i ) 2 + ( y i + v ^ y i ) 2 z i + v ^ z i − atan x i 2 + y i 2 z i .
R F N / t o t = 100 ∗ σ F N 2 / σ v ^ 2 ,
C ( τ ) = σ φ , λ 2 [ 1 , r _ c , … , r _ c n ]
Σ a n g l e = [ Σ ϕ Σ ϕ , λ Σ ϕ , λ Σ λ ] .
C ( τ ) = σ v ^ 2 [ R F N / t o t 100 1 2 ( | τ + 1 | 2 − 2 | τ | 2 + | τ − 1 | 2 ) + ( 1 − R F N / t o t 100 ) ]

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