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Mårtensson, Stig-Göran
Publications (1 of 1) Show all publications
Mårtensson, S.-G. (2022). Simple computation of coordinates and uncertainty of ‘hidden’ points from two coordinated points that are collinear with the hidden point. Survey review - Directorate of Overseas Surveys, 54(387), 543-553
Open this publication in new window or tab >>Simple computation of coordinates and uncertainty of ‘hidden’ points from two coordinated points that are collinear with the hidden point
2022 (English)In: Survey review - Directorate of Overseas Surveys, ISSN 0039-6265, E-ISSN 1752-2706, Vol. 54, no 387, p. 543-553Article in journal (Refereed) Published
Abstract [en]

Estimating the measurement uncertainties of coordinates of points that are not accessible by direct geodetic surveying (hidden points) is the topic of this study. The simplicity by which the uncertainties can be found for such hidden points when practicing indirect observations by total station or by Global Navigation Satellite System (GNSS) is demonstrated. A three-dimensional solution is obtained by total station observations using a two-prism hidden-point rod and a two-dimensional solution by GNSS observations on the ground. An intention with the study is that methods and results should apply for general geodetic purposes, like engineering surveying. The derived uncertainty formulae have been verified by Monte Carlo simulations. An important finding is their geometric dependence by the quotient between the two distances involved when two coordinated points are collinear with a third hidden point.

Keywords
Hidden point, Closed-form formula, Collinearity, Two-prism hidden-point rod, Monte Carlo simulation
National Category
Geophysics Other Earth Sciences
Identifiers
urn:nbn:se:hv:diva-17979 (URN)10.1080/00396265.2021.1991174 (DOI)000716814400001 ()2-s2.0-85119117018 (Scopus ID)
Available from: 2021-12-30 Created: 2021-12-30 Last updated: 2025-09-30
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