| 1. |
- Abdollahzadeh, Makan, 1982-, et al.
(författare)
-
Application of Molodensky's Method for Precise Determination of Geoid in Iran
- 2011
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Ingår i: Journal of Geodetic Science. - Poland : Versita. - 2081-9919 .- 2081-9943. ; 1:3, s. 259-270
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Tidskriftsartikel (refereegranskat)abstract
- Determination of the geoid with a high accuracy is a challenging task among geodesists. Its precise determination is usually carried out by combining a global geopotential model with terrestrial gravity anomalies measured in the region of interest along with some topographic information. In this paper, Molodensky's approach is used for precise determination of height anomaly. To do this, optimum combination of global geopotential models with the validated terrestrial surface gravity anomalies and some deterministic modification schemes are investigated. Special attention is paid on the strict modelling of the geoidal height and height anomaly difference. The accuracy of the determined geoid is tested on the 513 points of Iranian height network the geoidal height of which are determined by the GPS observations.
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| 2. |
- Alfredsson, Anders, et al.
(författare)
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A first step towards a national realisation of the international height reference system in Sweden with a comparison to RH 2000
- 2023
-
Ingår i: Journal of Geodetic Science. - : de Gruyter. - 2081-9919 .- 2081-9943. ; 13:1
-
Tidskriftsartikel (refereegranskat)abstract
- The International Height Reference System (IHRS) was defined by the International Association of Geodesy in 2015. Since then, the international geodetic community has been working on the specification and establishment of its realisation, the International Height Reference Frame (IHRF). This frame will primarily be realised by geopotential numbers (or physical heights) in a sparse global reference network. In Sweden, only one such global station is planned. Regional and national realisations (or densifications) computed in accordance with the IHRS definition are needed to enable the best possible unification of height datums. The main purpose of this article is to make a case study for Sweden regarding the national realisation of IHRS and to investigate in what way preliminary IHRF differs from the current Swedish levelling-based realisation of the European Vertical Reference System, RH 2000. The two different quasigeoid models that we consider best over Sweden at the present time are used to compute the preliminary IHRS realisations in the study. The realisations are compared to each other and to RH 2000. It is shown that a very significant part of the difference to RH 2000 is due to the different postglacial land uplift epochs, permanent tide concepts, and zero levels. The standard deviation for the difference between one of the preliminary national IHRS realisations and RH 2000 is reduced from 75.5 to 19.2 mm after correction of the postglacial land uplift and permanent tide effects. The corresponding mean differences are –208.5 and –454.7 mm, respectively. The magnitude of the mean difference thus increases when the corrections in question are applied.
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| 3. |
- Alizadeh Khameneh, Mohammad Amin, et al.
(författare)
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Optimisation of Lilla Edet Landslide GPS Monitoring Network
- 2015
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Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 5:1, s. 57-66
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Tidskriftsartikel (refereegranskat)abstract
- Since the year 2000, some periodic investigations have been performed in the Lilla Edet region to monitor and possibly determine the landslide of the area with the GPS measurements. The responsible consultant has conducted this project by setting up some stable stations for GPS receivers in the risky areas of Lilla Edet and measured the independent baselines amongst the stations according to their observation plan. Here, we optimise the existing surveying network and determine the optimal configuration of the observation plan based on different criteria. We aim to optimise the current network to become sensitive to detect 5 mm possible displacements in each net point. The network quality criteria of precision, reliability and cost are used as object functions to perform single-, bi- and multi-objective optimisation models. It has been shown in the results that the single-objective model of reliability, which is constrained to the precision, provides much higher precision than the defined criterion by preserving almost all of the observations. However, in this study, the multi-objective model can fulfil all the mentioned quality criteria of the network by 17% less measurements than the original observation plan, meaning 17% of saving time, cost and effort in the project.
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| 4. |
- Beeck, S. S., et al.
(författare)
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ROTI maps of Greenland using kriging
- 2021
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 11:1, s. 83-94
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Tidskriftsartikel (refereegranskat)abstract
- GNSS satellite signals are affected by the media when traversing Earth's atmosphere, and the performance of GNSS based positioning and navigation is correlated with these effects. In the ionosphere, the signals are affected by the number of electrons along the signal path which can be quantified by the total electron content. The focus of this article is scintillation effects caused by electrons in the Arctic ionosphere, and the rate of the total electron content index, the ROTI, is used as a measure of the scintillation. Data from permanent GNSS reference stations in Greenland is used to generate maps of the ROTI in Greenland, and the novelty of the work in this paper is the application of the ordinary kriging method as the basis for ROTI maps in the Arctic. Further, the choice of satellite constellations as well as the elevation mask used in the data analyses are analyzed and discussed. Also, the performance of using ordinary kriging for ROTI maps during times with both a low and a very high geomagnetic activity are discussed. The results show that ordinary kriging performs well during high geomagnetic activity, while during low activity the natural neighbor interpolation method is a better choice for the Arctic.
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| 5. |
- Eshagh, Mehdi, Professor, 1977-, et al.
(författare)
-
A case study on displacement analysis of Vasa warship
- 2018
-
Ingår i: Journal of Geodetic Science. - : DE GRUYTER POLAND SP ZOO. - 2081-9919 .- 2081-9943. ; 8:1, s. 43-54
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Tidskriftsartikel (refereegranskat)abstract
- Monitoring deformation of man-made structures is very important to prevent them from a risk of collapse and save lives. Such a process is also used for monitoring change in historical objects, which are deforming continuously with time. An example of this is the Vasa warship, which was under water for about 300 years. The ship was raised from the bottom of the sea and is kept in the Vasa museum in Stockholm. A geodetic network with points on the museum building and the ship's body has been established and measured for 12 years for monitoring the ship's deformation. The coordinate time series of each point on the ship and their uncertainties have been estimated epoch-wisely. In this paper, our goal is to statistically analyse the ship's hull movements. By fitting a quadratic polynomial to the coordinate time series of each point of the hull, its acceleration and velocity are estimated. In addition, their significance is tested by comparing them with their respective estimated errors after the fitting. Our numerical investigations show that the backside of the ship, having highest elevation and slope, has moved vertically faster than the other places by a velocity and an acceleration of about 2 mm/year and 0.1 mm/year(2), respectively and this part of the ship is the weakest with a higher risk of collapse. The central parts of the ship are more stable as the ship hull is almost vertical and closer to the floor. Generally, the hull is moving towards its port and downwards.
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| 6. |
- Eshagh, Mehdi, Professor, 1977-
(författare)
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An optimal design of GNSS interference localisation wireless security network based on time-difference of arrivals for the Arlanda international airport
- 2022
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Ingår i: Journal of Geodetic Science. - : De Gruyter Open. - 2081-9919 .- 2081-9943. ; 12:1, s. 154-164
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Tidskriftsartikel (refereegranskat)abstract
- Today, most of the aircrafts are navigated by global navigation satellite systems (GNSSs). Landing is a dangerous phase of a flight especially when an airport runway is not clearly seen from the aircrafts. In such cases, GNSSs are useful for a safe landing under the circumstances that healthy signals, free of any interference, reach to GNSSs receiver antennas mounted on the aircrafts. This shows the importance of establishing GNSS interference localisation security networks around airports. Designing a good configuration for the points with GNSS antennas at for receiving interference signals is important for a successful localisation of the interference device. Here, the time-difference of the arrivals of an interference signal to such points or anchor nodes (ANs), are used as observables, and a security network with four ANs is optimally designed along the runways of the Arlanda airport to reduce the dilution of precision (DOP) of the network. Our study showed that by such an optimisation, the maximum DOP value can reduce by 50% meaning a significant increase in the probability of a successful interference device localisation.
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| 7. |
- Eshagh, Mehdi, Professor, 1977-
(författare)
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Analysis of the gravity field, direct and inverse problems
- 2022
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Ingår i: Journal of Geodetic Science. - : De Gruyter Open. - 2081-9919 .- 2081-9943. ; 12:1, s. 244-245
-
Recension (refereegranskat)abstract
- This new book deals with, as its titles says, the analysis and process of gravity field of the Earth. The book is mathematically oriented, and the authors have explained how Mathematics is used for local analysis of the gravity field. The basic and required background knowledge, needed for understanding the book, are given in early chapters as well as appendices. They are used for explaining gravity field analysis from measurement surveys, corrections, and processes to direct and inverse problems in exploration Geophysics with interesting exercises, numerical and real examples.
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| 8. |
- Eshagh, Mehdi, Professor, 1977-, et al.
(författare)
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On quality of NKG2015 geoid model over the Nordic countries
- 2019
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Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 9:1, s. 97-110
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Tidskriftsartikel (refereegranskat)abstract
- The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system(GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.
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| 9. |
- Eshagh, Mehdi, 1977-
(författare)
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On Vening Meinesz-Moritz and flexural theories of isostasy and their comparison over Tibet Plateau
- 2016
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 6, s. 139-151
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Tidskriftsartikel (refereegranskat)abstract
- Gravity and topographic/bathymetric data are used for gravimetric modelling of Moho discontinuity by hydrostatic or flexural theories of the isostasy. Here, two hydrostatic models, based on the Vening Meinesz-Moritz (VMM) principle, and two based on the loading theories and flexural isostasy are compared over Tibet Plateau. It is shown that the Moho models generated based on the VMM theory and flexural isostasy have very good agreements if the mean compensation depth and the mean elastic thickness are selected properly. However, the model computed based on the flexural isostasy is smoother. A more rigorous flexural model, which considers the membrane stress and curvature of the lithosphere, is used to model the Moho surface over the study area. It is shown that the difference between the Moho models, derived by considering and ignoring these parameters, is not significant. By combination of the flexural and VMM hydrostatic models new mathematical formulae for crustal gravity anomalies are provided and it is shown that the crustal gravity anomalies produced by them are also equivalent.
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| 10. |
- Håkansson, Martin, 1982-
(författare)
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Satellite dependency of GNSS phase biases between receivers and between signals
-
Ingår i: Journal of Geodetic Science. - 2081-9919 .- 2081-9943.
-
Tidskriftsartikel (refereegranskat)abstract
- The existence of hardware induced phase biases might influence the accuracy in precise positioning if not handled properly. This is extra problematic if the biases are dependent on the satellite tracked, as these biases no longer will be common between the satellites and thus are not absorbed by the receiver clock term of the positioning solution. In this paper, we carried out two studies to investigate whether there exists a satellite dependency of the relative phase biases. Even though small in size, satellite dependent variations were found in both cases.In the first case, relative receiver phase biases were studied, while the satellite dependency of relative phase biases between signals (e.g. between carrier phases from C/A-code and P-code tracking) was investigated in the second case. The biases in the first case had a size of 0.8 mm between the satellites with the largest and smallest values, and additionally showed temporal variations that were consistent over time. The corresponding size of the biases second case was 3.5 mm, and no temporal variations were found.
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| 11. |
- Håkansson, Martin
(författare)
-
Satellite dependency of GNSS phase biases between receivers and between signals
- 2017
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 7:1, s. 130-140
-
Tidskriftsartikel (refereegranskat)abstract
- The existence of hardware induced phase biases might influence the accuracy in precise positioning if not handled properly. This is extra problematic if the biases are dependent on the satellite tracked, as these biases no longer will be common between the satellites, and thus will not be absorbed by the receiver clock term of the positioning solution. In this paper, we carried out two studies to investigate whether there exists a satellite dependency of the relative phase biases. Even though small in size, satellite dependent variations were found in both cases. In the first case, relative receiver phase biases were studied, while relative phase biases between signals (e.g. between carrier phases from C/A-code and P-code tracking) were investigated in the second case. The biases in the first case had a size of 0.8 mm between the satellites with the largest and smallest values, and additionally showed temporal variations that were consistent over time. The corresponding sizes of the biases second case were 2 mm and 3.5 mm for GPS L1 and L2 respectively, and no temporal variations were found.
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| 12. |
- Ivchenko, Nickolay, 1976-, et al.
(författare)
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Post-flight trajectory reconstruction of suborbital free-flyers using GPS raw data
- 2017
-
Ingår i: Journal of Geodetic Science. - : De Gruyter Open Ltd. - 2081-9919 .- 2081-9943. ; 7:1, s. 94-104
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes the reconstruction of postflight trajectories of suborbital free flying units by using logged GPS raw data. We took the reconstruction as a global least squares optimization problem, using both the pseudo-range and Doppler observables, and solved it by using the trust-region-reflective algorithm, which enabled navigational solutions of high accuracy. The code tracking was implemented with a large number of correlators and least squares curve fitting, in order to improve the precision of the code start times, while a more conventional phased lock loop was used for Doppler tracking. We proposed a weighting scheme to account for fast signal strength variation due to free-flier fast rotation, and a penalty for jerk to achieve a smooth solution. We applied these methods to flight data of two suborbital free flying units launched on REXUS 12 sounding rocket, reconstructing the trajectory, receiver clock error and wind up rates. The trajectory exhibits a parabola with the apogee around 80 km, and the velocity profile shows the details of payloadwobbling. The wind up rates obtained match the measurements from onboard angular rate sensors.
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| 13. |
- Jakobsen, Jakob, et al.
(författare)
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Simulation of GNSS reflected signals and estimation of position accuracy in GNSS-challenged environment
- 2015
-
Ingår i: Journal of Geodetic Science. - : De Gruyter Open. - 2081-9919 .- 2081-9943. ; 5:1, s. 47-56
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Tidskriftsartikel (refereegranskat)abstract
- The paper describes the development and testing of a simulation tool, called QualiSIM. The tool estimates GNSS-based position accuracy based on a simulation of the environment surrounding the GNSS antenna, with a special focus on city-scape environments with large amounts of signal reflections from non-line-of-sight satellites. The signal reflections are implemented using the extended geometric path length of the signal path caused by reflections from the surrounding buildings. Based on real GPS satellite positions, simulated Galileo satellite positions, models of atmospheric effect on the satellite signals, designs of representative environments e.g. urban and rural scenarios, and a method to simulate reflection of satellite signals within the environment we are able to estimate the position accuracy given several prerequisites as described in the paper. The result is a modelling of the signal path from satellite to receiver, the satellite availability, the extended pseudoranges caused by signal reflection, and an estimate of the position accuracy based on a least squares adjustment of the extended pseudoranges. The paper describes the models and algorithms used and a verification test where the results of QualiSIM are compared with results from collection of real GPS data in an environment with much signal reflection.
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| 14. |
- Jansson, Patric, 1965-, et al.
(författare)
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The effect of correlation on uncertainty estimates – with GPS examples
- 2013
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter. - 2081-9919 .- 2081-9943. ; 3:2, s. 111-120
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Tidskriftsartikel (refereegranskat)abstract
- This article deals with the effect of correlation on the estimates of measurement uncertainty, with some focus on Global Positioning Satellite (GPS) time series analysis. Analytical derivations and Monte Carlo simulations form the theoretical basis, which shows that uncompensated correlation produces unrealistic uncertainty estimates. Tools for handling correlation in connection with estimation of uncertainty, construction of confidence intervals, hypothesis testing, design of measurement strategies, and development of tolerances are outlined and demonstrated. The GPS observation time series used in the article has a short to medium range correlation, and can therefore be handled with the presented tools - based on a simple Location-model and stationary stochastic processes.
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| 15. |
- Shirazian, Masoud
(författare)
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Incorporation of the GPS satellite ephemeris covariance matrix into the precise point positioning
- 2013
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 3:3, s. 143-150
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Tidskriftsartikel (refereegranskat)abstract
- In GPS positioning, usually the satellite ephemeris are fixed in the observation equations using broadcast or published values. Therefore, to have a realistic covariance matrix for the observations one must incorporate a well-defined covariance matrix of the satellite ephemeris into the observations covariance matrix. Contributions so far have discussed only the variance and covariance of the observations. Precise Point Positioning (PPP) is a technique aimed at processing of measurements from a single (stand-alone) GPS receiver to compute high-accurate position. In this paper, the covariance matrix of the satellite ephemeris and its impact on the position estimates through the PPP are discussed.
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| 16. |
- Sjoberg, Lars E.
(författare)
-
On the geoid and orthometric height vs. quasigeoid and normal height
- 2018
-
Ingår i: Journal of Geodetic Science. - : SCIENDO. - 2081-9919 .- 2081-9943. ; 8:1, s. 115-120
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Tidskriftsartikel (refereegranskat)abstract
- The geoid, but not the quasigeoid, is an equipotential surface in the Earth's gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid, while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth's topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth's surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain, which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling.
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| 17. |
- Sjoberg, Lars E., et al.
(författare)
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The zero gravity curve and surface and radii for geostationary and geosynchronous satellite orbits
- 2017
-
Ingår i: Journal of Geodetic Science. - : De Gruyter Open. - 2081-9919 .- 2081-9943. ; 7:1, s. 43-50
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Tidskriftsartikel (refereegranskat)abstract
- A geosynchronous satellite orbits the Earth along a constant longitude. A special case is the geostationary satellite that is located at a constant position above the equator. The ideal position of a geostationary satellite is at the level of zero gravity, i.e. at the geocentric radius where the gravitational force of the Earth equals the centrifugal force. These forces must be compensated for several perturbing forces, in particular for the lunisolar tides. Considering that the gravity field of the Earth varies not only radially but also laterally, this study focuses on the variations of zero gravity not only on the equator (for geostationary satellites) but also for various latitudes. It is found that the radius of a geostationary satellite deviates from its mean value of 42164.2 km only within +/- 2 m, mainly due to the spherical harmonic coefficient J(22), which is related with the equatorial flattening of the Earth. Away from the equator the zero gravity surface deviates from the ideal radius of a geosynchronous satellite, and more so for higher latitudes. While the radius of the former surface increases towards infinity towards the poles, the latter decreases about 520 m from the equator to the pole. Tidal effects vary these radii within +/- 2.3 km.
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| 18. |
- Sjöberg, Lars, 1947-
(författare)
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Arne Bjerhammar- a personal summary of his academic deeds
- 2021
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Ingår i: Journal of Geodetic Science. - : DE GRUYTER POLAND SP Z O O. - 2081-9919 .- 2081-9943. ; 11:1, s. 1-6
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Arne Bjerhammar is well known worldwide mainly for his research in physical geodesy but also for introducing a new matrix algebra with generalized inverses applied in geodetic adjustment. Less known are his developments in geodetic engineering and contributions to satellite and relativistic geodesy as well as studies on the relation between the Fennoscandia land uplift and the regional gravity low. Most likely part of his research has contributed to worldwide political relaxation during the cold war, which deed was honored by a certificate of achievement awarded by the Department of Research of the US army as well as the North Star Order by the King of Sweden. Arne Bjerhammar’s pioneer scientific production, in particular on a world geodetic system, towards what would become GPS, as well as relativistic geodesy, is still of great interest among the worldwide geodetic community, while the memories and spirit along his outstanding academic deeds have more or less fainted away from his home university (KTH) only a decade after he passed away.
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| 19. |
- Sjöberg, Lars E., et al.
(författare)
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A numerical study of the analytical downward continuation error in geoid computation by EGM08
- 2011
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Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 1:1, s. 2-8
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Tidskriftsartikel (refereegranskat)abstract
- Today the geoid can be conveniently determined by a set of high-degree spherical harmonics, such as EGM08 with a resolution of about 5'. However, such a series will be biased when applied to the continental geoid inside the topographic masses. This error we call the analytical downward continuation (DWC) error, which is closely related with the so-called topographic potential bias. However, while the former error is the result of both analytical continuation of the potential inside the topographic masses and truncation of a series, the latter is only the effect of analytical continuation.This study compares the two errors for EGM08, complete to degree 2160. The result shows that the topographic bias ranges from 0 at sea level to 5.15 m in the Himalayas region, while the DWC error ranges from -0.08 m in the Pacific to 5.30 m in the Himalayas. The zero-degree effects of the two are the same (5.3 cm), while the rms of the first degree errors are both 0.3 cm. For higher degrees the power of the topographic bias is slightly larger than that for the DWC error, and the corresponding global rms values reaches 25.6 and 25.3 cm, respectively, at nmax=2160. The largest difference (20.5 cm) was found in the Himalayas. In most cases the DWC error agrees fairly well with the topographic bias, but there is a significant difference in high mountains. The global rms difference of the two errors clearly indicates that the two series diverge, a problem most likely related with the DWC error.
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| 20. |
- Sjöberg, Lars E., et al.
(författare)
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A numerical test of the topographic bias
- 2018
-
Ingår i: Journal of Geodetic Science. - : DE GRUYTER POLAND SP ZOO. - 2081-9919 .- 2081-9943. ; 8:1, s. 14-17
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Tidskriftsartikel (refereegranskat)abstract
- In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjoberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre).
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| 21. |
- Sjöberg, Lars E.
(författare)
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Closed-form and iterative weighted least squares solutions of Helmert transformation parameters
- 2013
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 3:1, s. 7-11
-
Tidskriftsartikel (refereegranskat)abstract
- The Helmert transformation is the most common transformation between different geodetic systems. In 2-D, in contrast to higher dimensions, it is a well-known procedure how to determine the 4 transformation parameters in a closed form. Here we derive the closed-form weighted least squares solution in m-dimensional space for an arbitrary number (≥ m) of coordinate set-ups in two related systems. The solution employs singular value decomposition (SVD) for the rotation matrix, while the translation vector and scale parameters are obtained in simpler ways. To avoid the SVD routine, we also present an iterative approach to solve for the rotation matrix. The paper is completed with a test procedure for detecting outlying coordinate pairs.
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| 22. |
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| 23. |
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| 24. |
- Sjöberg, Lars Erik, 1947-
(författare)
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Local Least Squares Spectral Filtering and Combination by Harmonic Functions on the Sphere
- 2011
-
Ingår i: Journal of Geodetic Science. - Poland : Versita. - 2081-9943 .- 2081-9919. ; 1:4, s. 355-360
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Tidskriftsartikel (refereegranskat)abstract
- Least squares spectral combination is a well-known technique in physical geodesy. The established technique either suffers from the assumption of no correlations of errors between degrees or from a global optimisation of the variance or mean square error of the estimator. Today Earth gravitational models are available together with their full covariance matrices to rather high degrees, extra information that should be properly taken care of. Here we derive the local least squares spectral filter for a stochastic function on the sphere based on the spectral representation of the observable and its error covariance matrix. Second, the spectral combination of two erroneous harmonic series is derived based on their full covariance matrices. In both cases the transition from spectral representation of an estimator to an integral representation is demonstrated. Practical examples are given. Taking advantage of the full covariance matrices in the spectral combination implies a huge computational burden in determining the least squares filters and combinations for high-degree spherical harmonic series. A reasonable compromise between accuracy of estimator and workload could be to consider only one weight parameter/degree, yielding the optimum filtering and combination of Laplace series.
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| 25. |
- Sjöberg, Lars E.
(författare)
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New solutions for the geoid potential W0 and the Mean Earth Ellipsoid dimensions
- 2013
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 3:4, s. 258-265
-
Tidskriftsartikel (refereegranskat)abstract
- Earth Gravitational Models (EGMs) describe the Earth’s gravity field including the geoid, except for its zero-degree harmonic, which is a scaling parameter that needs a known geometric distance for its calibration. Today this scale can be provided by the absolute geoid height as estimated from satellite altimetry at sea. On the contrary, the above technique cannot be used to determine the geometric parameters of the Mean Earth Ellipsoidal (MEE), as this problem needs global data of both satellite altimetry and gravimetric geoid models, and the standard technique used today leads to a bias for the unknown zero-degree harmonic of the gravimetric geoid height model. Here we present a new method that eliminates this problem and simultaneously determines the potential of the geoid (W0) and the MEE axes. As the resulting equations are non-linear, the linearized observation equations are also presented.
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| 26. |
- Sjöberg, Lars Erik, 1947-
(författare)
-
On the Best Quadratic Minimum Bias Non-Negative Estimator of a Two-Variance Component Model
- 2011
-
Ingår i: Journal of Geodetic Science. - Poland : Versita. - 2081-9943 .- 2081-9919. ; 1:3, s. 280-285
-
Tidskriftsartikel (refereegranskat)abstract
- Variance components (VCs) in linear adjustment models are usually successfully computed by unbiased estimators. However, for many unbiased VC techniques estimated variance components might be negative, a result that cannot be tolerated by the user. This is, for example, the case with the simple additive VC model aσ2/1 + bσ2/2 with known coefficients a and b, where either of the unbiasedly estimated variance components σ2/1 + σ2/2 may frequently come out negative. This fact calls for so-called non-negative VC estimators. Here the Best Quadratic Minimum Bias Non-negative Estimator (BQMBNE) of a two-variance component model is derived. A special case with independent observations is explicitly presented.
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| 27. |
- Sjöberg, Lars Erik, 1947-
(författare)
-
On the Definition and Realization of a Global Vertical Datum
- 2011
-
Ingår i: Journal of Geodetic Science. - Poland : Versita. - 2081-9943 .- 2081-9919. ; 1:2, s. 154-157
-
Tidskriftsartikel (refereegranskat)abstract
- A Global Vertical Datum (GVD) is naturally defined by the geoid, and there is a well-established consensus to adopt Gauss-Bessel-Listing's definition of the geoid (i.e. as being the level surface of the Earth's gravity field that best fits the undisturbed sea level). The main problem in defining the geoid is therefore to fix its constant geopotential (W00). Nevertheless, this definition can be interpreted as to fit either the geopotential of sea surface to a constant (W0), or to minimize the height of sea level with respect to the geoid. Although the two interpretations lead to apparently different solutions, we show that they are practically the same. To improve the estimation of W0, we propose to weight the included data according to their a priori error estimates. Finally we discuss the use of GNSS/levelling data for vertical datum connections, concluding that such data, although indispensable for regional vertical datum connections, in combination with satellite altimetry over the oceans are practically useless for determining the GVD. Also, such a joint adjustment of the GVD and regional vertical datum biases yields inferior local connections vs. a separate adjustment with fixed GVD.
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| 28. |
- Sjöberg, Lars E.
(författare)
-
On the topographic bias and density distribution in modelling the geoid and orthometric heights
- 2018
-
Ingår i: Journal of Geodetic Science. - : DE GRUYTER POLAND SP ZOO. - 2081-9919 .- 2081-9943. ; 8:1, s. 30-33
-
Tidskriftsartikel (refereegranskat)abstract
- It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators.
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| 29. |
- Sjöberg, Lars E.
(författare)
-
On the topographic effects by Stokes’ formula
- 2014
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 4:1, s. 130-135
-
Tidskriftsartikel (refereegranskat)abstract
- Traditional gravimetric geoid determination relies on Stokes’ formula with removal and restoration of the topographic effects. It is shown that this solution is in error of the order of the quasigeoid-to-geoid difference, which is mainly due to incomplete downward continuation (dwc) of gravity from the Earth’s surface to the geoid. A slightly improved estimator, based on the surface Bouguer gravity anomaly, is also biased due to the imperfect harmonic dwc the Bouguer anomaly. Only the third estimator,which uses the (harmonic) surface no-topography gravity anomaly, is consistent with the boundary condition and Stokes’ formula, providing a theoretically correct geoid height. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the “secondary indirect topographic effect”, which is a necessary correction in removing all topographic signals.
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| 30. |
- Sjöberg, Lars E.
(författare)
-
Quality Estimates in Geoid Computation by EGM08
- 2011
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 1:4, s. 361-366
-
Tidskriftsartikel (refereegranskat)abstract
- The high-degree Earth Gravitational Model EGM08 allows for geoid determination with a resolution of the order of 5'. Using this model for estimating the quasigeoid height, we estimate the global root mean square (rms) commission error to 5 and 11 cm, based on the assumptions that terrestrial gravity contributes to the model with an rms standard error of 5 mGal and correlation length 0:01° and 0:1°, respectively. The omission error is estimated to—0:7Δg [mm], where Δg is the regional mean gravity anomaly in units of mGal.In case of geoid determination by EGM08, the topographic bias must also be considered. This is because the Earth's gravitational potential, in contrast to its spherical harmonic representation by EGM08, is not a harmonic function at the geoid inside the topography. If a correction is applied for the bias, the main uncertainty that remains is that from the uncertainty in the topographic density, which will still contribute to the overall geoid error.
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| 31. |
- Sjöberg, Lars E.
(författare)
-
Solutions to Linear Inverse Problems on the Sphere by Tikhonov Regularization, Wiener filtering and Spectral Smoothing and Combination — A Comparison
- 2012
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 2:1, s. 31-37
-
Tidskriftsartikel (refereegranskat)abstract
- Solutions to linear inverse problems on the sphere, common in geodesy and geophysics, are compared for Tikhonov's method of regularization, Wiener filtering and spectral smoothing and combination as well as harmonic analysis. It is concluded that Wiener and spectral smoothing, although based on different assumptions and target functions, yield the same estimator. Also, provided that the extra information on the signal and error degree variances is available, the standard Tikhonov method is inferior to the other methods, which, in contrast to Tikhonov's approach, match the spectral errors and signals in an optimum way. We show that the corresponding Tikhonov matrix for optimum regularization can only be determined approximately. Moreover, as Tikhonov's method solves an integral equation, it is less computationally efficient than the other methods, which use forward integration. Also harmonic analysis uses direct integration and is not hampered, as previous methods, with spectral leakage. Spectral combination, in addition to filtering, has the advantage of combining different data sets by least squares spectral weighting.
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| 32. |
- Sjöberg, Lars E.
(författare)
-
Solutions to the direct and inverse navigation problems on the great ellipse
- 2012
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 2:3, s. 200-205
-
Tidskriftsartikel (refereegranskat)abstract
- The Great Ellipse (GE) is the curve of intersection between the surface and a plane through the center of an ellipsoid. For arcs within a few thousands of kilometres it agrees within a few metres with the geodesic. As the direct and indirect navigation problems for the GE can be solved almost entirely by closed formulas (in contrast to the corresponding geodetic problems of the geodesic), navigation on the GE is mostly preferred. Here we take advantage of the Clairaut constant on the GE in solving the navigation problems.
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| 33. |
- Sjöberg, Lars E.
(författare)
-
Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration
- 2012
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 2:3, s. 162-171
-
Tidskriftsartikel (refereegranskat)abstract
- We derive computational formulas for determining the Clairaut constant, i.e. the cosine of the maximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of revolution. In all cases the Clairaut constant is unique. The inverse geodetic problem on the ellipsoid is to determine the geodesic arc between and the azimuths of the arc at the given points. We present the solution for the fixed Clairaut constant. If the given points are not(nearly) antipodal, each azimuth and location of the geodesic is unique, while for the fixed points in the ”antipodal region”, roughly within 36”.2 from the antipode, there are two geodesics mirrored in the equator and with complementary azimuths at each point. In the special case with the given points located at the poles of the ellipsoid, all meridians are geodesics. The special role played by the Clairaut constant and the numerical integration make this method different from others available in the literature.
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| 34. |
- Sjöberg, Lars E.
(författare)
-
The geoid or quasigeoid – which reference surface should be preferred for a national height system?
- 2013
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 3:2, s. 103-109
-
Tidskriftsartikel (refereegranskat)abstract
- Most European states use M. S. Molodensky’s concept of normal heights for their height systems with a quasigeoid model as the reference surface, while the rest of the world rely on orthometric heights with the geoid as the zero-level. Considering the advances in data caption and theory for geoid and quasigeoid determinations, the question is which system is the best choice for the future. It is reasonable to assume that the latter concept, in contrast to the former, will always suffer from some uncertainty in the topographic density distribution, while Molodensky’s approach to quasigeoid determination has a convergence problem. On the contrary, geoid and quasigeoid models computed by analytical continuation (e.g., rcr technique or KTH method) have no integration problem, and the quasigeoid can always be determined at least as accurate as the geoid. As the numerical instability of the analytical continuation is better controlled in the KTH method vs. the rcr method, we propose that any future height system be based on normal heights with a quasigeoid model computed similar to or directly based on the KTH method (Least squares modification of Stokes formula with additive corrections).
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| 35. |
- Sjöberg, Lars E.
(författare)
-
The topographic bias in gravimetric geoid determination revisited
- 2019
-
Ingår i: Journal of Geodetic Science. - : Sciendo. - 2081-9919 .- 2081-9943. ; 9:1, s. 59-64
-
Tidskriftsartikel (refereegranskat)abstract
- The topographic potential bias at geoid level is the error of the analytically continued geopotential from or above the Earth's surface to the geoid. We show that the topographic potential can be expressed as the sum of two Bouguer shell components, where the density distribution of one is spherical symmetric and the other is harmonic at any point along the normal to a sphere through the computation point. As a harmonic potential does not affect the bias, the resulting topographic bias is that of the first component, i.e. the spherical symmetric Bouguer shell. This implies that the so-called terrain potential is not likely to contribute significantly to the bias. We present three examples of the geoid bias for different topographic density distributions.
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| 36. |
- Sjöberg, Lars, 1947-, et al.
(författare)
-
Estimation of Crustal Motions at the Permanent GPS Station SVEA, Antarctica from 2005 to 2009
- 2011
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 1:3, s. 215-220
-
Tidskriftsartikel (refereegranskat)abstract
- Estimation of Crustal Motions at the Permanent GPS Station SVEA, Antarctica from 2005 to 2009: In November 2004 the permanent GPS station SVEA (Latitude: 74°34' 34"S, Longitude: 11° 13' 31"W, Height 1261.2 m) was installed in Drottning Maud's Land, Antarctica. The main aim of this paper is to evaluate the collected data for on-going crustal motions. About 40% ("3-days weekly") of the continuous four years GPS data from 2005 to 2009 was processed together with the simultaneous data of five IGS reference stations using Bernese GPS software V 5.0. A linear regression analysis was used to estimate the linear motion of the station, yielding the estimated velocities' components (in mm/year) of 6.6± 0.4 North, -1.4 ± 0.2 East and 4.4 ± 0.6 Up. Although all components appear highly significant, the abnormal development of the E-W component needs further analyses. Post-glacial rebound is estimated to contribute only to 0.2-0.3 mm/yr (James and Ivin, 1998) of the vertical uplift rate, suggesting that the observed vertical motion mainly has another origin, possibly tectonic. The crustal motion results should be regarded as preliminary, and they need both further data and analyses to be confirmed. It is also concluded that the remote continuously running GPS station SVEA works well after more than five years of operation with only annual checks and data retrieval in the harsh environment of Antarctica.
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| 37. |
- Sjöberg, Lars, 1947-
(författare)
-
Geoid model validation and topographic bias
- 2022
-
Ingår i: Journal of Geodetic Science. - : De Gruyter Open. - 2081-9919 .- 2081-9943. ; 12:1, s. 38-41
-
Tidskriftsartikel (refereegranskat)abstract
- Recently a number of geoid campaigns were performed to verify different types of geoid and quasigeoid modeling techniques. Typically, GNSS-leveling was employed as an independent method, but in some cases zenith camera astronomic deflection data were also used in astrogeodetic determinations of the geoid and/or quasigeoid. However, due to the uncertainty in the topographic density distribution data (and thereby in orthometric heights), we conclude that neither GNSS-leveling nor astrogeodetic techniques can reliably verify differences between gravimetric geoid models at several centimeter levels in rough mountainous regions. This is because much the same topographic data are used both in the gravimetric geoid models and in their verifications by geometric and/or astrogeodetic geoid models. On the contrary, this is not a problem in verifying gravimetric quasigeoid models, as they are independent of the topographic density distribution, and so is the related normal height used in GNSS-leveling.
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| 38. |
- Sjöberg, Lars, 1947-
(författare)
-
On the gravity and geoid effects of glacial isostatic adjustment in Fennoscandia : a short note
- 2015
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter. - 2081-9919 .- 2081-9943. ; 5, s. 189-191
-
Tidskriftsartikel (refereegranskat)abstract
- Many geoscientists argue that there is a gravity low of 10-30 mGal in Fennoscandia as a remaining fingerprint of the last ice age and load, both vanished about 10 kyr ago. However, the extraction of the gravity signal related with Glacial Isostatic Adjustment (GIA) is complicated by the fact that the total gravity field is caused by many significant density distributions in the Earth. Here we recall a methodology originating with A. Bjerhammar 35 years ago, that emphasizes that the present land uplift phenomenon mainly occurs in the region thatwas covered by the ice cap, and it is highly correlated with the spectral window of degrees 10-22 of the global gravity field, whose lower limit fairly well corresponds to the wavelength that agrees with the size of the region. This implies that, although in principle the GIA is a global phenomenon, the geoid and gravity lows as well as the land upheaval in Fennoscandia are typically regional phenomena that cannot be seen in a global correlation study as it is blurred by many irrelevant gravity signals. It is suggested that a regional multi-regression analysis with a band-limited spectral gravity signal as the observable, a method tested already 2 decades ago, can absorb possible significant disturbing signals, e.g. from topographic and crustal depth variations, and thereby recover the GIA signal.
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| 39. |
- Sjöberg, Lars, 1947-
(författare)
-
Rigorous geoid-from-quasigeoid correction using gravity disturbances
- 2015
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 5:1, s. 115-118
-
Tidskriftsartikel (refereegranskat)abstract
- We present rigorous solutions for the geoid-fromquasigeoid correction (GQC) using Taylor expansions of surface gravity disturbances along the vertical from the Earth's surface to the geoid. One solution takes advantage of the topographic potential bias at the geoid, which can be expressed by a simple formula. This implies that the accurate GQC does not need a terrain correction.
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| 40. |
- Sjöberg, Lars, 1947-
(författare)
-
The development of physical geodesy during 1984-2014 : - a personal review
- 2015
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter. - 2081-9919 .- 2081-9943. ; 5, s. 1-8
-
Tidskriftsartikel (refereegranskat)abstract
- This article is a personal review of the development of physical geodesy during 1984-2014. The period is characterized by an intensive advance in both data and theory to meet the growing technical demands in GPS/GNSS applications and scientific needs in geoscience. As a result,many parts of theworld are nowmapped with a 1cmdetailed geoid model, and the global long- to mediumwavelengths of the gravity field and geoid are homogeneously determined to 1 mGal and 1 cm by satellite-only dedicated satellite gravity missions. The future can expect to see even higher demands for accuracy and reliability to satisfy the specifications for a pure geoid model based vertical datum.
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| 41. |
- Sjöberg, Lars, 1947-
(författare)
-
The three Swedish kings of geodesy : Speech at the NKG General Assembly dinner in 2022
- 2023
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 13:1
-
Tidskriftsartikel (refereegranskat)abstract
- During the 1950s-1970s, there were three geodesy professors in Sweden. Before and after that period the only such position was at KTH in Stockholm. One in the triple proposed the creation of the Nordic Geodetic Commission, which was realized in 1953 and still exists in much the same form as originally proposed.
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| 42. |
- Sjöberg, Lars, 1947-
(författare)
-
The topographic bias in Stokes’ formula vs. the error of analytical continuation by an Earth Gravitational Model- are they the same?
- 2015
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter. - 2081-9919 .- 2081-9943. ; 5, s. 171-179
-
Tidskriftsartikel (refereegranskat)abstract
- Geoid determination below the topographic surface in continental areas using analytical continuation of gravity anomaly and/or an external type of solid spherical harmonics determined by an Earth GravitationalModel (EGM) inevitably leads to a topographic bias, as the true disturbing potential at the geoid is not harmonic in contrast to its estimates. We show that this bias differs for the geoid heights represented by Stokes’ formula, an EGMand for the modified Stokes formula. The differences are due to the fact that the EGM suffers from truncation and divergence errors in addition to the topographic bias in Stokes’ original formula.
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| 43. |
- Ssengendo, Ronald, et al.
(författare)
-
The Uganda Gravimetric Geoid Model computed by the KTH Method
- 2015
-
Ingår i: Journal of Geodetic Science. - : De Gruyter Open. - 2081-9919 .- 2081-9943. ; 5:2, s. 35-46
-
Tidskriftsartikel (refereegranskat)abstract
- For many developing countries such as Uganda, precise gravimetric geoid determination is hindered by the low quantity and quality of the terrestrial gravity data. With only one gravity data point per 65 km2, gravimetric geoid determination in Uganda appears an impossible task. However, recent advances in geoid modelling techniques coupled with the gravity-field anomalies from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission have opened new avenues for geoid determination especially for areas with sparse terrestrial gravity. The present study therefore investigates the computation of a gravimetric geoid model over Uganda (UGG2014) using the Least Squares Modification of Stokes formula with additive corrections. UGG2014 was derived from sparse terrestrial gravity data from the International Gravimetric Bureau, the 3 arc second SRTM ver4.1 Digital Elevation Model from CGIAR-CSI and the GOCE-only global geopotential model GO_CONS_GCF_2_TIM_R5. To compensate for the missing gravity data in the target area, we used the surface gravity anomalies extracted from the World Gravity Map 2012. Using 10 Global Navigation Satellite System (GNSS)/levelling data points distributed over Uganda, the RMS fit of the gravimetric geoid model before and after a 4-parameter fit is 11 cm and 7 cm respectively. These results show that UGG2014 agrees considerably better with GNSS/levelling than any other recent regional/global gravimetric geoid model. The results also emphasize the significant contribution of the GOCE satellite mission to the gravity field recovery, especially for areas with very limited terrestrial gravity data. With an RMS of 7 cm, UGG2014 is a significant step forward in the modelling of a “1-cm geoid” over Uganda despite the poor quality and quantity of the terrestrial gravity data used for its computation.
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| 44. |
- Yildiz, Hasan, et al.
(författare)
-
Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test area
- 2012
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9919 .- 2081-9943. ; 2:1, s. 53-64
-
Tidskriftsartikel (refereegranskat)abstract
- The remove-compute-restore (RCR) technique for regional geoid determination implies that both topography and low-degree global geopotential model signals are removed before computation and restored after Stokes' integration or Least Squares Collocation (LSC) solution. The Least Squares Modification of Stokes' Formula (LSMS) technique not requiring gravity reductions is implemented here with a Residual Terrain Modelling based interpolation of gravity data. The 2-D Spherical Fast Fourier Transform (FFT) and the LSC methods applying the RCR technique and the LSMS method are tested over the Auvergne test area. All methods showed a reasonable agreement with GPS-levelling data, in the order of a 3-3.5 cm in the central region having relatively smooth topography, which is consistent with the accuracies of GPS and levelling. When a 1-parameter fit is used, the FFT method using kernel modification performs best with 3.0 cm r.m.s difference with GPS-levelling while the LSMS method gives the best agreement with GPS-levelling with 2.4 cm r.m.s after a 4-parameter fit is used. However, the quasi-geoid models derived using two techniques differed from each other up to 33 cm in the high mountains near the Alps. Comparison of quasi-geoid models with EGM2008 showed that the LSMS method agreed best in term of r.m.s.
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| 45. |
- Yuan, Yunxia, et al.
(författare)
-
Post-flight trajectory reconstruction of suborbital free-flyers using GPS raw data
-
Ingår i: Journal of Geodetic Science. - 2081-9919 .- 2081-9943.
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- This paper describes the reconstruction of postflight trajectories of suborbital free flying units by using logged GPS raw data. We took the reconstruction as a global least squares optimization problem, using both the pseudo-range and Doppler observables, and solved it by using the trust-region-reflective algorithm, which enabled navigational solutions of high accuracy. The code tracking was implemented with a large number of correlators and least squares curve fitting, in order to improve the precision of the code start times, while a more conventional phased lock loop was used for Doppler tracking.We proposed a weighting scheme to account for fast signal strength variation due to free-flier fast rotation, and a penalty for jerk to achieve a smooth solution. We applied these methods to flight data of two suborbital free flying units launched on REXUS 12 sounding rocket, reconstructing the trajectory, receiver clock error and wind up rates. The trajectory exhibits a parabola with the apogee around 80 km, and the velocity profile shows the details of payload wobbling. The wind up rates obtained match the measurements from onboard angular rate sensors.
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| 46. |
- Kareinen, Niko Petteri, 1986, et al.
(författare)
-
Experience from geodetic very long baseline interferometry observations at Onsala using a digital backend
- 2015
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9943. ; 5:1, s. 26-34
-
Tidskriftsartikel (refereegranskat)abstract
- The Onsala Space Observatory has installed amodern digital backend for geodetic and astronomicalVery Long Baseline Interferometry (VLBI). This systemconsists of a Digital Base-Band Converter (DBBC) and aMark 5B+ recorder. From 2011 until late 2014 this newsystem was run for geodetic VLBI observations in paral-lel with the old system consisting of a Mark 4 rack andMark 5A recording system. Several of these observed ses-sions were correlated at the correlator in Bonn includingboth data sets. We present results from the analysis andcomparison of these sessions. Both the original observeddelays and corresponding geodetic parameters are com-pared. No significant differences are detected, for eitherthe raw observations or for the geodetic parameters. Thisshows that the digital backend can be used operationallyfor geodetic VLBI observations.
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| 47. |
- Timmen, Ludger, et al.
(författare)
-
Observed secular gravity trend at Onsala station with the FG5 gravimeter from Hannover.
- 2015
-
Ingår i: Journal of Geodetic Science. - : Walter de Gruyter GmbH. - 2081-9943. ; 5:1, s. 18-25
-
Tidskriftsartikel (refereegranskat)abstract
- Annual absolute gravity measurements with aFG5 instrument were performed in Onsala Space Observatoryby the Institute of Geodesy of the Leibniz UniversitätHannover from 2003 to 2011 and have been continued withthe upgraded meter FG5X in 2014. Lantmäteriet, Gävle,with their FG5 absolute gravimeter have visited Onsalasince 2007. Because small systematic errors may be inherentin each absolute gravimeter, their measuring level anda resulting bias (offset) between the instruments must becontrolled over time by means of inter-comparison. From2007 to 2014, 8 direct comparisons took place well distributedover the time span. A complete re-processing ofthe absolute gravity observations with the Hannover instrumenthas been conducted to improve the reduction ofunwanted gravity effects. A new tidal model is based oncontinuous time series recorded with the GWR superconductinggravimeter at Onsala since 2009. The loading effectof the Kattegat is described with a varying sea bottompressure (water and air mass load) and has been validated with the continuous gravity measurements. For theland uplift,which is a result of the still ongoing glacial isostaticadjustment in Fennoscandia, a secular gravity trendof −0.22 μGal/yr was obtained with a standard deviationof 0.17 μGal/yr. That indicates a slight uplift but is still notsignificantly different from zero.
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