Simple Solution to the Three Point Resection Problem

Ligas, Marcin

doi:10.1061/(asce)su.1943-5428.0000104

Cited by 5 publications

(3 citation statements)

References 4 publications

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“…Çalışma, ℝ𝑥ℝ = ℝ 2 koordinat düzleminde gerçekleştirilmiştir. Günümüzde kullanılan geriden kestirme yöntemleri: Collins, Kaestner, Delambre, Cassini, Ansermet ve Akarsu yöntemleridir (Hallidey, 1962;Alman, 1963;Bradley, 1972;Danial, 1978;El Hassan, 1986;Hu ve Kuang, 1998;Greulich, 1999;Tan, 2004;Burtch, 2005;Akarsu, 2008a;Font-Lagunes ve Batlle, 2009;Porta ve Thomas, 2009;Dekov, 2012;Ligas, 2013). Geçmişte geliştirilen bazı geriden kestirme yöntemleri ise (Willebrord, 1617;McCaw, 1918) (Akarsu, 2008a) çözüm yöntemini bilim dünyasına sunmuşlardır (Akarsu, 2005a;Akarsu, 2008b;Akarsu2008c).…”

Section: Introductionunclassified

Dış doğrultu ölçmeleriyle geriden kestirmede Collins ve Akarsu yöntemleri

Akarsu

2023

Geomatik

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Yeryuvarında tanımlanmış olan bir iki boyutlu (2B) dik koordinat sisteminde, koordinatı bilinmeyen noktadan (doğrultu ölçmeleri yapılan nokta) koordinatları bilinen (en az dört nokta) noktalara, en az iki tam dizi doğrultu ölçmelerinde hesaplanan düzlem açılar ile koordinatların hesaplanmasına geriden kestirme problemi denir. Bir, iki, üç veya çok noktanın koordinatları geriden kestirme yöntemiyle hesaplanabilmektedir. Günümüzde kullanılan geriden kestirme yöntemleri: Collins, Kaestner, Delambre, Cassini, Ansermet ve Akarsu yöntemleridir. Bir alıcı ile küresel konum belirleme sistemleri ile nokta konum koordinatlarının belirlenmesi, geriden kestirme yöntemine dayanması nedeniyle daha da önemli hale gelmiştir. Bu çalışmada, geriden kestirme noktasındaki dış açılar ile geriden kestirme probleminin çözümü, Collins ve Akarsu yöntemleri ile çözümünün teorik açıklamaları yapılmıştır. Ayrıca, sayısal bir uygulama ile de Collins yöntemiyle hesaplanan kestirme noktasının kesin koordinatlarına ait standart sapmaları; ve Akarsu çözüm yönteminde ise ise; değerleri elde edilmiştir. Her iki çözüm yöntemiyle elde edilen değerler, bulgular ve tartışma bölümünde yorumlanmıştır.

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Section: Introductionunclassified

Dış doğrultu ölçmeleriyle geriden kestirmede Collins ve Akarsu yöntemleri

Akarsu

2023

Geomatik

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“…The three-point resection method (also known as the "three-point problem") is used to compute the coordinates of an unknown point by occupying the resected point and measuring angles and distance toward three known points, since the angles between three known points are determined at the unknown point (ElHassan, 1986). The idea of computing the coordinates of an unknown point using relative angular measurements to three known stations is a basic concept in surveying engineering (El Hassan, 1989) and it is a very useful technique for fixing positions quickly where it is best needed for setting-out purposes which has been discussed and solved analytically or graphically in the last centuries in most previous articles and books, such as (ElHassan, 1986;Font-Llagunes & Batlle, 2009;Haralic et al, 1991;Ligas, 2013;Problem, n.d.;Wang et al, 2018). Moreover, (El Hassan, 1989) tried to detect the accuracy of the three-point resection method by changing the position of resected and control points, and this paper has reached to the relative location of the resected point, indicating that the three control points have a big affection on deciding the accuracy of the resected point.…”

Section: Introductionmentioning

confidence: 99%

Accuracy Investigation of Three-Point Resection Methodusing Known Points Distribution in Four-Quadrants

Osman

Cahyadi

Elhag

2021

JMEST

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This paper presents a simple way of finding the accuracy of three-point resection problem. The main idea is to distribute known points in four-quadrants and compute the coordinates of the resected point (P),then investigate the affection of known points positions in one quadrant or combination quadrant for the accuracy of resected point (which is a new idea in the literature). This article aims to find outthe affections of distribution control points in different quadrants on the accuracy of the resected point, and also choosing the best positions of the three-points interms of their positions in one quadrantor their positions in combination quadrants. The relative positions of the known points and the resected point are playing the main role to decidethe accuracy of the resected point. Thestudy of the relationship between relative positions of unknown point will be explained in detail, other known-points and the accuracy of the unknown point will beintroduced,and the positions of known points (Distributed in quadrants) of having the best accuracy of the resected point will bedefined.

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“…The last example is computing the Cartesian coordinates X D , Y D of a point D by the resection solution presented by (Ligas, 2013) . We should realize that in surveying engineering, one should usually avoid the situation where the resection point lies very close to the danger circle.…”

Section: Three-point Resection Problemmentioning

confidence: 99%

Propagation of uncertainty by Monte Carlo simulations in case of basic geodetic computations

Wyszkowska

2017

Geodesy and Cartography

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Abstract:The determination of the accuracy of functions of measured or adjusted values may be a problem in geodetic computations. The general law of covariance propagation or in case of the uncorrelated observations the propagation of variance (or the Gaussian formula) are commonly used for that purpose. That approach is theoretically justifi ed for the linear functions. In case of the non-linear functions, the fi rst-order Taylor series expansion is usually used but that solution is affected by the expansion error. The aim of the study is to determine the applicability of the general variance propagation law in case of the non-linear functions used in basic geodetic computations. The paper presents errors which are a result of negligence of the higher-order expressions and it determines the range of such simplifi cation. The basis of that analysis is the comparison of the results obtained by the law of propagation of variance and the probabilistic approach, namely Monte Carlo simulations. Both methods are used to determine the accuracy of the following geodetic computations: the Cartesian coordinates of unknown point in the three-point resection problem, azimuths and distances of the Cartesian coordinates, height differences in the trigonometric and the geometric levelling. These simulations and the analysis of the results confi rm the possibility of applying the general law of variance propagation in basic geodetic computations even if the functions are non-linear. The only condition is the accuracy of observations, which cannot be too low. Generally, this is not a problem with using present geodetic instruments.

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Simple Solution to the Three Point Resection Problem

Cited by 5 publications

References 4 publications

Dış doğrultu ölçmeleriyle geriden kestirmede Collins ve Akarsu yöntemleri

Dış doğrultu ölçmeleriyle geriden kestirmede Collins ve Akarsu yöntemleri

Accuracy Investigation of Three-Point Resection Methodusing Known Points Distribution in Four-Quadrants

Propagation of uncertainty by Monte Carlo simulations in case of basic geodetic computations

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