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  • 1.
    Abdollahzadeh, Makan
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Najafi-Alamdari, Mehdi
    Geodesy, KNToosi Uni. Tech..
    Application of Molodensky's Method for Precise Determination of Geoid in Iran2011In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 1, no 3, p. 259-270Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Alizadeh Khameneh, Mohammad Amin
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Eshagh, Mehdi
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning. University West, Division of Surveying Engineering.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Optimisation of Lilla Edet Landslide GPS Monitoring Network2015In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 5, no 1, p. 57-66Article in journal (Refereed)
    Abstract [en]

    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.

  • 3.
    Eshagh, Mehdi
    et al.
    Univ West, Dept Engn Sci, Trollhattan, Sweden..
    Johansson, Filippa
    Univ West, Dept Engn Sci, Trollhattan, Sweden..
    Karlsson, Lenita
    Univ West, Dept Engn Sci, Trollhattan, Sweden..
    Horemuz, Milan
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning.
    A case study on displacement analysis of Vasa warship2018In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 8, no 1, p. 43-54Article in journal (Refereed)
    Abstract [en]

    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.

  • 4.
    Håkansson, Martin
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning. Lantmäteriet.
    Satellite dependency of GNSS phase biases between receivers and between signalsIn: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943Article in journal (Refereed)
    Abstract [en]

    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. 

  • 5. Jakobsen, Jakob
    et al.
    Jensen, Anna B. O.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Nielsen, Allan Aasbjerg
    Simulation of GNSS reflected signals and estimation of position accuracy in GNSS-challenged environment2015In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 5, no 1, p. 47-56Article in journal (Refereed)
    Abstract [en]

    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.

  • 6.
    Jansson, Patric
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Persson, Clas-Göran
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    The effect of correlation on uncertainty estimates – with GPS examples2013In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 3, no 2, p. 111-120Article in journal (Refereed)
    Abstract [en]

    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.

  • 7.
    Sjoberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning.
    On the geoid and orthometric height vs. quasigeoid and normal height2018In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 8, no 1, p. 115-120Article in journal (Refereed)
    Abstract [en]

    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.

  • 8.
    Sjoberg, Lars E.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Grafarend, E. W.
    Joud, Seyed Mehdi Shafiei
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    The zero gravity curve and surface and radii for geostationary and geosynchronous satellite orbits2017In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 7, no 1, p. 43-50Article in journal (Refereed)
    Abstract [en]

    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.

  • 9.
    Sjöberg, Lars
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    On the gravity and geoid effects of glacial isostatic adjustment in Fennoscandia: a short note2015In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 5, p. 189-191Article in journal (Refereed)
    Abstract [en]

    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.

  • 10.
    Sjöberg, Lars
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    The development of physical geodesy during 1984-2014: - a personal review2015In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 5, p. 1-8Article in journal (Refereed)
    Abstract [en]

    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.

  • 11.
    Sjöberg, Lars
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    The topographic bias in Stokes’ formula vs. the error of analytical continuation by an Earth Gravitational Model- are they the same?2015In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 5, p. 171-179Article in journal (Refereed)
    Abstract [en]

    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.

  • 12.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Closed-form and iterative weighted least squares solutions of Helmert transformation parameters2013In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 3, no 1, p. 7-11Article in journal (Refereed)
    Abstract [en]

    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. 

  • 13.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Comments to X. Li and Y. M. Wang (2011) Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications, JGS 1(2): 136-1422012In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 2, no 1, p. 136-142Article in journal (Refereed)
    Abstract [en]

    Li and Wang recently compared geoid determination by various gravimetric methods for modifying Stokes' formula vs. using GPS/levelling geoid heights as a reference model. Possible large systematic errors in the differences of gravimetric and GPS/levelling geoid models deteriorate the results and conclusions. Moreover, spectral combination, the only stochastic method in the study, was applied in an unrealistic way.

  • 14.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Erik W. Grafarend and Joseph L. Awange: Applications of Linear and Nonlinear Models – Fixed Effects, Random Effects, and Total Least Squares2013In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 3, no 1, p. 77-78Article, book review (Other academic)
  • 15.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    New solutions for the geoid potential W0 and the Mean Earth Ellipsoid dimensions2013In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 3, no 4, p. 258-265Article in journal (Refereed)
    Abstract [en]

    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. 

  • 16.
    Sjöberg, Lars E.
    KTH.
    On the topographic bias and density distribution in modelling the geoid and orthometric heights2018In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 8, no 1, p. 30-33Article in journal (Refereed)
    Abstract [en]

    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.

  • 17.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    On the topographic effects by Stokes’ formula2014In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 4, no 1, p. 130-135Article in journal (Refereed)
    Abstract [en]

    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. 

  • 18.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Quality Estimates in Geoid Computation by EGM082011In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 1, no 4, p. 361-366Article in journal (Refereed)
    Abstract [en]

    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.

  • 19.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Rigorous geoid-from-quasigeoid correction using gravity disturbances2015In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943Article in journal (Refereed)
  • 20.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Solutions to Linear Inverse Problems on the Sphere by Tikhonov Regularization, Wiener filtering and Spectral Smoothing and Combination — A Comparison2012In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 2, no 1, p. 31-37Article in journal (Refereed)
    Abstract [en]

    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.

  • 21.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Solutions to the direct and inverse navigation problems on the great ellipse2012In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 2, no 3, p. 200-205Article in journal (Refereed)
    Abstract [en]

    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.

  • 22.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration2012In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 2, no 3, p. 162-171Article in journal (Refereed)
    Abstract [en]

    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.

  • 23.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    The geoid or quasigeoid – which reference surface should be preferred for a national height system?2013In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 3, no 2, p. 103-109Article in journal (Refereed)
    Abstract [en]

    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).

  • 24.
    Sjöberg, Lars E.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    A numerical study of the analytical downward continuation error in geoid computation by EGM082011In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 1, no 1, p. 2-8Article in journal (Refereed)
    Abstract [en]

    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.

  • 25.
    Sjöberg, Lars E.
    et al.
    KTH.
    Joud, M. S. S.
    Div Geodesy & Satellite Positioning, Stockholm, Sweden..
    A numerical test of the topographic bias2018In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 8, no 1, p. 14-17Article in journal (Refereed)
    Abstract [en]

    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).

  • 26.
    Sjöberg, Lars
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Walyeldeen, Hassan Edres
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Horemuz, Milan
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Estimation of crustal motions at the permanent GPS station SVEA, Antarctica, from 2005 to 20092011In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 1, no 3Article in journal (Refereed)
    Abstract [en]

    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.

  • 27.
    Ssengendo, Ronald
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Sjöberg, Lars
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Gidudu, Anthony
    Makerere University.
    The Uganda Gravimetric Geoid Model computed by the KTH Method2015In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 5, no 2, p. 35-46Article in journal (Refereed)
    Abstract [en]

    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. 

  • 28. Yildiz, Hasan
    et al.
    Forsberg, Rene
    Ågren, Jonas
    Tscherning, J
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test area2012In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 2, no 1, p. 53-64Article in journal (Refereed)
    Abstract [en]

    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.

  • 29.
    Yuan, Yunxia
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Linden, Erik
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Ivchenko, Nickolay
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Post-flight trajectory reconstruction of suborbital free-flyers using GPS raw dataIn: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943Article in journal (Other academic)
    Abstract [en]

    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.

1 - 29 of 29
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