ALBERT

Description: The goal of our study is to determine accurate time series of geophysical Earth rotation excitations to learn more about global dynamic processes in the Earth system. For this purpose, we developed an adjustment model which allows to combine precise observations from space geodetic observation systems, such as Satellite Laser Ranging (SLR), Global Navigation Satellite Systems, Very Long Baseline Interferometry, Doppler Orbit determination and Radiopositioning Integrated on Satellite, satellite altimetry and satellite gravimetry in order to separate geophysical excitation mechanisms of Earth rotation. Three polar motion time series are applied to derive the polar motion excitation functions (integral effect). Furthermore we use five time variable gravity field solutions from Gravity Recovery and Climate Experiment to determine not only the integral mass effect but also the oceanic and hydrological mass effects by applying suitable filter techniques and a land–ocean mask. For comparison the integral mass effect is also derived from degree 2 potential coefficients that are estimated from SLR observations. The oceanic mass effect is also determined from sea level anomalies observed by satellite altimetry by reducing the steric sea level anomalies derived from temperature and salinity fields of the oceans. Due to the combination of all geodetic estimated excitations the weaknesses of the individual processing strategies can be reduced and the technique-specific strengths can be accounted for. The formal errors of the adjusted geodetic solutions are smaller than the RMS differences of the geophysical model solutions. The improved excitation time series can be used to improve the geophysical modeling.

Description: This paper introduces a new approach for modeling solar radiation pressure (SRP) effects on Global Navigation Satellite Systems (GNSSs). It focuses on the Galileo In-Orbit Validation (IOV) satellites, for which obvious SRP modeling deficits can be identified in presently available precise orbit products. To overcome these problems, the estimation of empirical accelerations in the Sun direction (D), solar panel axis (Y) and the orthogonal (B) axis is complemented by an a priori model accounting for the contribution of the rectangular spacecraft body. Other than the GPS satellites, which comprise an almost cubic body, the Galileo IOV satellites exhibit a notably rectangular shape with a ratio of about 2:1 for the main body axes. Use of the a priori box model allows to properly model the varying cross section exposed to the Sun during yaw-steering attitude mode and helps to remove systematic once-per-revolution orbit errors that have so far affected the Galileo orbit determination. Parameters of a simple a priori cuboid model suitable for the IOV satellites are established from the analysis of a long-term set of GNSS observations collected with the global network of the Multi-GNSS Experiment of the International GNSS Service. The model is finally demonstrated to reduce the peak magnitude of radial orbit errors from presently 20 cm down to 5 cm outside eclipse phases.

Description: We present a comprehensive numerical analysis of spherical, spheroidal, and ellipsoidal harmonic series for gravitational field modeling near small moderately irregular bodies, such as the Martian moons. The comparison of model performances for these bodies is less intuitive and distinct than for a highly irregular object, such as Eros. The harmonic series models are each associated with a distinct surface, i.e., the Brillouin sphere, spheroid, or ellipsoid, which separates the regions of convergence and possible divergence for the parent infinite series. In their convergence regions, the models are subject only to omission errors representing the residual field variations not accounted for by the finite degree expansions. In the regions inside their respective Brillouin surfaces, the models are susceptible to amplification of omission errors and possible divergence effects, where the latter can be discerned if the error increases with an increase in the maximum degree of the model. We test the harmonic series models on the Martian moons, Phobos and Deimos, with moderate oblateness of \(〈\) 0.4. The possible divergence effects and amplified omission errors of the models are illustrated and quantified. The three models yield consistent results on a bounding sphere of Phobos in their common convergence region, with relative errors in potential of \(\sim \) 0.01 and \(\sim \) 0.001 % for expansions up to degree 10 and degree 20 respectively. On the surface of Phobos, the spherical and spheroidal models up to degree 10 both have maximum relative errors of \(\sim \) 1 % in potential and \(\sim \) 100 % in acceleration due ostensibly to divergence effect. Their performances deteriorate more severely on the more irregular Deimos. The ellipsoidal model exhibits much less distinct divergence behavior and proves more reliable in modeling both potential and acceleration, with respective maximum relative errors of \(\sim \) 1 and \(\sim \) 10 %, on both bodies. Our results show that for the Martian moons and other such moderately irregular bodies, the ellipsoidal harmonic series should be considered preferentially for gravitational field modeling.

Description: Recent studies have extensively discussed total least squares (TLS) algorithms for solving the errors-in-variables (EIV) model with equality constraints but rarely investigated the inequality-constrained EIV model. The most existing inequality-constrained TLS algorithms assume that all the elements in the coefficient matrix are random and independent and that their numerical efficiency is significantly limited due to combinatorial difficulty. To solve the above issues, we formulate a partial EIV model with inequality constraints of both unknown parameters and the random elements of the coefficient matrix. Based on the formulated EIV model, the inequality-constrained TLS problem is transformed into a linear complementarity problem through linearization. In this way, the inequality-constrained TLS method remains applicable even when the elements of the coefficient matrix are subject to inequality constraints. Furthermore, the precision of the constrained estimates is put forward from a frequentist point of view. Three numerical examples are presented to demonstrate the efficiency and superiority of the proposed algorithm. The application is accomplished by preserving the structure of random coefficient matrix and satisfying the constraints simultaneously, without any combinatorial difficulty.

Description:    Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy with 100 km spatial resolution can be achieved. Content Type Journal Article Pages 1-16 DOI 10.1007/s00190-011-0486-7 Authors Th. Gruber, Institute of Astronomical and Physical Geodesy, Technische Universität München, Arcisstrasse 21, 80333 Munich, Germany P. N. A. M. Visser, Delft Institute of Earth Observation and Space Systems (DEOS), Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands Ch. Ackermann, Institute of Astronomical and Physical Geodesy, Technische Universität München, Arcisstrasse 21, 80333 Munich, Germany M. Hosse, Institute of Astronomical and Physical Geodesy, Technische Universität München, Arcisstrasse 21, 80333 Munich, Germany Journal Journal of Geodesy Online ISSN 1432-1394 Print ISSN 0949-7714

Description:    The efficacy of robust M-estimators is a well-known issue when dealing with observational blunders. When the number of observations is considerably large—long time series for instance—one can take advantage of the asymptotic normality of the M-estimation and compute reasonable estimates for the unknown parameters of interest. A few leading M-estimators have been employed to identify the most likely functional model for GPS coordinate time series. This includes the simultaneous detection of periodic patterns and offsets in the GPS time series. Estimates of white noise, flicker noise, and random walk noise components are also achieved using the robust M-estimators of (co)variance components, developed in the framework of the least-squares variance component estimation (LS-VCE) theory. The method allows one to compute confidence interval for the (co)variance components in asymptotic sense. Simulated time series using white noise plus flicker noise show that the estimates of random walk noise fluctuate more than those of flicker noise for different M-estimators. This is because random walk noise is not an appropriate noise structure for the series. The same phenomenon is observed using the results of real GPS time series, which implies that the combination of white plus flicker noise is well described for GPS time series. Some of the estimated noise components of LS-VCE differ significantly from those of other M- estimators. This reveals that there are a large number of outliers in the series. This conclusion is also affirmed by performing the statistical tests, which detect (large) parts of the outliers but can also leave parts to be undetected. Content Type Journal Article Pages 1-19 DOI 10.1007/s00190-011-0489-4 Authors A. Khodabandeh, Department of Surveying and Geomatics Engineering, Geodesy Division, Faculty of Engineering, University of Tehran, North Kargar Ave., Amir-Abad, Tehran, Iran A. R. Amiri-Simkooei, Department of Surveying Engineering, Faculty of Engineering, University of Isfahan, 81746-73441 Isfahan, Iran M. A. Sharifi, Department of Surveying and Geomatics Engineering, Geodesy Division, Faculty of Engineering, University of Tehran, North Kargar Ave., Amir-Abad, Tehran, Iran Journal Journal of Geodesy Online ISSN 1432-1394 Print ISSN 0949-7714

Description:    We examine the electromagnetic coupling of a GPS antenna–monument pair in terms of its simulated affect on long GPS coordinate time series. We focus on the Earth and Polar Observing System (POLENET) monument design widely deployed in Antarctica and Greenland in projects interested particularly in vertical velocities. We base our tests on an absolute robot calibration that included the top ~0.15 m of the monument and use simulations to assess its effect on site coordinate time series at eight representative POLENET sites in Antarctica over the period 2000.0–2011.0. We show that the neglect of this calibration would introduce mean coordinate bias, and most importantly for velocity estimation, coordinate noise which is highly sensitive to observation geometry and hence site location and observation period. Considering only sub-periods longer than 2.5 years, we show vertical site velocities may be biased by up to ±0.4 mm/year, and biases up to 0.2 mm/year may persist for observation spans of 8 years. Changing between uniform and elevation-dependent observation weighting alters the time series but does not remove the velocity biases, nor does ambiguity fixing. The effect on the horizontal coordinates is negligible. The ambiguities fixed series spectra show noise between flicker and random walk with near-white noise at the highest frequencies, with mean spectral indices (frequencies 〈20 cycles per year) of approximately −1.3 (uniform weighting) and −1.4 (elevation-dependent weighting). While the results are likely highly monument specific, they highlight the importance of accounting for monument effects when analysing vertical coordinate time series and velocities for the highest precision and accuracy geophysical studies. Content Type Journal Article Pages 1-11 DOI 10.1007/s00190-011-0491-x Authors Matt A. King, School of Civil Engineering and Geosciences, Newcastle University, Cassie Building, Newcastle upon Tyne, NE1 7RU UK Michael Bevis, School of Earth Sciences, Ohio State University, 125 South Oval Mall, Columbus, OH 43210-1522, USA Terry Wilson, School of Earth Sciences, Ohio State University, 125 South Oval Mall, Columbus, OH 43210-1522, USA Bjorn Johns, UNAVCO, 6350 Nautilus Drive, Boulder, CO 80301-5554, USA Frederick Blume, UNAVCO, 6350 Nautilus Drive, Boulder, CO 80301-5554, USA Journal Journal of Geodesy Online ISSN 1432-1394 Print ISSN 0949-7714

Description:    Seventeen long series of tidal gravity observations with superconducting gravimeters (SGs) belonging to the GGP network allowed to determine the main tidal waves generated by the tidal potential of third degree in the Diurnal (M1), Semi-Diurnal (3MK2, 3MO2) and Ter-Diurnal (M3) bands with a precision of 0.1%, although the amplitudes of these waves are below 10 nm s −2 (1 μgal). Special analysis techniques have been used to separate M1, 3MK2 and 3MO2 from the neighbouring waves generated by the second degree potential. The 11 European stations form a geographically homogeneous subgroup and it is thus possible to derive some conclusions concerning the ocean tides loading and the body tides models. The results for M1, 3MK2 and 3MO2 are not in contradiction with the recent models and the results for M3 are even in agreement with them. Content Type Journal Article Pages 1-11 DOI 10.1007/s00190-011-0492-9 Authors Bernard Ducarme, Georges Lemaître Centre for Earth and Climate Research, Catholic University of Louvain, 3 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium Journal Journal of Geodesy Online ISSN 1432-1394 Print ISSN 0949-7714

Description:    Future satellite missions dedicated to measuring time-variable gravity will need to address the concern of temporal aliasing errors; i.e., errors due to high-frequency mass variations. These errors have been shown to be a limiting error source for future missions with improved sensors. One method of reducing them is to fly multiple satellite pairs, thus increasing the sampling frequency of the mission. While one could imagine a system architecture consisting of dozens of satellite pairs, this paper explores the more economically feasible option of optimizing the orbits of two pairs of satellites. While the search space for this problem is infinite by nature, steps have been made to reduce it via proper assumptions regarding some parameters and a large number of numerical simulations exploring appropriate ranges for other parameters. A search space originally consisting of 15 variables is reduced to two variables with the utmost impact on mission performance: the repeat period of both pairs of satellites (shown to be near-optimal when they are equal to each other), as well as the inclination of one of the satellite pairs (the other pair is assumed to be in a polar orbit). To arrive at this conclusion, we assume circular orbits, repeat groundtracks for both pairs of satellites, a 100-km inter-satellite separation distance, and a minimum allowable operational satellite altitude of 290 km based on a projected 10-year mission lifetime. Given the scientific objectives of determining time-variable hydrology, ice mass variations, and ocean bottom pressure signals with higher spatial resolution, we find that an optimal architecture consists of a polar pair of satellites coupled with a pair inclined at 72°, both in 13-day repeating orbits. This architecture provides a 67% reduction in error over one pair of satellites, in addition to reducing the longitudinal striping to such a level that minimal post-processing is required, permitting a substantial increase in the spatial resolution of the gravity field products. It should be emphasized that given different sets of scientific objectives for the mission, or a different minimum allowable satellite altitude, different architectures might be selected. Content Type Journal Article Pages 1-18 DOI 10.1007/s00190-011-0493-8 Authors D. N. Wiese, Colorado Center for Astrodynamics Research, University of Colorado at Boulder, 431 UCB, Boulder, CO 80309, USA R. S. Nerem, Colorado Center for Astrodynamics Research, University of Colorado at Boulder, 431 UCB, Boulder, CO 80309, USA F. G. Lemoine, NASA Goddard Space Flight Center, Planetary Geodynamics Laboratory, Greenbelt, MD 20771, USA Journal Journal of Geodesy Online ISSN 1432-1394 Print ISSN 0949-7714

Description:    The consistency of the Chang’E-1 and SELENE reference frames as realized by the footprint positions of laser altimetry measurements of the lunar surface during both missions was analyzed using a global 12-parameter model for small (with respect to unity) deformations and rigid body motions. The rigid body motion and deformation parameters between the two reference frames estimated from nearly-colocated without tie measurements are found to be consistent, i.e., nearly zero for the estimates of the translations, rotations and shear parameters. However, the estimated three strain parameters, which are similar in magnitude and sign, reveal a prominent scale difference, between the Chang’E-1 and SELENE reference frames, of about 0.9 × 10 −5 . The scale difference can be attributed to calibration of the data sets using the known coordinates of the lunar laser ranging stations all located on the near side of the Moon. Content Type Journal Article Pages 1-9 DOI 10.1007/s00190-011-0495-6 Authors H. Bâki Iz, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China Y. Q. Chen, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China C. K. Shum, Division of Geodetic Science, School of Earth Sciences, The Ohio State University, Columbus, USA X. L. Ding, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China B. A. King, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China W. Chen, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China M. Berber, Department of Civil, Environmental, and Geomatics Engineering, Florida Atlantic University, Boca Raton, USA Journal Journal of Geodesy Online ISSN 1432-1394 Print ISSN 0949-7714