On Deflection of the Vertical Components and Their Transformations

Soler, Tomás; Han, Jen-Yu; Weston, Neil D.

doi:10.1061/(asce)su.1943-5428.0000126

Cited by 11 publications

(12 citation statements)

References 9 publications

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“…Since the n -frame and n′ -frame are defined by the physical plumb line and the normal gravity, the signature of DOV is reflected in the coordinate transformation matrix from n -frame to n′ -frame

is determined by Equation (5) with DOVs [ 17 ]. In essence, the key problem with DOV measurement is to obtain the transformation matrix

.…”

Section: The Methods For Dov Measurementmentioning

confidence: 99%

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An Improved Method for Dynamic Measurement of Deflections of the Vertical Based on the Maintenance of Attitude Reference

Dai

Wang

Zhan

et al. 2014

Sensors

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A new method for dynamic measurement of deflections of the vertical (DOV) is proposed in this paper. The integration of an inertial navigation system (INS) and global navigation satellite system (GNSS) is constructed to measure the body's attitude with respect to the astronomical coordinates. Simultaneously, the attitude with respect to the geodetic coordinates is initially measured by a star sensor under quasi-static condition and then maintained by the laser gyroscope unit (LGU), which is composed of three gyroscopes in the INS, when the vehicle travels along survey lines. Deflections of the vertical are calculated by using the difference between the attitudes with respect to the geodetic coordinates and astronomical coordinates. Moreover, an algorithm for removing the trend error of the vertical deflections is developed with the aid of Earth Gravitational Model 2008 (EGM2008). In comparison with traditional methods, the new method required less accurate GNSS, because the dynamic acceleration calculation is avoided. The errors of inertial sensors are well resolved in the INS/GNSS integration, which is implemented by a Rauch–Tung–Striebel (RTS) smoother. In addition, a single-axis indexed INS is adopted to improve the observability of the system errors and to restrain the inertial sensor errors. The proposed method is validated by Monte Carlo simulations. The results show that deflections of the vertical can achieve a precision of better than 1″ for a single survey line. The proposed method can be applied to a gravimetry system based on a ground vehicle or ship with a speed lower than 25 m/s.

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is determined by Equation (5) with DOVs [ 17 ]. In essence, the key problem with DOV measurement is to obtain the transformation matrix

.…”

Section: The Methods For Dov Measurementmentioning

confidence: 99%

“…

where δα represents the final rotation around the astronomical zenith axis to make the geodetic coordinates and astronomical coordinates coincident. According to [ 17 ], δα = η tan L , where L is the local latitude.…”

Section: The Methods For Dov Measurementmentioning

confidence: 99%

An Improved Method for Dynamic Measurement of Deflections of the Vertical Based on the Maintenance of Attitude Reference

Dai

Wang

Zhan

et al. 2014

Sensors

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“…al (2016) show that the vertical displacements of the geoid and the crust are in opposite directions. In addition to these, Soler et. al (2013) emphasised that astrogeodetic VDs, accompanied by terrestrial gravity, gradiometric observations, and localized seismology, could disclose shallow underground mass anomalies.…”

Section: The Importance Of the Astrogeodetic Observationmentioning

confidence: 98%

The Use of the Automated Digital Zenith Camera System in Istanbul for the Determination of Astrogeodetic Vertical Deflection

et al. 2019

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“…The cartesian coordinate is not used directly in mapping on the grid but provides a model for transforming between different ellipsoids. Its values can also readily be converted to geodetic coordinates (Soler et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Comparison between the azimuths of astronomical and geodetic coordinates in Ghana

Asante¹,

Ayer²,

Ziggah³

et al. 2023

JGhIE

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Astronomic azimuths are bearings, which are referenced to the true north direction whereas geodetic azimuths are those referenced to a grid north direction. The difference between these two directions can be expressed through the deflection of the vertical. This deflection of the vertical refers to the difference between the normal to the geoid (Astronomic) and the normal to the ellipsoid (geodetic). The deflection of the vertical components are used to convert between astronomic and geodetic coordinates and azimuths using Laplace equations. This paper compares astronomic and geodetically derived coordinates at eight Laplace stations constituting twenty-eight baselines for which both geodetic and astronomic azimuths were derived. The comparison of azimuths shows that differences of 000°00'05.95" up to 000°23'06.93" exist between the two different versions of azimuths. These differences are not accounted for in application of the simplified Laplace equations under the assumptions made in their derivation. It is, thence, recommended that an alternative didactic approach based on rotations of three-dimensional right-handed local frames as used in Helmert’s coordinate transformations be explored for transformation between astronomic and geodetic coordinates.

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On Deflection of the Vertical Components and Their Transformations

Cited by 11 publications

References 9 publications

An Improved Method for Dynamic Measurement of Deflections of the Vertical Based on the Maintenance of Attitude Reference

An Improved Method for Dynamic Measurement of Deflections of the Vertical Based on the Maintenance of Attitude Reference

The Use of the Automated Digital Zenith Camera System in Istanbul for the Determination of Astrogeodetic Vertical Deflection

Comparison between the azimuths of astronomical and geodetic coordinates in Ghana

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