## Trimble GX200 and Riegl LMS-Z390i sensor self-calibration |

Optics Express, Vol. 19, Issue 3, pp. 2676-2693 (2011)

http://dx.doi.org/10.1364/OE.19.002676

Acrobat PDF (1441 KB)

### Abstract

This paper aims to establish and develop a calibration model for two time-of-flight terrestrial laser scanners (TLS): Trimble GX200 and Riegl LMS-Z390i. In particular, the study focuses on measurement errors and systematic instrumental errors to compile an error model for TLS. An iterative and robust least squares procedure is developed to compute internal calibration parameters together with a TLS data set geo-reference in an external reference system. To this end, a calibration field is designed that performs as an experimental platform that tests the different laser scanner methods. The experimental results show the usefulness and potential of this approach, especially when high-precision measurements are requires.

© 2011 OSA

## 1. Introduction

### 1.1 Previous work

- - Quantitative description of the accuracy achievable with a particular instrument. The performance evaluation is both important and essential in understanding the limitations and characteristics of the scanners, as well as to compare equipment. However, performance evaluation does not analyze systematic and methodological errors in detail, so investigations and calibrations are required.
- - Identification of the significant systematic errors (calibration parameters) in the instrument. These parameters constitute a calibration model, which can be used to correct the systematic instrumental errors. The calibration procedure can be carried out by system calibration (self-calibration) or a component calibration [4].

8. M. Johansson, “Explorations into the Behaviour of three Different High-Resolution Ground-based Laser Scanners in the Built Environment”, presented at *Proceedings of the CIPA WG 6 International Workshop on Scanning for Cultural Heritage Recording*, Corfu, Greece, 2003, http://www.isprs.org/commission5/workshop

14. D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. **131**(4), 135–142 (2005). [CrossRef]

14. D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. **131**(4), 135–142 (2005). [CrossRef]

15. D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. **61**(5), 307–324 (2007). [CrossRef]

## 2. Analysis of instrumental errors

18. M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. **10**(3), 170–178 (1992). [CrossRef]

### 2.1 Errors in the Measurement of Ranges (Laser Rangefinder)

*Range offset error (k*represents a discrepancy between electrical and mechanical zero position at the scanner.

_{0}),*Range scale error (m),*represents a scale factor in the measured range, which depends on the measured range.

### 2.2 Errors in the measurement of angles (deflection and rotation units)

*Vertical and horizontal offset errors*are an additive constant to the measured vertical or horizontal angle. These errors are similar to the eclimeter error (vertical offset error) and the horizontal limb error (horizontal offset error) in topographic equipment. These errors could be caused by mirror and encoder mechanical misalignment or zero offset within the analogue-to-digital converter.

*Vertical and horizontal scale errors*are linearly dependent on the measured angle. The reason for these errors may be a false gain-control within the analogue to digital converter or faults of the encoder. This error, in the case of vertical angles, could be explained as follows: because the angular position of the scanning mirror is sampled by the encoder in fixed increments, the vertical angle is recorded as a sum of these increments. If the actual value of such an increment differs from the nominal value, the scale error appears. Something similar could be extrapolated to the case of horizontal angles because the horizontal directions in Trimble GX200 and Riegl LMS-390i are derived with the aid of a servomotor from mechanical increments of the scanning head.

*θ*and

_{scan}*θ*are the vertical angle measured by the laser and the corrected vertical angle, respectively, and

_{corr}*θ*and

_{0}*δθ*are the offset (eclimeter) and vertical scale errors, respectively. Furthermore,

*φ*and

_{scan}*φ*are the horizontal angles measured by the laser and the corrected horizontal angle, respectively, and

_{corr}*φ*and

_{0}*δφ*are the offset (horizontal limb) and horizontal scale error, respectively.

### 2.3 Axes errors

- - Vertical axis. For panoramic TLS, such as Trimble GX200 or Riegl LMS-Z390i, this is the rotation axis of the scanning head. It is possible that this axis lies in the vertical scanning plane, i.e. the plane in which the laser beam moves in the vertical direction to scan the object.
- - Collimation axis. Assuming the divergent laser beam is conical, this is the axis that passes through the centre of the scanning mirror and the centre of the laser spot on the object surface. Roughly speaking, the collimation axis of a TLS coincides with the laser beam.
- - Horizontal axis. The rotation axis of the scanning mirror that passes through its centre.

*Collimation axis error (c)*is the angle between the collimation axis and the normal to the horizontal axis, which is measured in the plane containing the collimation and horizontal axes.

*Horizontal axis error (i)*is the angle between the horizontal axis and the normal to the vertical axis, which is measured in the plane containing the horizontal and vertical axes.

*Vertical axis error (v)*is the orthogonality offset of the vertical axis, i.e., the vertical axis and the rotation base are not perfectly orthogonal. This error could generate the classical topographic error:

*precession vertical*axis error, which causes a rotation variation of the laser scanner around its vertical axis, which normally oscillates sinusoidally. The reasons for this error are the mechanical characteristics of the laser scanner. Likewise, this error could be affected and even increased by the instability of the base of the scanner, especially when the scanner is stationed on a survey tribrach and a wobbling of the scanner could appear. In particular, in the case of the Trimble GX200 this error could be considered insignificant because a dual axis compensator is incorporated. However, this error should remain in the Riegl LMS-Z390i because this equipment does not incorporate this compensator.

*2α*(Fig. 1(b)).

*θ*, the laser beam azimuth is

*2α*(Fig. 2(b)).

## 3. Self-calibration model

- - Geo-referencing all data sets to the same reference system based on high-precision engineering geodesy, which performs as “ground truth”. Thus, a three-dimensional transformation reinforced with a robust estimator and a stochastic test is implemented.
- - Integrating the systematic TLS instrumental errors in the same way that the collinearity model integrates the internal camera parameters.
- - Allowing system feedback such that once the calibration parameters have been estimated and the laser scanner observations have been corrected, a new adjustment will be performed to detect possible systematic errors not considered initially in the self-calibration model.
- - Estimating precision, accuracy and reliability for each one of the observations and self-calibration parameters of the TLS. Thus, statistical approaches are incorporated that allow us to analyze the precision of the observations and parameters, as well as estimating their reliability and detecting possible gross errors. Particularly, the accuracy of observations and adjusted unknowns are of prime interest when analyzing quality in an adjustment procedure. On the contrary, the precision of observations and unknowns are directly related with the calculated stochastic values which provide information about the quality of the functional model with respect to the input data. Therefore, the precision describes an internal quality of the adjustment process, while the accuracy performs as an external validation which should only be used if a comparison to reference data of higher accuracy is performed.

### 3.1 The functional model

*Δφ*) and vertical (

_{corr}*Δθ*) angles are estimated as follows: where

_{corr}*c*,

*i*,

*φ*,

_{0}*δφ*,

*θ*and

_{0}*δθ*are the errors corresponding to the collimation axis, horizontal axis, horizontal offset and scale, and vertical offset and scale, respectively, and

*φ*and

_{scan}*θ*are the horizontal and vertical angle measurements, respectively.

_{scan}*X Y Z*]

^{T}are the coordinates of the target centres in the external coordinate system (engineering geodesy), which are also referred to as “true” coordinates; [

*ΔX ΔY ΔZ*]

^{T}is the vector of translation parameters;

*R*(

*α*) is the rotation matrix between the two systems, which is a function of the rotation angles (

_{1}, α_{2}, α_{3}*α*) about the

_{1}, α_{2}, α_{3}*x*,

*y*and

*z*coordinate axes, respectively. While the coordinates of the target centres in the laser scanner coordinate system [

*x y z*]

^{T}are defined by the observations

*r*,

_{scan}*φ*and

_{scan}*θ*as distances, horizontal and vertical angles, respectively; and the systematic instrumental errors

_{scan}*k*,

_{0}*m*,

*c, i*,

*θ*,

_{0}*φ*,

_{0}*δθ*and

*δφ*, as distance offset and scale errors, collimation and horizontal axes errors, vertical and horizontal offset errors, and vertical and horizontal scale errors, respectively.

*F*contains the laser scanner observations

^{0}*r*,

_{scan}*φ*and

_{scan}*θ*. The approximate values for the angles

_{scan}*α*and

_{1}*α*are set to zero because these scanners were leveled during the experiments. Likewise, the approximate values for all the calibration parameters are set to zero because it is reasonable to assume that the manufacturer tries to minimize the instrumental errors as much as possible.

_{2}### 3.2 The stochastic model

*v*is the residual vector,

*W*is the weight matrix and

*x*is the unknown vector.

*Σ*has been computed as follows:where

_{ll}*R*(

*α*) is the rotation matrix,

_{1}, α_{2}, α_{3}*J*is the Jacobian matrix of the derivates of TLS coordinates [

*x y z*]

^{T}with respect to

*r*,

_{scan}*φ*and

_{scan}*θ*;

_{scan}*Σ*is the diagonal variance-covariance matrix of the “true” topographic coordinates of the targets; and

_{XYZ}*Σ*is computed as follows:where

_{inst}*σ*,

_{r}*σ*and

_{φ}*σ*are the accuracies of the TLS observables

_{θ}*r*,

_{scan}*φ*and

_{scan}*θ*, respectively, including the beam divergence

_{scan}*σ*, which are provided by the manufacturers. Nevertheless, it is important to remark that these technical specifications are due to individual point measurements, while the extraction of the centre of the targets is performed considering many points around the targets.

_{beam}- - First, the modified Danish robust estimator is applied while supported by a variable exponential weight function (12), which updates the weight matrix
*W*iteratively by taking the residual*v*of the previous iteration. This estimator is only applied in the first iteration to detect the most unfavourable gross errors. - - Second, the normalized residuals
*v*are computed in the following iterations through the T-Student distribution and the Pope test, so based on the data snooping strategy (Kraus [24], ), the gross errors can be detected._{Pope}

*√C*contains the redundancy number that is determined from the diagonal of the residual cofactor matrix (

_{VV}*C*), and

_{vv}## 4. Experimental results

### 4.1 Design and signalling of calibration field

15. D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. **61**(5), 307–324 (2007). [CrossRef]

### 4.2 Field work

- - Scan-based surveying of the special targets, using the maximum TLS resolution (2-3 mm) with automatic centre extraction.
- - Topographic-based surveying of the centre of the special targets, which establishes an external reference frame using high-precision topographic equipment: Leica TCA2003. In this sense, the engineering geodesy performs as “ground truth”, which is a reference for all TLS measurements. The horizontal angles are observed by the directional method: reading the horizontal circle in both the hindsight and foresight directions.

### 4.3 Laboratory work

#### 4.3.1 Computation of input data set

*ρ,θ,α*) and Cartesian (

*X,Y,Z*) coordinates that correspond to the geometric target centres that define the calibration network. Likewise, the point cloud of each one of these targets is obtained, which could be used as an alternative process (planar target modelling) in those cases in which automatic target extraction does not work [26].

*ρ,θ,α*) and Cartesian (

*X,Y,Z*) coordinates that correspond to the geometric target centres that define the calibration network. These observations constitute the external reference system (data) and are considered to be “ground truth”.

#### 4.3.2 Analysis of possible systematic trends

- - The laser Trimble GX200 presents low dispersion (deviation) in the distribution of errors, with the errors approximately normally distributed with zero means for the case of all observations. However, the horizontal observation errors are two times higher than the vertical angle errors, which could indicate a possible systematic trend (offset or scale error).
- - The laser Riegl LMS-Z390i presents a higher dispersion (deviation) in all errors, with the distance error as the most favourable according to the range specifications provided by the manufacturer. Again, it should be remarked the dispersion obtained by the vertical angle and especially the horizontal angle, which could be caused by another systematic trend.
- - It is interesting to note how particular observations could follow a different distribution, probably due to the presence of gross errors. Therefore, the above mentioned robust statistical approaches will be required in order to detect and reject these observations.

#### 4.3.3 Self-calibration results

*Std. Dev.*refers to the standard deviation of unit weight, while the

*Value*refers to the value of the unknown parameter.Regarding external parameters (Table 2), one can see how the Trimble GX200 incorporates a vertical dual axis compensator because the angles in the XY plane are

*α*= 0.0156° (56”) and

_{1}*α*= −0.0031° (11”), with a vertical deviation of 0.0157° (57”). However, that is not the case for the Riegl LMS-Z390i, which takes values of

_{2}*α*= −0.4333° (26’) and

_{1}*α*= −0.0302° (2’), with a vertical deviation of 26’.

_{2}_{L}) and the topographic coordinates (Z

_{T}), divided by the number of control points minus 1:In this case, the linear equivalent displacement of the

*α*angle is 6 cm at 100 m. Note that this equation measures the effectiveness of the levelling compensation by the tilt angles and not the levelling accuracy because any accidental errors in the

_{1}*Z*coordinates due to the laser scanner being off level are accounted for by the

*α*and

_{1}*α*transformation angles.

_{2}*m*, exhibits a scale correction of 1mm/100m, while the Riegl LMS-Z390i exhibits 5mm/10m. It seems clear that the value shows by Riegl is not realistic and thus not useful. On the other hand, a special remark should be made to the offset vertical error,

*θ*, which presents a standard deviation larger than its value for both laser scanners. Again, a possible correlation with this parameter could be a cause of its lack of significance.

_{0}- • A correlation between collimation axis error,
*c*, and horizontal axis error,*i*, which could affect the horizontal angle observations. It is important to remark that both errors take part in the correction of the horizontal angle. - • A correlation between range offset,
*k*and scale factor,_{0}*m*, which could confirm the possible unstable and opposite values obtained for both parameters in the case of Riegl. - • A correlation between offset vertical error,
*θ*and range offset,_{0}*k*, which could explain the lack of significance of vertical error,_{0}*θ*with a standard deviation larger than its value. Besides, any source of error in scanning mirror, such as its imperfection or its own performance, could be considered as a systematic trend in the offset vertical error._{0}

## 5. Conclusions and future perspectives

- • The systematic instrumental errors and trends have been identified successfully for Trimble GX200, and thus, the precision and accuracy of the measurements have been improved.
- • The reported self-calibration approach indicates that within certain limits, results from TrimbleGX200 are of interest and could be useful for field work.
- • This is not the case for Riegl LMS-Z390i, since an optimization of the accuracy has not been achieved and several systematic trends remain.
- • Try to cope with correlation between parameters may produce better results. In particular, we could confirm that the controversial scale parameter,
*m*, it should not be included in the self-calibration model, especially when the test field dimensions are reduced (indoor test field). This parameter should be incorporated in outdoor test fields where larger distances can be considered. Nevertheless, in these cases the atmospheric influences must be considered as well. - • Accuracy, precision and reliability have been estimated for statistical analysis. This stochastic approach has been supported by several bivariant plots between TLS errors and TLS observations, which have lead to identification of possible systematic trends.
- • The self-calibration model proposed guarantees reliability because it has been reinforced with an iterative least squares process that incorporates robust estimators and statistical tests.
- • A software that diagnoses and corrects TLS field measurements before being processed,
*CalibTLS*, has been developed. - • The self-calibration model proposed is scalable since allows continuous improvement and feedback based on analysis and testing.
- • A step forward in TLS calibration protocols and their standardisation has been accomplished, so they can be applied easily and economically.

## Acknowledgments

## References and links

1. | R. Staiger, “The Geometrical Quality of Terrestrial Laser Scanner (TLS)” presented at FIG Working Week 2005, Cairo, Egypt, 16–21 April. 2005. |

2. | W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. |

3. | D. Lichti., “Calibration and testing of a terrestrial scanner,” Int. Arch. Photogramm. Remote Sens. |

4. | T. Schulz, “Calibration of a Terrestrial Laser Scanner for Engineering Geodesy”. Dissertation ETH Zurich Nº 17036. 2007. |

5. | G. S. Cheok, S. Leigh, and A. Rukhin, “Calibration Experiments of a Laser Scanner,” National Institute of Standards and Technology U. S. Department of Commerce Gaithersburg, MD 20899, 2002. |

6. | Th. Kersten, H. Sternberg, and K. Mechelke, “Investigations into the Accuracy Behaviour of the Terrestrial Laser Scanning System Trimble GS100”,in |

7. | K. Mechelke, T. P. Kersten, and M. Lindstaedt, “Comparative investigations into the accuracy behaviour of the new generation of terrestrial laser scanning systems”, in |

8. | M. Johansson, “Explorations into the Behaviour of three Different High-Resolution Ground-based Laser Scanners in the Built Environment”, presented at |

9. | T. Schulz, and H. Ingensand, “Influencing Variables, Precision and Accuracy of Terrestrial Laser Scanners” presented at INGEO 2004 and FIG Regional Central and Eastern European Conference on Engineering Surveying, Bratislava, Slovakia, 11–13 November. 2004. |

10. | T. Schulz and H. Ingensand, “Terrestrial Laser Scanning – Investigations and Applications for High Precision Scanning” presented at FIG Working Week 2004, Athens, Greece, 22–27 May. 2004. |

11. | Y. Reshetyuk, “Self-calibration and direct georeferencing in terrestrial laser scanning”. Doctoral thesis in Infrastructure, Geodesy Royal Institute of Technology, Stockholm, Sweden. TRITA-TEC-PHD 09–001. ISBN 978–91–85539–34–5. (2009) |

12. | A. Rietdorf, R. Gielsdorf, and L. Grundig, “A Concept for the Calibration of Terrestrial Laser Scanners”, in INGEO 2004 and FIG Regional Central and Eastern Conference on Engineering Surveying, Bratislava, Slovakia. 11–13 November. 2004. |

13. | Y. Reshetyuk, “Calibration of terrestrial laser scanners for the purposes of geodetic engineering”, presented at the 3rd IAG/ 12th FIG Symposium, Baden, Germany, 22–24 May. 2006. |

14. | D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. |

15. | D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. |

16. | J. Chow, D. Lichti, and B. Teskey, “Self-calibration of the Trimble (Mensi) GS200 Terrestrial Laser Scanner”, |

17. | J. Chow, B. Teskey, and D. Lichti, “Self-calibration and evaluation of the Trimble GX terrestrial laser scanner”, in Proceedings of The 2010 Canadian Geomatics Conference and Symposium of Commission I, ISPRS, Volume XXXVIII, Calgary, Canada, 15–18 June, 2010. |

18. | M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. |

19. | C. D. Ghilani, and P. R. Wolf, |

20. | M. Balzani, A. Pellegrinelli, N. Perfetti, and F. Uccelli, “A terrestrial laser scanner: accuracy tests” in |

21. | S. J. Gordon and D. Lichti, “Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions,” Survey Review |

22. | P. A. Domingo, “Investigación sobre los Métodos de Estimación Robusta aplicados a la resolución de los problemas fundamentales de la Fotogrametría”. Doctoral Thesis. University of Cantabria, Santander, 2000. |

23. | A. J. Pope, “The statistics of residuals and the detection of outliers”, NOAA Technical Report NOS 65 NGS 1, National Ocean Service, National Geodetic Survey, US Department of Commerce. Rockville, MD, (1976), p.133. |

24. | K. Kraus, |

25. | J. Armesto, B. Riveiro-Rodríguez, D. González-Aguilera, T. Rivas-Brea, “Terrestrial laser scanning intensity data applied to damage detection for historical buildings”, Journal of Archaeological Science 37 (12), 3037-3047 (2010). |

26. | J. Chow, A. Ebeling, B. Teskey, “Low Cost Artificial Planar Target Measurement Techniques for Terrestrial Laser Scanning”, presented at FIG Congress 2010, Sydney, Australia, 11–16 April. 2010. |

**OCIS Codes**

(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors

(120.3940) Instrumentation, measurement, and metrology : Metrology

(280.3420) Remote sensing and sensors : Laser sensors

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: September 23, 2010

Revised Manuscript: November 14, 2010

Manuscript Accepted: November 18, 2010

Published: January 27, 2011

**Citation**

D. González-Aguilera, P. Rodríguez-Gonzálvez, J. Armesto, and P. Arias, "Trimble GX200 and Riegl LMS-Z390i sensor self-calibration," Opt. Express **19**, 2676-2693 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2676

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### References

- R. Staiger, “The Geometrical Quality of Terrestrial Laser Scanner (TLS)” presented at FIG Working Week 2005, Cairo, Egypt, 16–21 April. 2005.
- W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34(5), 696–701 (2003).
- D. Lichti and ., “Calibration and testing of a terrestrial scanner,” Int. Arch. Photogramm. Remote Sens. 33, 485–492 (2000).
- T. Schulz, “Calibration of a Terrestrial Laser Scanner for Engineering Geodesy”. Dissertation ETH Zurich Nº 17036. 2007.
- G. S. Cheok, S. Leigh, and A. Rukhin, “Calibration Experiments of a Laser Scanner,” National Institute of Standards and Technology U. S. Department of Commerce Gaithersburg, MD 20899, 2002.
- Th. Kersten, H. Sternberg, and K. Mechelke, “Investigations into the Accuracy Behaviour of the Terrestrial Laser Scanning System Trimble GS100”,in Optical 3D Measurement Techniques VII Vol. 1, Gruen & Kahmen, eds.(2005), pp. 122–131.
- K. Mechelke, T. P. Kersten, and M. Lindstaedt, “Comparative investigations into the accuracy behaviour of the new generation of terrestrial laser scanning systems”, in Optical 3-D Measurement Techniques VIII Vol. I, Gruen & Kahmen, eds. (2007), pp. 319–327.
- M. Johansson, “Explorations into the Behaviour of three Different High-Resolution Ground-based Laser Scanners in the Built Environment”, presented at Proceedings of the CIPA WG 6 International Workshop on Scanning for Cultural Heritage Recording, Corfu, Greece, 2003, http://www.isprs.org/commission5/workshop
- T. Schulz, and H. Ingensand, “Influencing Variables, Precision and Accuracy of Terrestrial Laser Scanners” presented at INGEO 2004 and FIG Regional Central and Eastern European Conference on Engineering Surveying, Bratislava, Slovakia, 11–13 November. 2004.
- T. Schulz and H. Ingensand, “Terrestrial Laser Scanning – Investigations and Applications for High Precision Scanning” presented at FIG Working Week 2004, Athens, Greece, 22–27 May. 2004.
- Y. Reshetyuk, “Self-calibration and direct georeferencing in terrestrial laser scanning”. Doctoral thesis in Infrastructure, Geodesy Royal Institute of Technology, Stockholm, Sweden. TRITA-TEC-PHD 09–001. ISBN 978–91–85539–34–5. (2009)
- A. Rietdorf, R. Gielsdorf, and L. Grundig, “A Concept for the Calibration of Terrestrial Laser Scanners”, in INGEO 2004 and FIG Regional Central and Eastern Conference on Engineering Surveying, Bratislava, Slovakia. 11–13 November. 2004.
- Y. Reshetyuk, “Calibration of terrestrial laser scanners for the purposes of geodetic engineering”, presented at the 3rd IAG/ 12th FIG Symposium, Baden, Germany, 22–24 May. 2006.
- D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. 131(4), 135–142 (2005). [CrossRef]
- D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. 61(5), 307–324 (2007). [CrossRef]
- J. Chow, D. Lichti, and B. Teskey, “Self-calibration of the Trimble (Mensi) GS200 Terrestrial Laser Scanner”, in Proceedings of ISPRS Commision V Mid-Term Symposium, “Close range Image Measurement Techniques”, Newcastle upon Tyne, United Kingdom, 22–24 June, 2010.
- J. Chow, B. Teskey, and D. Lichti, “Self-calibration and evaluation of the Trimble GX terrestrial laser scanner”, in Proceedings of The 2010 Canadian Geomatics Conference and Symposium of Commission I, ISPRS, Volume XXXVIII, Calgary, Canada, 15–18 June, 2010.
- M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. 10(3), 170–178 (1992). [CrossRef]
- C. D. Ghilani, and P. R. Wolf, Adjustment Computations: Spatial Data Analysis. 4th edition(John Wiley & Sons, 2006)
- M. Balzani, A. Pellegrinelli, N. Perfetti, and F. Uccelli, “A terrestrial laser scanner: accuracy tests” in Proceedings of 18th International Symposium CIPA 2001,(2001),pp. 445 – 453.
- S. J. Gordon and D. Lichti, “Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions,” Survey Review 37(292), 448–468 (2004).
- P. A. Domingo, “Investigación sobre los Métodos de Estimación Robusta aplicados a la resolución de los problemas fundamentales de la Fotogrametría”. Doctoral Thesis. University of Cantabria, Santander, 2000.
- A. J. Pope, “The statistics of residuals and the detection of outliers”, NOAA Technical Report NOS 65 NGS 1, National Ocean Service, National Geodetic Survey, US Department of Commerce. Rockville, MD, (1976), p.133.
- K. Kraus, Advanced Methods and Applications. Vol.2. Fundamentals and Standard Processes. Vol.1. Institute for Photogrammetry Vienna University of Technology. Ferd. Dummler Verlag. Bonn. (1993)
- J. Armesto, B. Riveiro-Rodríguez, D. González-Aguilera, T. Rivas-Brea, “Terrestrial laser scanning intensity data applied to damage detection for historical buildings”, Journal of Archaeological Science 37 (12), 3037-3047 (2010).
- J. Chow, A. Ebeling, B. Teskey, “Low Cost Artificial Planar Target Measurement Techniques for Terrestrial Laser Scanning”, presented at FIG Congress 2010, Sydney, Australia, 11–16 April. 2010.

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