I. N. Tziavos

Applications of GPS technology in the land transportation system

Abstract The global positioning system (GPS) allows the accurate positioning of an object using satellite signals. There are a lot of applications of this technology in many scientific fields all over the world. In recent years, the rapid increase in the development of the geographic information system technology (GIS) has led to the development of GPS/GIS applications. Therefore, the geometric and geographic information obtained by the use of GPS can be introduced to GIS database and thus thematic maps can be produced. In the framework of this paper, a short overview of applications in the area of transportation in Greece and abroad is presented. Emphasis is placed on an ongoing application in railway mapping, through the presentation of its pilot phase in Greece. The use of modern technologies, the problems identified and the results produced are presented and discussed.

Comparisons of spectral techniques for geoid computations over large regions

The Stokes formula is efficiently evaluated by the one-and two- dimensional (1D, 2D) fast Fourier transform (FFT) technique in the plane and on the sphere in order to obtain precise geoid determinatiover a large area such as Europe. Using a high-pass filtered spherical harmonic reference model (OSU91A truncated to different degrees), gridded gravity anomalies and geoid heights were produced and the anomalies were used as input in the FFT software. Various tests were performed with respect to the different kernel functions used, to the spherical computations in bands, as well as to windowing, edge effects and extent of the area. It is thus demonstrated that, in geoid computations over large regions, the 1D spherical FFT and the 2D multiband spherical FFT in combination with discrete spectra for the kernel functions and 100% zero-padding give better results than those obtained by the other transform techniques. Additionally, numerical tests were carried out at the same test area using the planar fast Hartley transform (FHT) instead of the FFT and the results obtained by the two attractive alternatives were compared regarding the requirements in both computer time and computer memory needed in geoid height computations.

Statistical Models and Latest Results in the Determination of the Absolute Bias for the Radar Altimeters of Jason Satellites using the Gavdos Facility

The dedicated calibration site for satellite radar altimeters in Gavdos, Greece, has been operational as of 2004. The island of Gavdos is located along a repeating ground track of Jason satellites, adjacent to Envisat, where the altimeter and radiometer do not experience significant land intrusion. In this article, the models and techniques for calculating the satellite altimeter bias, as well as the software tool called “TUCalibrit,” are presented. In summary, over cycles 209–259 for Jason-1 and cycles 1–40 for Jason-2, the altimeter biases have been estimated as B(J1) = +103.6 mm ± 4.7 mm and B(J2) = +181.9 mm ± 6.7 mm, respectively.

On the Determination of Marine Geoid Models by Least-Squares Collocation and Spectral Methods Using Heterogeneous Data

In the frame of the EU-sponsored GAVDOS project the need of a new high-resolution and high-accuracy geoid model for the calibration of altimeters onboard satellites like JASON-1, ENVISAT and EURO-GLOSS and for sea level monitoring purposes has become apparent. That was mainly due to the fact that the already available models have been estimated using outdated datasets and fail to meet the wanted, cm-level, accuracy requirements. To determine the new geoid models multi-satellite (ERS1 and GEOSAT) altimetry and land and marine gravity data have been used. The EGM96 global geopotential model has been employed, while the effect of the bathymetry has been taken into account using recently developed local Digital Depth Models (DDMs). Several solutions have been estimated based on the different datasets used and the two main methodologies followed, i.e., the Fast Fourier Transform (FFT) based Input Output System Theory (IOST) and Least Squares Collocation (LSC). The accuracy of the new models was assessed through comparisons with TOPEX/POSEIDON (T/P) data and the GEOMED geoid solution for the area under study. Finally, the consistency between the estimated solutions has been determined by comparing the geoid height value they provide at the Gavdos Tide Gauge (TG) station on the isle of Gavdos. From the results it was found that the precision of the new geoid models is between ±0.9 and ±3.3 cm, their accuracy ranges between ±5 and ±10 cm and their consistency is at the ±0.5 − 6 cm level.

The Development of the European Gravimetric Geoid Model EGG07

The European Gravity and Geoid Project (EGGP) is a project within IAG Commission 2, reporting to Sub-commission 2.4. The main goal of the project is to compute an improved European geoid and quasigeoid model based on new and improved data sets which have become available since the last computation in 1997 (EGG97). The improvements include better global geopotential models from the CHAMP and GRACE missions, better digital elevation models (DEMs) in some regions (e.g., new national DEMs, SRTM3, GTOPO30), updated gravity data sets for selected areas, updated ship and altimetric gravity data, improved procedures for the merging of ship and altimetric data, the use of GPS/levelling data, as well as refined computation techniques

Evaluation of GOCE/GRACE Global Geopotential Models over Greece with Collocated GPS/Levelling Observations and Local Gravity Data

The advent of the GOCE and GRACE missions during the last decade have brought new insights and promising results both in the static and time-variable representation of the Earth’s gravity field. The focus of this work is directed to the evaluation of most available Global Geopotential Models (GGMs) from GOCE and GRACE, both satellite only as well as combined ones. The evaluation is carried out over an extensive network of collocated GPS/Levelling benchmarks (BMs) which covers the entire part of continental Greece and with respect to the reductions the GGMs provide in existing gravity data in order to assess their performance in a scenario that a remove-compute-restore procedure would be followed for geoid determination. From the evaluation with GPS/Levelling BMs, it was concluded that the GOCE/GRACE GGMs provide an absolute accuracy at the 12–15 cm level, up to degree and order (d/o) 250, when considering the geoid omission error. This is comparable and in some cases better than the performance of EGM2008 in Greece. Moreover, the latest (Release 3) versions of the GGMs provide considerably better results compared to the earlier version by 1–5 cm. In terms of relative errors, GOCE/GRACE GGMs reach the 1 cm level for baselines between 50 and 60 km, while for longer ones, 80–90 km, their performance is analogous to the local geoid model and the ultra-high degree combined GGMs. Finally, GOCE/GRACE GGMs manage to provide the same, as EGM2008, level of reduction to the local gravity anomalies, with a std at the 26.7–27.8 mGal level, when evaluated up to d/o 250.

A study of the contributions of various gravimetric data types on the estimation of gravity field parameters in the mountains

In this paper, new rigorous, simpler, and more efficient formulas are used to estimate the effect of the terrain on geoid undulations and deflections of the vertical. The new formulas are based on the successive application in the spectral domain of Molodenskys vertical derivative operator to powers of heights. A number of numerical tests are carried out in the area of British Columbia (BC) in western Canada. Geoid undulations and deflections of the vertical are computed by combining a geopotential model complete to degree and order 360, mean 5 arc min × 5 arc min free air gravity anomalies and height data on a 1 km × 1 km grid. In geoid undulation computations, the indirect effect of Helmerts second condensation reduction is taken into account. To assess the quality of the predicted deflections of the vertical and geoid undulations, the computed quantities are compared to a set of astronomic deflections of the vertical and geoid undulations derived from a combination of Global Positioning System with leveled orthometric heights. Test results present a precision of about ±2.0 arc sec for deflections, thus fulfilling the requirements for the reduction of geodetic measurements in any case. The achievable precision for geoid undulation differences, close to ±0.50 m, is also acceptable to determine an accurate relative geoid in the test area useful for various geodetic applications.

Calibration/validation of GOCE data by terrestrial torsion balance observations

One promising method for the external validation and calibration of the upcoming GOCE satellite mission data is the use of ground gravity field data continued upward to satellite altitude. There is a unique situation for Hungary in this respect since surface gravity gradients are available at 20143 points over an approximately 48700 km2 area, measured by the classical E6tv6s torsion balance. The concept of this contribution is to test the usability of these point gravity gradient observations for upward continuation to the GOCE satellite orbit in combination with different geopotential models and other gravity field information.

Towards a cm-geoid for Hungary: Recent efforts and results

Abstract Some steps were taken recently for Hungary aiming at the determination of geoid heights with a cm-accuracy. The present HGTUB98 gravimetric solution was based on terrestrial gravity data, height data and the EGM96 geopotential model, and was computed with the 1D Spherical FFT method. The gravity data were used in the area 45.5 ° ≤ϑ ≤ 49 °, 16 ° ≤ λ ≤ 23 °, the resolution of the grid was 30″ × 50″. The DTM used had a resolution of 1 km × 1 km. Our solution was evaluated using GPS/levelling data at 340 and 308 points respectively and at 138 vertical deflection points. We have compared our solution to the European EGG97 geoid solution, the gravimetric solution HGR97B developed by A. Kenyeres and the litospheric geoid solution by G. Papp. We have correlated our recent HGTUB98 solution to the Moho model of Central Europe. The comparison with GPS/levelling yielded respectively an accuracy of ±8.7 cm and ±4.4 cm (in terms of standard deviation) when a linear trend was removed. The comparison of the 1D planar FFT solution for the deflections of the vertical with 138 astrogeodetic deflections yielded an accuracy (in terms of standard deviation) of ±0.62″ and ±0.52″ for ξ and η, respectively.

Gravity Data Base Generation and Geoid Model Estimation Using Heterogeneous Data

The computation of high-resolution and high-precision geoid models in the Eastern part of the Mediterranean Sea usually suffers from the few gravity observations available. In the frame of the EU-sponsored GAVDOS project, a systematic attempt has been made to collect all available gravity data for an area located in the Southern part of Greece and determine new and high-resolution geoid models. Thus, all available gravity data have been collected for both land and marine regions and an editing/blunder-removal processing scheme has been followed to generate an optimal gravity dataset for use in geoid determination. The basic analysis and validation of the gravity data-bank was based on a gross-error detection visualization and collocation scheme. The Least Squares Collocation (LSC) method was employed to predict gravity at known stations and then validate the observations and detect blunders. The finally generated gravity database presents a resolution of 1 arcmin in both latitude and longitude while its external and internal accuracies were estimated to about ±5 mGal and ±0.2 – ±0.4 mGal, respectively. Based on the derived gravity database a gravimetric geoid model was developed using the well-known remove-compute-restore method with an application of a 1D Fast Fourier Transform (FFT) to evaluate Stokes’ integral. Altimetric geoid solutions have been also determined from the GEOSAT and ERS1 geodetic mission altimetry data. Finally, combined geoid models have been computed using the FFT-based Input Output System Theory (IOST) and the LSC methods. The consistency of the geoid models estimated was assessed by comparing the geoid height value at the Gavdos Tide Gauge (TG) station on the isle of Gavdos. Their accuracy was determined through comparisons with stacked T/P sea surface heights. From the comparisons performed it was found that the accuracy of the gravimetric, altimetric and combined models was at the ±14.5 cm, ±8.6 cm and ±12.5 cm level, and their consistency at about ±2 cm.