The Use of Second-generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-levelling Data

Soltanpour, A.; Nahavandchi, Hossein; Featherstone, Will

doi:10.1007/s00190-006-0033-0

Cited by 20 publications

(15 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Featherstone 1998), and we have already conducted experiments in this regard (Featherstone 2000;Soltanpour et al 2006;Featherstone and Sproule 2006;Darbeheshti and Featherstone 2010). In much of the geodetic literature, this has been called a 'correction' or 'corrector' surface 1 This paper describes the computation of AUSGeoid09 as a model of the surface of zero elevation of the AHD, focussing partly on the new challenges (and benefits) that EGM2008 has set for regional quasigeoid modelling.…”

Section: Motivationmentioning

confidence: 99%

The AUSGeoid09 model of the Australian Height Datum

Featherstone

Kirby

Hirt

et al. 2010

J Geod

Self Cite

View full text Add to dashboard Cite

Abstract. AUSGeoid09 is the new Australia-wide gravimetric quasigeoid model that has been a posteriori fitted to the Australian Height Datum (AHD) so as to provide a product that is practically useful for the more direct determination of AHD heights from Global Navigation Satellite Systems (GNSS). This approach is necessary because the AHD is predominantly a third-order vertical datum that contains a ~1 m north-south tilt and ~0.5 m regional distortions with respect to the quasigeoid, meaning that GNSS-gravimetricquasigeoid and AHD heights are inconsistent. Since the AHD remains the official vertical datum in Australia, it is necessary to provide GNSS users with effective means of recovering AHD heights. The gravimetric component of the quasigeoid model was computed using a hybrid of the remove-compute-restore technique with a degree-40 deterministically modified kernel over a one-degree spherical cap, which is superior to the remove-compute-restore technique alone in Australia (with or without a cap). This is because the modified kernel and cap combine to filter long-wavelength errors from the terrestrial gravity anomalies. The zero-tide EGM2008 global gravitational model to degree and order 2190 was used as the reference field. Other input data are: ~1.4 million land gravity anomalies from Geoscience Australia, 1'x1' DNSC2008GRA altimeter-derived gravity anomalies offshore, the 9"x9" GEODATA-DEM9S Australian digital elevation model, and a readjustment of Australian National Levelling Network (ANLN) constrained to the CARS2006 dynamic ocean topography model. In order to determine the numerical integration parameters for the modified kernel, the gravimetric component of AUSGeoid09 was compared with 911 GNSS-observed ellipsoidal heights at benchmarks. The standard deviation of fit to the GNSS-AHD heights is ±222 mm, which dropped to ±134 mm for the readjusted GNSS-ANLN heights, showing that careful consideration now needs to be given to the quality of the levelling data used to assess gravimetric quasigeoid models. The publicly released version of AUSGeoid09 also includes a geometric component that models the difference between the gravimetric quasigeoid and the zero surface of the AHD at 6,794 benchmarks. This a posteriori fitting used least-squares collocation (LSC) in cross-validation mode to determine a correlation length of 75 km for the analytical covariance function, whereas the noise was taken from the estimated standard deviation of the GNSS ellipsoidal heights. After this LSC surface-fitting, the standard deviation of fit reduced to ±30 mm, one third of which is attributable to the uncertainty in the GNSS ellipsoidal heights.

show abstract

Section: Motivationmentioning

confidence: 99%

The AUSGeoid09 model of the Australian Height Datum

Featherstone

Kirby

Hirt

et al. 2010

J Geod

Self Cite

View full text Add to dashboard Cite

show abstract

“…An alternative approach to the combination of geometric and gravimetric height anomalies with the goal to obtain an optimal transformation of GPS ellipsoidal heights into the national height system, has been introduced by Dinter et al (1997) and refined by Jäger ( , 2000 and Jäger and Schneid (2001). Least squares collocation (LSC) is also commonly used, but numerous other approaches have been trialled (e.g., Soltanpour et al 2006;Lysaker et al 2007). In practice, the "corrector surface" f is parameterized in different ways.…”

Section: Introductionmentioning

confidence: 99%

“…In practice, the "corrector surface" f is parameterized in different ways. For instance, de Min (1996) uses a bivariate linear algebraic polynomial in latitude and longitude for the area of the Netherlands; de Bruijne et al (1997) use a linear combination of a bilinear polynomial and a trigonometric polynomial in latitude and longitude with 28 parameters for the North Sea region; Grebenitcharsky et al (2005) use a four-parameter trigonometric model for Canada originally suggested by Heiskanen and Moritz (1967); uses a bivariate algebraic polynomial defined on triangular meshes for parts of Germany; Featherstone (2000) compares splines under tension and LSC; Nahavandchi and Soltanpour (2006) use, among others, cubic splines. The proper choice of a corrector surface, which is a model identification problem, is still an open issue.…”

Section: Introductionmentioning

confidence: 99%

On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies

Prutkin

Klees

2007

J Geod

View full text Add to dashboard Cite

We consider the problem of local (quasi-)geoid modelling from terrestrial gravity anomalies. Whereas this problem is uniquely solvable (up to spherical harmonic degree one) if gravity anomalies are globally available, the problem is non-unique if gravity anomalies are only available within a local area, which is the typical situation in local/regional gravity field modelling. We derive a mathematical description of the kernel of the gravity anomaly operator. The non-uniqueness can be removed using external height anomaly information, e.g., provided by GPS-levelling. The corresponding problem is formulated as a Cauchy problem for the Laplace equation. The existence and uniqueness of the solution of the Cauchy problem is guaranteed by the Cauchy-Kowalevskaya theorem. We propose several numerical procedures to compute the solution of the Cauchy problem from given differences between gravimetric and geometric height anomalies. We apply the numerical techniques to real data over the Netherlands and Germany. We show that we can compute a unique quasi-geoid from observed gravimetric and geometric height anomalies, which agree with the data within the expected noise level. We conclude that observed differences between gravimetric height anomalies and geometric height anomalies derived from GPS and levelling cannot only be attributed to systematic errors in the data sets, but are also caused by the intrinsic non-uniqueness of the problem of local quasi-geoid modelling from gravity anomalies. Hence, GPS-levelling data are necessary to get a unique solution, which also implies that they should not be I. Prutkin · R. Klees (B) Delft Institute of Earth Observation and Space Systems (DEOS), Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands e-mail: r.klees@tudelft.nl used to validate local quasi-geoid solutions computed on the basis of gravity anomalies.

show abstract

“…Many previous studies were interested in investigating these GPS/leveling methods for the creation of local geoid models as [Zhong, 1997-Featherstone et al 1998-Erol and Celic, 2004-Erol and Erol, 2013-Seyed M. K. et al, 2016. Also, the optimal combination of GPS and leveling observations along with the available geoid models were investigated by [Featherstone, 2000-Soltanpour et al, 2006-You, 2006.…”

mentioning

confidence: 99%

Study of the Potential of a Local Geoid Model for Extracting the Orthometric Heights from GPS Measurements in Topographic Works

2017

CER

View full text Add to dashboard Cite

Due to the rapid development and expansion of geodetic applications, the determination of orthometric heights in an accurate manner is considered as one of the most required conditions to carry out such projects. Obtaining orthometric heights using traditional methods of levelling is time and cost consuming. Hence, investigating other techniques that provide the same accuracy, as leveling methods, but requiring less time and cost is very gainful. Recently, satellite positioning techniques and their applications are being used increasingly in geodetic projects. So, it is interesting to study the efficiency of such techniques for obtaining orthometric heights. GPS methods provide highly accurate measurement of ellipsoidal heights. However, the conversion of ellipsoid heights to orthometric heights may be achieved using geoid models. The objective of this research is to study the efficiency of using a local geoid model as an alternative method to obtain orthometric heights from GPS measurements. This paper proposes a methodology to generate such local geoid models. Then, the results of using the generated local geoid model for Jeddah city in Saudi Arabia are presented. These results indicate that the difference among estimated undulations values from the local geoid model and undulations values calculated from leveling techniques ranges from 1.8 cm to -1.1 cm. with a maximum standard deviation of 56 mm. These results confirm that the creation of a local geoid model is an effective method that gives the required accuracy for topographic works.

show abstract

The Use of Second-generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-levelling Data

Cited by 20 publications

References 31 publications

The AUSGeoid09 model of the Australian Height Datum

The AUSGeoid09 model of the Australian Height Datum

On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies

Study of the Potential of a Local Geoid Model for Extracting the Orthometric Heights from GPS Measurements in Topographic Works

Contact Info

Product

Resources

About