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Statistical analysis of discrepancies in high precision levelling

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Bulletin Géodésique (1946-1975)

Abstract

An investigation was made of the behaviour of the variable\(x_{ij} = \rho _{ij} /\sqrt {R_{ij} } \) (where ρij are the discrepancies between the direct and reverse measurements of the height of consecutive bench marks and theR ij are their distance apart) in a partial net of the Italian high precision levelling of a total length of about1.400 km.

The methods of analysis employed were in general non-parametric individual and cumulative tests; in particular randomness, normality and asymmetry tests were carried out. The computers employed wereIBM/7094/7040. From the results evidence was obtained of the existence of an asymmetry in respect to zero of thex ij confirming the well-known results given firstly by Lallemand. A new result was obtained from the tests of randomness which put in evidence trends of the mean values of thex ij and explained some anomalous behaviours of the cumulative discrepancy curves. The extension of this investigation to a broader net possibly covering other national nets would be very useful to get a deeper insight into the behaviour of the errors in high precision levelling. Ad hoc programs for electronic computers are available to accomplish this job quickly.

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Authors and Affiliations

  1. Istituto di Topografia, Geodesia e Geofisica Mineraria, Università degli Studi di Bologna, Bologna, Italy

    A. Chiarini & L. Pieri

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  1. A. Chiarini
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  2. L. Pieri
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Chiarini, A., Pieri, L. Statistical analysis of discrepancies in high precision levelling. Bull. Geodesique 99, 5–27 (1971). https://doi.org/10.1007/BF02521676

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