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Multiple transit times and least squares for gyroscopic azimuth

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Abstract

Principles of North determination using suspended gyrocompasses are reviewed. Accuracy is evaluated and a procedure with two series of measurements symmetrical with respect to the zero torsion tape position is mathematically proven to be the “best” (minimum variance). Our purpose is to prove that a 20″ accuracy (1 σ) instrument was brought to a level of accuracy four times better by using multiple transit times and least squares fit. Over a total of 15 North determinations based on more than a thousand transit times, an external standard error of 4″.4 was obtained using a WildGAK-1.

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References

  • G.G. BENNETT: The Modified Transit Method of Observation with the Wild GAK-1 Gyro Theodolite. Can. Surv., Vol. 24, No. 1, pp. 108–116, 1970.

    Google Scholar 

  • G. BOMFORD: Geodesy, Oxford Un. Press, 3rd ed. reprinted, 1971.

    Google Scholar 

  • R. FORSBERG and C.C. TSCHERNING: The Use of Height Data in Gravity Field Approximation by Collocation. JGR, 86, pp. 7843–7854, 1981.

    Article  Google Scholar 

  • H. GOLDSTEIN: Classical Mechanics. Addison-Wesley Pub. Co. 2nd ed., 1980.

    Google Scholar 

  • E. GRAFAREND: Fehlertheoretische Untersuchungen und Chronometrische Messverfahren beim Einsatz von Aufsatzkreiseln in Kombination mit dem electro optischen Entfernungsmessgerät AGA-Geodimeter 4B. DGK, Reihe C, Heft Nr. 112, 1967.

  • E. GRAFAREND: Chronometrische Nordbestimmung mit Vermessungskreiseln. ZfV, 3, 1969.

  • L.F. GREGERSON: An Investigation of the MOM GiB2 Gyroscopic Theodolite. Can. Surv.}, Vol. 24, No. 1, pp. 117–134, 1970.

  • F. HALMOS: Neue ungarische Kreisel theodolite. ZfV, 6, 1969.

  • F. HALMOS: High Precision Measurement and Evaluation Method for Azimuth Determination with Gyrotheodolites. Manuscripta Geodaetica, Vol. 2, pp. 213–231, 1977.

    Google Scholar 

  • R.V. HOGG and A.T. CRAIG: Introduction to Mathematical Statistics. Macmillan, New-York, 2nd ed., sixth printing, 1965.

    Google Scholar 

  • L.M.A. JEUDY: Théorie du gyrocompas suspendu II. Equations des petites oscillations. Manuscripta Geodaetica, Vol. 7, No. 1, pp. 37–76, 1982.

    Google Scholar 

  • A.H.W. KEARSLEY, M.G. SIDERIS, J. KRYNSKI, R. FORSBERG, K.P. SCHWARZ: White Sands Revisited - A Comparison of Techniques to Predict Deflections of the Vertical. UCSE Report No. 30007, Calgary, 1985.

    Google Scholar 

  • E.M. MIKHAIL: Observations and Least Squares. Harper and Row, New York, 1976.

    Google Scholar 

  • G.J. STRASSER and H.R. SCHWENDENER: A North-seeking Gyro Attachment for the Theodolite. Bull. Gdod., No. 79, pp. 23–38, 1966.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Geodetic Sciences and Remote Sensing, Laval University, G1K 7P4, Quebec, Canada

    Luc M. A. Jeudy

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  1. Luc M. A. Jeudy
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Jeudy, L.M.A. Multiple transit times and least squares for gyroscopic azimuth. Bull. Geodesique 60, 288–296 (1986). https://doi.org/10.1007/BF02522337

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  • DOI: https://doi.org/10.1007/BF02522337

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