This paper shows how the angular uncertainties can be determined for a rotary-laser automatic theodolite of the type used in (indoor-GPS) iGPS networks. Initially, the fundamental physics of the rotating head device is used to propagate uncertainties using Monte Carlo simulation. This theoretical element of the study shows how the angular uncertainty is affected by internal parameters, the actual values of which are estimated. Experiments are then carried out to determine the actual uncertainty in the azimuth angle. Results are presented that show that uncertainty decreases with sampling duration. Other significant findings are that uncertainty is relatively constant throughout the working volume and that the uncertainty value is not dependent on the size of the reference angle.
J E Muelaner1, Z Wang1, J Jamshidi1, P G Maropoulos1,
A R Mileham1, E B Hughes2, and A B Forbes2
1: Department of Mechanical Engineering, University of Bath, Bath, UK
2: National Physical Laboratory, Teddington, UK
IMechE, Part B: J. Engineering Manufacture, 2008.
Volume and page number information
223(B3): p. 217-229
- Hedges, T. M., Takagi, H., Pratt, T., and Sobel, M. J.
Position measurement system and method using cone
math calibration. United States Patent US 6,535,282 B2
Mar. 18, 2003.
- Sharke, P. Measuring across space and time; large-scale
metrology moves GPS in out of the rain. Mech. Engng,
2003, 125(1), 48.
- Sell, C. On the right lines. Engineer, 2005, 293(7680), 30.
- Djurdjanovic, D. and Ni, J. Online stochastic control
of dimensional quality in multistation manufacturing
systems. Proc. IMechE, Part B: J. Engineering Manufacture,
2007, 221, 865–880.
- Gottwald, R. SPACE – an automated non-contact
3-D-measuring-system for industrial applications.
Seventh International Conference on Robot Vision and
Sensory Controls, Zurich, Switzerland, 2–4 Feb, 1988.
- Gilby, J. H. and Parker, G. A. Laser tracking system to
measure robot arm performance. Sensor Rev., 1982, 2(3),
- Logsdon, T. The Navstar global positioning system, 1992
(Chapman and Hall, London).
- Watson, J. T. A new approach to large coordinate
measurement using four tracking interferometers. In
Proceedings of the Third International Precision
Engineering Seminar, Interlaken, Switzerland, 1985,
pp. 68–71 (Butterworths, London).
- Hughes, E. B., Wilson, A., and Peggs, G. N. Design of a
high-accuracy CMM based on multi-lateration techniques.
Manuf. Technol., 2000, 49(1), 391–394.
- Zhang, D., Rolt, S., and Maropoulos, P. G. Modelling
and optimisation of novel laser multilateration schemes
for high-precision applications. J. Meas. Sci. Technol.,
2005, 16, 2541–2547.
- Maropoulos, P. G., Zhang, D., Rolt, S., Chapman, P.,
and Rogers, B. C. Integration of measurement planning
with aggregate product modelling for spacecraft design
and assembly. Proc. IMechE, Part B: J. Engineering
Manufacture, 2006, 220, 1687–1695.
- Sprent, A. The Anglescan positioning system. The 25th
Australian Survey Congress: Observing New Directions,
Melbourne, Australia, 1983.
- Triggs, B., Mclauchlan, P., Hartley, R., and Fitzgibbon,
A. Bundle adjustment – a modern synthesis. Lect. Notes
Comput. Sci., 1999, 1883, 1–4.
- Brown, D. C. Densification of urban geodetic nets.
Photogramm. Engng Remote Sens., 1977, 43(4), 447–467.
- Hadem, I. Bundle adjustment in industrial photogrammetry.
Photogrammetria, 1981, 37(2), 45–60.
- ISO 10360-2:2002. Geometric product specifications
acceptance and reverification tests for coordinate measuring
machines (CMMs) – part 2: CMMs used for measuring
- ASME B89.4.19. Performance evaluation of laser-based
spherical coordinate measurement systems, 2006.
- Industrial theodolites & total stations data sheet en.pdf.
2008, available from http://www.leica-geosystems.com/
- ISO 17123-1:2002. Optics and optical instruments – field
procedures for testing geodetic and surveying instruments
– part 1: theory.
- PD 6461-3:1995. General metrology. Guide to the
expression of uncertainty in measurement (GUM).
- Bobroff, N. Recent advances in displacement measuring
interferometry. Meas. Sci. Technol., 1993, 4(9),
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