Precise height determination using simultaneous-reciprocal trigonometric levelling

Ceylan, Ayhan; Baykal, Orhan

doi:10.1179/003962608x290997

Cited by 8 publications

(8 citation statements)

References 3 publications

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“…The main methods to transfer the height across the river are geometric levelling and trigonometric levelling. The accuracy of determining the height difference of both of them meets that of second-order levelling has in a distance above hundreds of meters 4 , 9 , 10 . And the effect of refraction is the main factor to influence the precision of river-crossing levelling 19 .…”

Section: Methods Of River-crossing Levellingmentioning

confidence: 86%

“…Zhenglu 7 analyzed the errors of TL and derived the rigid formula of precise trigonometric levelling (PTL), in theory, to replace the first order levelling. Then the leap-frog method and simultaneous-reciprocal observation method were respectively put into practice for improving the accuracy of TL to achieve PTL 9 , 10 . Zou 11 combined the leap-frog method and simultaneous-reciprocal observation method and developed a motorized PTL system (MPTL) used in tough terrains.…”

Section: Introductionmentioning

confidence: 99%

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Precise levelling in crossing river over 5 km using total station and GNSS

Yang

Zou

2021

Sci Rep

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The trigonometric levelling using the simultaneous reciprocal method has been proved to meet the precision of second order levelling. But this method is invalid once the distance of river crossing is beyond 3.5 km due to the difficulty of target recognition at such a long distance. To expand the available range of this method, this paper focuses on solving the target aiming and distance observation over a long distance. A modular LED 5-prism (modified Leica GPR1 reflector) as an illuminated target instead of the common prism is introduced, and we adopt the sub-pixel image processing technique to recognize the center of the target image pictured by image assisted total station (Leica Nova TM50 I equipped with a coaxial camera). Based on the principle of precise trigonometric levelling, this paper utilizes two image assisted total stations using image processing technique to perform simultaneous reciprocal for zenith angle measurement and GNSS static measurement for slope distance measurement to determine the height difference of either river bank. And long-distance precise river-crossing levelling can be realized based on the mentioned above. Besides, it is successful to apply in the experiment of Fuzhou Bridge spanning 6.3 km in China. The result shows the standard deviation is ± 0.76 mm/km that is compatible with the precision of second order levelling has.

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Section: Methods Of River-crossing Levellingmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Precise levelling in crossing river over 5 km using total station and GNSS

Yang

Zou

2021

Sci Rep

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“…Figure 1 illustrates the short range trigonometric levelling with reciprocal and simultaneous measurement of zenith angles and slope distances. Field tests show that standard deviations of ≤ 2 mm / √ km are achievable, even along inclined terrain, at speed of 10 km/day when using sights no greater than 250 m for the reciprocal method (Ceylan and Baykal, 2008) assuming the PDL data as error free for the time being and equal weight of all sections (all sections assumed to be 250 m long), (Chrzanowski et al, 1985). The electronic total stations were set up on the 20 marked points of the 5 km run.…”

Section: Short Range Simultaneous Reciprocal Trigonometric Levellingmentioning

confidence: 99%

“…The studies relating to the GPS technique need ellipsoidal heights with centimetre or sub-centimetre accuracy which are obtained from the GPS solution. This will only be possible with an interconnected network or reference stations (Ayan, 2001;Ceylan and Baykal, 2008;Schofield, 2001) assuming the Precise Digital Levelling (PDL) data as minimal error for the time being and equal weight of all sections (all sections assumed to be 250 m long). In this study, accuracy of the height determination techniques has been compared the twenty vertical control points were marked in the project area.…”

Section: Introductionmentioning

confidence: 99%

Geodesy and Cartography

Pirti¹,

Hoşbaş²

2019

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Applications in geodesy and engineering surveying require the determination of the heights of the vertical control points in the national and local networks using different techniques. These techniques can be classified as geometric, trigonometric, barometric and Global Positioning System (GPS) levelling. The aim of this study is to analyse height differences obtained from these three techniques using precise digital level and digital level, total station (trigonometric levelling) and GPS which collects phase and code observations (GPS levelling). The accuracies of these methods are analysed. The results obtained show that the precise digital levelling is more stable and reliable than the other two methods. The results of the three levelling methods agree with each other within a few millimetres. The different levelling methods are compared. Geometric levelling is usually accepted as being more accurate than the other methods. The discrepancy between geometric levelling and short range trigonometric levelling is at the level of 8 millimetres. The accuracy of the short range trigonometric levelling is due the reciprocal and simultaneous observations of the zenith angles and slope distances over relative short distances of 250 m. The difference between the ellipsoidal height differences obtained from the GPS levelling used without geoid and the orthometric height differences obtained from precise geometric levelling is 4 millimetres. The geoid model which is obtained from a fifth order polynomial fit of the project area is good enough in this study. The discrepancy between the precise geometric and GPS levelling (with geoid corrections) is 4 millimetres over 5 km.

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“…To obtain accurate elevations with the Global Positioning System (GPS), the geoidal heights in the area must be known and applied. The height obtained through Global Positioning System (GPS) observation is known as the ellipsoidal height which cannot be used directly for practical surveying but needs to be transformed into orthometric heights, being the distance measured along the plumb line between the geoid and a point on the Earth's surface (Ceylan & Baykal, 2008;Atinc & Ramazan, 2019).…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Change between Ellipsoidal Height Differences and Equivalent Orthometric Height Difference

Herbert

Olatunji

2020

Ghana J. Geography

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Height is an important component in the determination of the position of a point. The study aimed at performing a comparative analysis of change between ellipsoidal height differences and the equivalent orthometric height difference of points. A hi-target Differential Global Positioning System (DGPS) was used to acquire GPS data with an occupation period of thirty (30) minutes on each point, which were processed using Hi-target Geomatics Office (HGO) software to obtain the ellipsoidal heights. An automatic level instrument was used to acquire leveling data, which were processed using the height of collimation method to obtain the orthometric heights. A total of fifty (50) points were occupied as common points for both the GPS and levelling observations at 20-meter intervals. The accuracy of the height difference was determined using standard deviation with the ellipsoidal height difference as 53.59cm and the orthometric height as 53.07cm respectively. A Root Mean Square Error value of 0.0621m was obtained as the accuracy of the change between the two height differences. Statistical analysis using the independent-sample Z test was used to analyze the data at a 5% significant level. The result shows no significant difference in the performance of the two height systems. It is worthy to note that GPS and spirit levelling height differences can be used interchangeably for any heighting in short distances for surveying and engineering applications.

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Precise height determination using simultaneous-reciprocal trigonometric levelling

Cited by 8 publications

References 3 publications

Precise levelling in crossing river over 5 km using total station and GNSS

Precise levelling in crossing river over 5 km using total station and GNSS

Geodesy and Cartography

Comparative Analysis of Change between Ellipsoidal Height Differences and Equivalent Orthometric Height Difference

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