At the beginning of the 21st century, a significant technological change took place in geodetic astronomy. In Zurich and Hannover, digital zenith camera systems were developed based on digital imaging sensors (charge-coupled device) that strongly improved the degree of automation, efficiency, and accuracy of the observation of the direction of the plumb line and its vertical deflection. This paper describes the instrumental design of the new digital zenith camera systems and gives an overview of the data processing with focus on the models used for astrometric data reduction and tilt correction. Results of frequently repeated observations of vertical deflections and comparison measurements show an accuracy of vertical deflection measurements of better than 0.1 arc sec. Application examples for vertical deflection data from zenith camera observations, such as the high-precision local gravity field determination in engineering projects and gravity field validation are summarized.

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Modern Determination of Vertical Deflections Using Digital Zenith Cameras

In order properly to apply transformations when using data derived from different GPS solutions, the effects of plate motion on the coordinates should be accurately taken into consideration. Only then can a rigorous comparison be established between results observed at different epochs. Equations are given to relate GPS-derived Cartesian coordinates and velocities affected by changes of their reference frames and epochs.

/pdf/a-compendium-of-transformation-formulas-useful-in-gps-work-2nhv7oh4vv.pdf

A compendium of transformation formulas useful in GPS work

The method of geometric-astronomical leveling is presented as a suited technique for the validation of GNSS (Global Navigation Satellite System) heights. In geometric-astronomical leveling, the ellipsoidal height differences are obtained by combining conventional spirit leveling and astronomical leveling. Astronomical leveling with recently developed digital zenith camera systems is capable of providing the geometry of equipotential surfaces of the gravity field accurate to a few 0.1 mm per km. This is comparable to the accuracy of spirit leveling. Consequently, geometric-astronomical leveling yields accurate ellipsoidal height differences that may serve as an independent check on GNSS height measurements at local scales. A test was performed in a local geodetic network near Hanover. GPS observations were simultaneously carried out at five stations over a time span of 48 h and processed considering state-of-the-art techniques and sophisticated new approaches to reduce station-dependent errors. The comparison of GPS height differences with those from geometric-astronomical leveling shows a promising agreement of some millimeters. The experiment indicates the currently achievable accuracy level of GPS height measurements and demonstrates the practical applicability of the proposed approach for the validation of GNSS height measurements as well as the evaluation of GNSS height processing strategies.

/pdf/mutual-validation-of-gnss-height-measurements-and-high-2x4e6id1rs.pdf

Mutual validation of GNSS height measurements and high-precision geometric-astronomical leveling

Deflection of the vertical is used in reducing geodetic measurements related to geoid networks (vertical and horizontal directions observations and length measurement, etc.) to ellipsoid plane and in geoid modeling processes. Generally, it is obtained by Astro-Geodetic and gravimetric techniques. These techniques are very complex and time-consuming. Ellipsoidal coordinates of points are easily obtained thanks to the widespread use of Satellite Positioning Techniques (GNNS) such as GPS in geodesy. When the orthometric heights of points are determined via geometric leveling, geoid height differences and deflection of the vertical components can be measured faster and much more easily by using GPS and leveling measurements than the other techniques. This study discusses the calculation of the deflection of vertical components via GPS and leveling measurements. The deflection of the vertical components obtained from GPS and leveling measurements were compared with global (EGM96 and CG03C) and local (TG03) geoid models. Deflection of the vertical components ξ (north-south) and η (east-west) were calculated as ξ = -4.15” ± 0.61”, η = 8.75” ± 0.69” via a GPS and leveling model; as ξ = -5.64”, η = 1.95” via the EGM96  geoid model; as ξ = -4.85”, η = 1.82” via the CG03C geoid model; as ξ = -7.47”, η = -0.51” via the TG03 model; and as ξ = -3.9”, η = 4.6” via Astro-Geodetic deflection of a vertical map of Turkey produced by Ayan (1976). When the values obtained from GPS and leveling measurements were compared with the values produced by the other techniques, the north-south component was found to be approximately consistent, while east-west component differed to same extent. Since very little data on the terrestrial gravity of Turkey was present in the EGM96 and CG03C global geoid models, it was not anticipated that the results obtained via these models would be comparable with other methods.

	 

	Key words: Deflection of the vertical, deflection of the vertical components, GPS/Leveling, EGM96, CG03C.

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Determination of the deflection of vertical components via GPS and leveling measurement: A case study of a GPS test network in Konya, Turkey

Large parabola dish antennae are in use for station-to-satellite communications, satellite tracking for precise orbit determination, very long baseline interferometry , and others. In this paper a procedure for the precise determination of the satellite tracking antenna reference point (ARP) position in the International Terrestrial Reference Frame is outlined. It is based on measurements made directly to the rotatable elevation housing of the antenna in various azimuth and elevation positions. The three-dimensional position of both rotation axes are obtained from the calculation of best-fitting circles. The resulting ARP is tied into a local geodetic network around the antenna to be observed by global positioning system (GPS) in combination with terrestrial measurements using a 3D data integration model including geoidal heights. ITRF coordinates are determined by static GPS observations using the products of the International Global Navigation Satellite Systems Service . Results are shown exemplarily fo...

Geodetic Determination of Radio Telescope Antenna Reference Point and Rotation Axis Parameters

The capabilities of the Global Positioning System (GPS) for accurately determining geodetic quantities are well established. Nevertheless, no comparison between deflections of the vertical as determined through GPS with leveling and values conventionally computer by astrogeodetic methods has yet been published. This investigation demonstrates that the accurate deflections of the vertical components ({eta}, {xi}) can be obtained independently of classical astronomic observations by combining geodetic leveling with satellite GOS positioning. The approach uses a radial configuration of baselines to determine the best (in a least square sense) values of ({eta}, {xi}) at the central station.

Archie E. Carlson

Papers

Determination of vertical deflections using the global positioning system and geodetic leveling