Showing papers in "Journal of Geodetic Science in 2014"

Precise orbit determination and point positioning using GPS, Glonass, Galileo and BeiDou

Abstract: State of the art Precise Point Positioning (PPP) is currently based on dual-frequency processing of GPS and Glonass navigation systems. The International GNSS Service (IGS) is routinely providing the most accurate or- bit and clock products for these constellations, allowing pointpositioningatcentimeter-levelaccuracy.Atthesame time, the GNSS landscape is evolving rapidly, with the deployment of new constellations, such as Galileo and BeiDou. The BeiDou constellation currently consists of 14 operational satellites, and the 4 Galileo In-Orbit Vali- dation (IOV) satellites are transmitting initial Galileo sig- nals. This paper focuses on the integration of Galileo and BeiDou in PPP, together with GPS and Glonass. Satellite orbits and clocks for all constellations are generated us- ing a network adjustment with observation data collected by the IGS Multi-GNSS Experiment (MGEX), as well as from Fugro proprietary reference station network. The or- bit processing strategy is described, and orbit accuracy for Galileo and BeiDou is assessed via orbit overlaps, for dif- ferent arc lengths. Kinematic post-processed multi-GNSS positioning results are presented. The benets of multi- constellation PPP are discussed in terms of enhanced availability and positioning accuracy.

Global Eustatic Sea-Level Variations for the Approximation of Geocenter Motion from Grace

Abstract: Abstract Global degree-1 coefficients are derived by means of the method by Swenson et al. (2008) from a model of ocean mass variability and RL05 GRACE monthly mean gravity fields. Since an ocean model consistent with the GRACE GSM fields is required to solely include eustatic sea-level variability which can be safely assumed to be globally homogeneous, it can be empirically derived from GRACE aswell, thereby allowing to approximate geocenter motion entirely out of the GRACE monthly mean gravity fields. Numerical experiments with a decade-long model time-series reveal that the methodology is generally robust both with respect to potential errors in the atmospheric part of AOD1B and assumptions on global degree-1 coefficients for the eustatic sea-level model. Good correspondence of the GRACE RL05-based geocenter estimates with independent results let us conclude that this approximate method for the geocenter motion is well suited to be used for oceanographic and hydrological applications of regional mass variability from GRACE,where otherwise an important part of the signal would be omitted.

On The Errors-In-Variables Model With Singular Dispersion Matrices

Abstract: Abstract While the Errors-In-Variables (EIV) Model has been treated as a special case of the nonlinear Gauss- Helmert Model (GHM) for more than a century, it was only in 1980 that Golub and Van Loan showed how the Total Least-Squares (TLS) solution can be obtained from a certain minimum eigenvalue problem, assuming a particular relationship between the diagonal dispersion matrices for the observations involved in both the data vector and the data matrix. More general, but always nonsingular, dispersion matrices to generate the “properly weighted” TLS solution were only recently introduced by Schaffrin and Wieser, Fang, and Mahboub, among others. Here, the case of singular dispersion matrices is investigated, and algorithms are presented under a rank condition that indicates the existence of a unique TLS solution, thereby adding a new method to the existing literature on TLS adjustment. In contrast to more general “measurement error models,” the restriction to the EIV-Model still allows the derivation of (nonlinear) closed formulas for the weighted TLS solution. The practicality will be evidenced by an example from geodetic science, namely the over-determined similarity transformation between different coordinate estimates for a set of identical points.

Optimal observational planning of local GPSnetworks: assessing an analytical method

Abstract: Abstract Precision, reliability and cost are the major criteria applied in optimization and design of geodetic networks. The terrestrial networks are being replaced quickly by permanent and campaign Global Positioning System (GPS) networks. These networks must be optimized using the same three criteria. In this article the optimization of the observational plan of local GPS networks (Second Order Design (SOD)) is considered using the precision criterion. This study is limited to the selection of optimal numbers and the best distribution of the non-trivial baselines throughout the network. This objective is accomplished based on the SOD solution through the analytical method in operational research by the means of quadratic programming algorithm. This presented method is tested on a real GPS network and appears to be a useful technique in terms of cost reduction in the field work by the provided observational plan and optimal distribution of the baselines throughout the network. Results indicate that weights of almost 36% of the baselines are negligiblewhen compared to the weights of the rest of the baselines; therefore, they could be eliminated fromthe observational plan, resulting in a 36% saving in the fieldwork cost.

On the topographic effects by Stokes' formula

Abstract: Traditional gravimetric geoid determination re- lies 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' for- mula, providing a theoretically correct geoid height. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the "sec- ondary indirect topographic effect", which is a necessary correction in removing all topographic signals.

Rapid static GNSS data processing using online services

Abstract: Abstract Recently, many organizations have begun providing online GNSS (Global Navigation Satellite System) data processing services. Currently, only one of these organizations i.e., OPUS (On-line Positioning Users Service) provides a rapid static data processing option. In case of static online data processing, the users are required to submit at least two hours of data to get reasonably precise results. To provide processing option with less than two hours of data, NGS (National Geodetic Survey) developed OPUS–RS for rapid static data processing so that usersmay submit as little as 15 minutes of dual frequency GNSS data. In this study, multiple observation sessions are conducted at the same locations to compare OPUS-RS generated coordinates among the different sessions to see whether separate values agree with each other. The results indicate that with OPUS-RS results the differences in horizontal coordinates agree with each other within 3.5 cm and vertical coordinates agree within 7.2 cm. For an independent check, OPUS-RS results are also compared against LGO(Leica Geo Office) produced Static results; this comparison yielded up to 4.5 cm variations among horizontal coordinate differences and variations among vertical coordinate differences are up to 11.4 cm.

Sensitivity of Goce Gradients on Greenland Mass Variation And Changes in Ice Topography

Abstract: Abstract The Gravity field and steady state Ocean Circulation Explorer (GOCE) maps variations in the gravity field by observing second order derivatives (gradients) of the Earth gravitational potential. Flying in the low altitude of 255 km and having a spatially dense data distribution of short wavelengths of the gravity field, GOCE may be used to enhance the time varying gravity signal coming fromthe GRACE satellites. The GOCE gradients may potentially be used for the determination of residual masses in local regions. This can be done using Least-Squares Collocation (LSC) or the Reduced Point Mass (RPM) method. In this study, different gravity field solutions are calculated by the use of RPM, LSC and GOCE gradients, respectively. Gravity field time series are created and presented for the six consecutive months of GOCE gradient observations, data being acquired between November 2009 and June 2010. Corresponding gravity anomaly results are used for the calculation of ice mass changes by the use of theRPMmethod. The results are then compared with the computed topographic effect of the ice by the use of a modified topographic correction and the Gravsoft TC program. The maximal gravity changes at the ground predicted from GOCE gradients are between 2 and 4 mGal for the period considered. The gravity anomaly estimation error arising from the GOCE gradient data using only Tzz with an associated error of 20 mE is 11 mGal. This analysis shows the potential of using GOCE data for observations of ice mass changes although the GOCE dataset is limited to only six months. We expect four years of GOCE gradient observations to be available by mid-2014. This will increase the accuracy and spatial resolution of the GOCE measurements, which may lead to an accuracy necessary for observing ice mass changes.

Detection of ionospheric signatures from GPS-derived total electron content maps

Abstract: Abstract The processing of measurement data from satellite constellations such as Global Navigation Satellite Systems (GNSS), including the well-known Global Positioning System (GPS), have been successfully applied to virtually all areas of geophysical sciences. In this work, a method is described where Geographical Information Systems (GIS) are employed to build hourly ionospheric Total Electron Content (TEC) maps for 2011 over the southern Iberian Peninsula. The maps used GPS-derived geometryfree linear combinations attained from station data from the Algarve, Alentejo (Portugal), Andalusia, Murcia and Valencia (Spain) regions. Following the construction of the ionospheric maps, it was possible to relate these results to natural phenomena. The observed phenomena included diurnal and seasonal variations: daytime TEC maxima, nighttime TEC peaks, summer TEC value decreases, and spring and fall TEC maxima. After validation of these periodic phenomena, detection of non-periodic changes, such as solar flares and tectonic interactions with the ionosphere were attempted. The results showed a TEC increase following a selected solar flare event and a potential TEC build-up prior to the 2011 Lorca earthquake. Further studies could open up the possibility of building early warning systems. The presented methods, based on available software packages, are also of value in monitoring the effect of the ionosphere on radio signals, satellite and mobile communication, power grids, and for accurate GNSS navigation.

On weighted total least squares adjustment for solving the nonlinear problems

Abstract: Abstract In the classical geodetic data processing, a non- linear problem always can be converted to a linear least squares adjustment. However, the errors in Jacob matrix are often not being considered when using the least square method to estimate the optimal parameters from a system of equations. Furthermore, the identity weight matrix may not suitable for each element in Jacob matrix. The weighted total least squares method has been frequently applied in geodetic data processing for the case that the observation vector and the coefficient matrix are perturbed by random errors, which are zero mean and statistically in- dependent with inequality variance. In this contribution, we suggested an approach that employ the weighted total least squares to solve the nonlinear problems and to mitigate the affection of noise in Jacob matrix. The weight matrix of the vector from Jacob matrix is derived by the law of nonlinear error propagation. Two numerical examples, one is the triangulation adjustment and another is a simulation experiment, are given at last to validate the feasibility of the developed method.

Adjusting altimetric sea surface height observations in coastal regions. Case study in the Greek Seas.

Abstract: When processing satellite altimetry data forMean Sea Surface (MSS) modelling in coastal environ-mentsmanyproblemsarise.Thedegradationoftheaccu-racyoftheSeaSurfaceHeight(SSH)observationsclosetothe coastline and the usually irregular pattern and vari-abilityoftheseasurfacetopographyarethetwodominantfactorswhichhavetobeaddressed.Inthepresentpaper,westudythestatisticalbehavioroftheSSHobservationsinrelationtotherangefromthecoastlineformanysatel-litealtimetrymissionsandwemakeane˙orttominimizethe e˙ects of the ocean variability. Based on the aboveconcepts we present a process strategy for the homoge-nizationofmultisatellitealtimetrydatathattakesadvan-tageofweightedSSHobservationsandapplieshighdegreepolynomialsfortheadjustmentandtheiruni˝cationatacommonepoch.Ateachstepwepresentthecontributionof each concept to MSS modelling and then we developa MSS, a marine geoid model and a grid of gravity FreeAirAnomalies(FAA)fortheareaunderstudy.Finally,weevaluatetheaccuracyoftheresultingmodelsbycompar-isonstostateoftheartglobalmodelsandotheravailabledatasuchasGPS/levelingpoints,marineGPSSSH’sandmarinegravityFAA’s,inordertoinvestigateanyprogressachievedbythepresentedstrategy.

The Case of the Homogeneous Errors-In-Variables Model

Abstract: Abstract Recently, it has been claimed that the Homogeneous Errors-In-Variables (HEIV) Model, where the lefthand side (LHS) vector is allowed to be multiplied with an unknown scale factor, would represent a generalization of the regular EIV-Model for which a number of efficient algorithms already exist. Unfortunately, due to the forced rank deficiency in the case of the HEIV-Model, an additional constraint needs to be introduced to guarantee uniqueness of the TLS solution (“datum constraint”). If this constraint is linear, a simple manipulation will reduce the HEIV-Model with one constraint to the regular EIV-Model. But also in the case of a non-linear datum constraint, by introducing parameter ratios as unknowns, an EIV-Model may result that can be treated by standard TLS adjustment, followed by a solution of the datum constraint for the additional LHS scale parameter. This approach will be applied to an example where the datum constraint is chosen to be quadratic.

Comparison of site velocities derived from collocated GPS, VLBI and SLR techniques at the Hartebeesthoek Radio Astronomy Observatory (Comparison of site velocities)

Abstract: The University of Pretoria, Vienna University of Technology, the National Research Foundation (NRF) of South Africa, Hart-RAO and Inkaba yeAfrica.

Detection of a sinusoidal oscillation of unknownfrequency in a time series – a geodetic approach

Abstract: Geodetic and geophysical time series may contain sinusoidal oscillations of unknown angular frequency. Often it is required to decide if such sinusoidal oscillations are truly present in a given time series. Here we pose the decision problem as a statistical hypothesis test, an approach very popular in geodesy and other scientific disciplines. In the case of unknown angular frequencies such a test has not yet been proposed. We restrict ourselves to the detection of a single sinusoidal oscillation in a one-dimensional time series, sampled at non-uniform time intervals.We compare two solutionmethods: the likelihood ratio test for parameters in a Gauss-Markov model and the analysis of the Lomb-Scargle periodogram.Whenever needed, critical values of these tests are computed using the Monte Carlo method. We analyze an exemplary time series from an absolute gravimetric observation by various tests. Finally, we compare their statistical power. It is found that the results for the exemplary time series are comparable. The LR test is more flexible, but always requires the Monte Carlo method for the computation of critical values. The periodogram analysis is computationally faster, because critical values can be approximately deduced from the exponential distribution, at least if the sampling is nearly uniform.

Fundamental triangulation networks in Denmark

Abstract: Abstract The first triangulation activity on Danish ground was carried out by the astronomer Tycho Brahe who resided on the island Hven. He wanted to determine the longitude difference of his observatory Uraniborg to Copenhagen. A by-product was a map of his island made in 1579. In 1761 the Royal Danish Academy of Sciences and Letters initiated a mapping project which should be based on the principle of triangulation. Eventually 24 maps were printed in varying scales, predominantly in 1:120 000. The last map was engraved in 1842. The Danish GradeMeasurement initiated remeasurements and redesign of the fundamental triangulation network. This network served scientific as well as cartographic purposes in more than a century. Only in the 1960s all triangulation sides were measured electronically. A combined least-squares adjustment followed in the 1970s