A New Modeling Approach for A Priori Uncertainties of Laser Tracker Angle Measurements
Publication: Journal of Surveying Engineering
Volume 149, Issue 4
Abstract
Methods for modeling the uncertainty in laser tracker angle measurements vary within the metrology industry, leading to confusion and questionable stochastic modeling for survey network adjustments and error propagation analysis. Interpreting the published laser tracker manufacturer performance specifications to determine an a priori sigma value for weighting azimuth and zenith angle measurements can be confusing and has led to differing implementations. This paper proposes a unique way to model survey network a priori laser tracker angular uncertainties based on laser tracker manufacturers’ published maximum permissible error (MPE) values referenced to current standards for weighting survey network measurements. This paper’s proposed model takes into account the disparate effects that pointing errors, target centering errors, and leveling errors have on azimuth and zenith angular uncertainties for measurements with steep sightings and at near ranges.
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Data Availability Statement
Some of the data that supports the findings of this study are available from the corresponding author upon reasonable request, including the repeatability test angle measurements.
Acknowledgments
This material is based upon work supported by the US Department of Energy, Office of Science, Office of Nuclear Physics and used resources of the Facility for Rare Isotope Beams (FRIB), which is a DOE Office of Science User Facility, operated by Michigan State University, under Award No. DE-SC0000661. The author would like to thank Luke Privatte for taking hundreds of measurements with the Leica AT402 and Vantage laser trackers for the repeatability test. Also, thanks to Doug Bruce for providing useful input during the writing of this paper. Finally, thanks to the reviewers who provided detailed comments to improve the content of this paper.
References
Anderson, J. M., and E. M. Mikhail. 1998. Surveying theory and practice. Boston: WCB/McGraw-Hill.
ASME. 2006. Performance evaluation of laser-based spherical coordinate measurement systems. ASME B89.4.19. New York: ASME.
Dorsey-Palmateer, J. W. 2018. “A new model for spherical instrument measurement uncertainty.” J. CMSC 13 (2): 18–23.
FARO Technologies, Inc. 2016. FARO laser tracker vantage user manual April 2016. Lake Mary, FL: FARO Technologies, Inc.
Ghilani, C. D. 2010. Adjustment computations spatial data analysis. 5th ed. Hoboken, NJ: Wiley.
Ghilani, C. D. 2016. “A correctly weighted least squares adjustment part 3, estimating standard errors in angular observations.” xyHt, 44–45, April 25, 2016.
Hexagon Metrology. 2012. Leica absolute tracker AT403 product brochure. Stockholm, Sweden: Hexagon Metrology.
Hexagon Metrology. 2018. Leica absolute tracker AT403 product brochure. Stockholm, Sweden: Hexagon Metrology.
Hexagon Metrology. 2021. SpatialAnalzer user manual. Stockholm, Sweden: Hexagon Metrology.
ISO. 2021. Geometrical product specifications (GPS)—Acceptance and reverification tests for coordinate measuring systems (CMS)—Part 10: Laser trackers. Geneva: ISO.
Leica Geosystems. 2009. “Leica TDRA6000 Product Brochure Version 01/2009.” Accessed October 1, 2022. https://www.geowild.hr: https://www.geowild.hr/wp-content/uploads/digital_products/leica%20tdra6000%20brochure_en.pdf.
Leica Geosystems. 2010. “Leica_Absolute_Tracker_AT401_white_paper.pdf.” Unterentfelden: Leica Geosystems. Accessed October 1, 2022. https://www.swisstek.com/images/wild_leica/Leica_Absolute_Tracker_AT401_white_paper.pdf.
Manwiller, P. E. 2020. “Three-dimensional network adjustment of laser tracker measurements for large-scale metrology applications.” J. Surv. Eng. 147 (1): 05020009. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000332.
Meid, A., and S. Sandwith. 2000. “Dynamic weighting of laser tracker measurements for bundle adjustment.” In Proc., Boeing Large Scale Optical Metrology Seminar. Melbourne, FL: Geodetic Systems.
Muralikrishnan, B., D. Sawyer, C. Blackburn, S. Phillips, B. Borchardt, and W. Estler. 2009. “ASME B89.4.19 performance evaluation tests and geometric misalignments in laser trackers.” J. Res. Natl. Inst. Stand. Technol. 114 (1): 21–35. https://doi.org/10.6028/jres.114.003.
Muralkrishnan, B., C. Blackburn, D. Sawyer, and S. Phillips. 2010. “Measuring scale errors in a laser tracker’s horizontal angle encoder through simple length measurement and two-face systems tests.” J. Res. Natl. Inst. Stand. Technol. 115 (5): 291–301. https://doi.org/10.6028/jres.115.022.
Ogundare, J. O. 2015. Precision surveying: The principles and geomatics practice. Hoboken, NJ: Wiley.
Ridler, N., B. Lee, J. Martens, and K. Wong. 2007. “Measurement uncertainty, traceability, and the GUM.” IEEE Microwave Mag. 8 (4): 44–53. https://doi.org/10.1109/MMW.2007.383952.
Thompson, A., N. Southon, F. Florian, G. Stupfler, and R. Leach. 2021. “Efficient empirical determination of maximum permissible error in coordinate metrology.” Meas. Sci. Technol. 32 (10): 105013.
Ulrich, T. 2016. Uncertainty modelling of high-precision trajectories. Karlsruhe, Germany: Karlsruher Institut für Technologie.
Wang, L., B. Muralikrishnan, O. I. Hernandez, C. Shakarji, and D. Sawyer. 2020. “Performance evaluation of laser trackers using the network method.” Measurement 165 (Dec): 108165. https://doi.org/10.1016/j.measurement.2020.108165.
Information & Authors
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Published In
Journal of Surveying Engineering
Volume 149 • Issue 4 • November 2023
Copyright
© 2023 Published by American Society of Civil Engineers.
History
Received: Dec 14, 2022
Accepted: Apr 24, 2023
Published online: Jun 26, 2023
Published in print: Nov 1, 2023
Discussion open until: Nov 26, 2023
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