Precise Height Determination Using Leap-Frog Trigonometric Leveling

Ceylan, Ayhan; Baykal, Orhan

doi:10.1061/(asce)0733-9453(2006)132:3(118)

Cited by 9 publications

(4 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: 87%

“…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: 87%

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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“…However, one assessment has illustrated that digital levelling can reach an accuracy of 2 mm/km with precision of 1 mm + 1 mm/km, respectively (Bitelli et al, 2018). Leap-frogging using 150 m distance steps found an elevation precision of 1.9 mm / √ km (Ceylan and Baykal, 2006).…”

Section: Relative Positioning Using Traditional Surveyingmentioning

confidence: 99%

Error in hydraulic head and gradient time-series measurements: a quantitative appraisal

Rau¹,

Post²,

Shanafield³

et al. 2019

Preprint

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Abstract. Hydraulic head and gradient measurements underpin practically all investigations in hydro(geo)logy. There is sufficient information in the literature to suggest that head measurement errors may be so large that flow directions can not be inferred reliably, and that their magnitude can have as great an effect on the uncertainty of flow rates as the hydraulic conductivity. Yet, educational text books contain limited content regarding measurement techniques and studies rarely report on measurement errors. The objective of our study is to review currently-accepted standard operating procedures in hydrological research and to determine the smallest head gradients that can be resolved. To this aim, we first systematically investigate the systematic and random measurements errors involved in collecting time series information on hydraulic head at a given location: (1) geospatial position, (2) point of head, (3) depth to water, and (4) water level time series. Then, by propagating the random errors, we find that with current standard practice, horizontal head gradients

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“…The manufacturer specified angular precision of these equipment are 1" and 0.5" for TCA1800 and TCA2003, respectively, and 1 mm + 1 ppm for distance measurements. The backsight and foresight distances are kept equal to within 0.5 m. The standard deviation in the height difference measured between two points, defined as s H , is given as (Ceylan and Baykal, 2006) 2sin 4…”

Section: Description Of the Data Used In This Studymentioning

confidence: 99%

The Stability of Tide Gauges in the South Pacific Determined from Multiepoch Geodetic Levelling, 1992 to 2010

2013

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Tide gauge data forms the basis for determining global or local sea level rise with respect to a global geocentric reference frame. Data from repeated precise levelling connections between the tide gauges and a series of coastal and inland benchmarks, including a Continuous GPS (CGPS) benchmarks, is used to determine the stability of tide gauges at 12 locations in the South Pacific. The method for determining this stability is based on using a constant velocity model which minimises the net movement amongst a set of datum benchmarks surveyed since the installation of the tide gauges. Tide gauges were found to be sinking, relative to the CGPS benchmark, in Pohnpei (FSM), Samoa, Vanuatu, Tonga, Nauru, Tuvalu, Fiji and Cook Islands (Is); listed in order of their sinking rate. A maximum of-1.01  0.63 mm/yr is computed at Pohnpei (FSM) and the minimum at Cook Is was statistically insignificant. The tide gauge levels were rising, relative to the CGPS benchmark in Solomon Is, Manus Is (PNG), Kiribati and Marshall Is, with a maximum of 3.12  0.49 mm/yr at Solomon Is and a minimum at Marshall Is, which was statistically insignificant. However, these estimates are unreliable for the Solomon Is and Marshall Is, which have recently established CGPS benchmarks and have been surveyed less than 3 times. In Tonga and Cook Is, the tide gauges were found to be disturbed or affected by survey errors whereas the Vanuatu results were affected by earthquakes. It was also found that the constant velocity model did not fit the observations at the tide gauges in Tonga, Cook Is, Fiji, Marshall Is and Vanuatu, which had large variations in their velocities. This is an indicator of the high frequency (short period) motion of the tide gauge structure, which cannot be measured by the levelling method since they have a higher frequency than the time interval between levelling surveys.

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Precise Height Determination Using Leap-Frog Trigonometric Leveling

Cited by 9 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

Error in hydraulic head and gradient time-series measurements: a quantitative appraisal

The Stability of Tide Gauges in the South Pacific Determined from Multiepoch Geodetic Levelling, 1992 to 2010

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