Difference methods have been routinely used to compute velocity and acceleration from precise positioning with global navigation satellite systems (GNSS). A low sampling rate (say a rate not greater than 1 Hz, for example) has been always implicitly assumed for applicability of the methods, because random measurement errors are significantly amplified, either proportional to the sampling rate in the

The increasing importance of terrestrial gravimetry in monitoring global change processes, in providing a reference for satellite measurements and in applications in metrology necessitates a stable reference system reflecting the measurement accuracy achievable by modern gravimeters. Therefore, over the last decade, the International Association of Geodesy (IAG) has developed a system to achieve accurate

The geoid can be computed from the quasigeoid by applying the geoid-to-quasigeoid separation. The geoid-to-quasigeoid separation is also needed for a vertical datum unification. Information about the actual topographic density distribution is required to determine accurately the geoid and orthometric heights. In this study, we estimate the effect of (lateral) anomalous topographic density on the geoid-to-quasigeoid

The signal of the GNSS satellites can be used to estimate the amount of water vapor in the atmosphere. For this reason, GNSS observations are nowadays routinely used by several meteorological institutes (e.g., MetOffice, Meteo France) to monitor weather events and to improve their weather forecasts quality. The analysis of a whole network of GNSS stations to estimate a full three-dimensional model

The emergence of quantum technologies, including cold atom-based accelerometers, offers an opportunity to improve the performances of space geodesy missions. In this context, CNES initiated an assessment study called GRICE (GRadiométrie à Interféromètres quantiques Corrélés pour l’Espace) in order to evaluate the contribution of cold atom technologies to space geodesy and to the end users of geodetic

In the geodetic community, an adjustment framework is established by the four components of model choice, parameter estimation, variance component estimation (VCE), and quality control. For linear ill-posed models, the parameter estimation and VCE have been extensively investigated. However, at least to the best of our knowledge, nothing is known about the quality control of hypothesis testing in ill-posed

In the summer of 2017, the National Geodetic Survey (NGS) conducted its third and final Geoid Slope Validation Survey in the rugged terrain of southern Colorado, USA. As in previous surveys, the intent is to acquire the most accurate and precise field observations to determine geoid slopes. In turn, these data can be used to quantify the accuracy of various geoid models as NGS looks ahead to creating

A key prerequisite for fast and reliable solution convergence time in precise point positioning with ambiguity resolution is the successful determination of the initial integer ambiguity parameters. In this contribution, a reliable approach of partial ambiguity resolution based on the BIE using the t-distribution (BIE-td) is proposed and compared against existing algorithms, such as the partial ambiguity

We present a new method to estimate common-mode components (CMC) in global positioning system (GPS) position time-series. The method (‘CMC Imaging’) is fully automated, relies entirely on robust statistics, and exploits the recent proliferation of GPS stations by allowing stations with relatively short time-series to be considered as filter stations as well. The spatial extent of the CMC is purposely

Based on the unifying framework of the detection, identification and adaption (DIA) estimators, quality control indices are refined and formulated by taking the uncertainty of the combined estimation-testing procedure into account and performing the propagation of uncertainty. These indices are used to measure the confidence levels of the testing decisions, the reliability of the specified alternative

We use global data from the Lunar Orbiter Laser Altimeter (LOLA) to retrieve the lunar tidal Love number \(h_2\) and find \(h_2 = 0.0387\pm 0.0025\). This result is in agreement with previous estimates from laser altimetry using crossover points of LOLA profiles. The Love numbers \(k_2\) and \(h_2\) are key constraints on planetary interior models. We further develop and apply a retrieval method based

A new approach to recover time-variable gravity fields from satellite laser ranging (SLR) is presented. It takes up the concept of lumped coefficients by representing the temporal changes of the Earth’s gravity field by spatial patterns via combinations of spherical harmonics. These patterns are derived from the GRACE mission by decomposing the series of monthly gravity field solutions into empirical

To avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias

We derive an empirical model of the sub-daily polar motion (PM) based on the multi-GNSS processing incorporating GPS, GLONASS, and Galileo observations. The sub-daily PM model is based on 3-year multi-GNSS solutions with a 2 h temporal resolution. Firstly, we discuss differences in sub-daily PM estimates delivered from individual GNSS constellations, including GPS, GLONASS, Galileo, and the combined

The study intercompares three stochastic interpolation methods originating from the same geostatistical family: least-squares collocation (LSC) known from geodesy, as well as ordinary kriging (OKR) and universal kriging (UKR) known from geology and other geosciences. The objective of this work is to assess advantages and drawbacks of fundamental differences in modeling between these methods in imperfect

The article “Gravity reference at the Argentinean–German Geodetic Observatory (AGGO) by co-location of superconducting and absolute gravity measurements”, written by Ezequiel D. Antokoletz, Hartmut Wziontek, Claudia N. Tocho, Reinhard Falk, was originally published Online First without Open Access.

Current International Association of Geodesy efforts within regional geoid determination include the comparison of different computation methods in the quest for the “1-cm geoid.” Internal (formal) and external (empirical) approaches to evaluate geoid errors exist, and ideally they should agree. Spherical radial base functions using the spline kernel (SK), least-squares collocation (LSC), and Stokes’s

Global navigation satellite system (GNSS) differential code bias (DCB) is a significant error source in ionosphere modeling that uses GNSS observation data. Given that the orbit altitudes of low earth orbit (LEO) satellites are above the F layer of ionosphere, ionized electrons come from the upper ionosphere or plasmasphere, so observations suffer from small signal delays. DCBs can be estimated using

Absolute gravimeters are used in geodesy, geophysics and physics for a wide spectrum of applications. Stable gravimetric measurements over timescales from several days to decades are required to provide relevant insight into geophysical processes. Users of absolute gravimeters participate in comparisons with a metrological reference in order to monitor the temporal stability of the instruments and

Deformation congruence models form the basis for conventional deformation analysis (CDA). In geometrical sense, these models connect an epochal object states—represented by its characteristic points—at stable/congruent points to disclose possible deformations. To this day, the deformation congruence models are usually specified using the global congruence test (GCT) procedure which, however, has a

Currently, Global Navigation Satellite Systems (GNSS) do not contribute to the realization of origin and scale of combined global terrestrial reference frame (TRF) solutions due to present system design limitations. The future Galileo-like medium Earth orbit (MEO) constellation, called “Kepler”, proposed by the German Aerospace Center DLR, is characterized by a low Earth orbit (LEO) segment and the

The Global Positioning System (GPS) has revolutionized the ability to monitor Earth-system processes, including Earth’s water cycle. Several analysis centers process GPS data to estimate ground-antenna positions at daily temporal resolution. Differences in processing strategies can lead to inconsistencies in coordinate-position estimates and therefore influence the analysis of crustal displacement

A unique architecture of Sentinel-3A and Sentinel-3B satellites includes the shared ultra-stable oscillator (USO) by the DORIS and GPS receivers. This concept enables to apply onboard GPS clock estimates in the DORIS processing substituting the DORIS polynomial clock model by the GPS epoch-wise model, together with a DORIS-specific clock offset. Such an approach is particularly profitable for the mitigation

The Gauss–Legendre quadrature (GLQ) integration is a numerical method to calculate the gravitational field of a tesseroid and the approximation error of the GLQ integration increases as the tesseroid gets closer to the computation point. There are two ways to counterbalance this effect. One way is the subdivision of a tesseroid into smaller units and the other way is to increase the quadrature order

Robust estimation in the errors-in-variables (EIV) model remains a difficult problem because of the leverage point and the masking effect and swamping effect. In this contribution, a new robust estimator is introduced for the EIV model. This method is a follow-up to least trimmed squares, which is applied to the Gauss–Markov model when only the observation vector contains outliers. We call this estimator

In the investigation and evaluation of geological hazards such as those caused by co-seismic displacement, displacement due to underground mining, landslides, volcanic eruptions, it is important to retrieve the complete three-dimensional ground displacement components. However, both conventional D-InSAR (differential synthetic aperture radar interferometry) and MT-InSAR (multi-temporal InSAR) can only

The very low-degree Earth’s gravity coefficients, associated with the largest-scale mass redistribution in the Earth’s fluid envelope (atmosphere, oceans and continental hydrology), are the most poorly known. In particular, the first three degree geopotential terms are important, as they relate to intrinsic Earth’s mass references: gravitational coefficient (GM) of the Earth (degree 0), geocenter motion

We show that far-zone topography-implied gravitational effects may be accurately computed via external spherical harmonics not only above the limit sphere encompassing all the masses, but also inside it on planetary topographies. Although a rigorous mathematical proof is still missing, our numerical experiments indicate that this is possible, provided that near-zone masses within a certain spherical

The geoid computation method currently used at the US National Geodetic Survey is based on the analytical downward continuation solution of the Molodensky geodetic boundary value problem. The quasigeoid is computed first in 1′ × 1′ grids for the whole area, and then, the geoid is obtained by adding the geoid–quasigeoid separation term based on the simple Bouguer anomalies. A few variations in data

The Continuous Very Long Baseline Interferometry (VLBI) Campaign 2017 (CONT17) was observed from November 28 to December 12, 2017 and featured three independent observing networks. Two legacy S/X networks of nominally 14 stations each observed in parallel for the full 15 days of the campaign. One of them was made possible in large part by the participation of the ten-station very long baseline array

Vertical surface displacements from continuous Global Positioning System (GPS) stations often show strong seasonal signals, which in some cases may be associated with surface mass loading, including hydrological, and non-tidal oceanic and atmospheric loading. In Antarctica, many GPS stations show vertical motions in phase with seasonal snow accumulation changes, but these variations cannot be fully

Reanalysis products have played an important role in space geodetic tropospheric delay retrieval and modeling in the past two decades. As the release of the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA5), with improved temporal-spatial resolutions compared to its predecessor, ECMWF Re-Analysis Interim (ERAI), the performance of ERA5 in tropospheric delay

As of December 2019, the core constellation of BeiDou Navigation Satellite System with global coverage (BDS-3) has been fully deployed with 24 MEO, 3 IGSO and 1 GEO satellites. In addition to the legacy B1I and B3I signals, BDS-3 satellites are capable of transmitting several new navigation signals, including B1C, B2a, B2b and B2a + b. The multi-frequency signals of BDS-3 bring new opportunities for

As one of the important factors influencing the ionospheric total electron content (TEC) estimation accuracy, receiver differential code biases (DCBs) should be properly removed from global navigation satellite system (GNSS) measurements. The intraday variability in receiver DCBs (rDCBs), which is usually ignored in the commonly used ionospheric observable retrieval procedure, has been identified as

Long-term series of reliable sea level (SL) data are essential for understanding the trends and causes of SL changes, for furthering knowledge about the effects of current climate change and for predicting future SL evolution. This study aims to extend the SL time series of measurements along the Israeli Mediterranean coastline by revisiting historical benchmarks (BM) along the Israeli coast, first

We evaluated the performance of GNSS absolute antenna calibrations and its impact on accurate positioning with a new assessment method that combines inter-antenna differentials and laser tracker measurements. We thus separated the calibration method contributions from those attainable by various geometric constraints and produced corrections for the calibrations. We investigated antennas calibrated

Despite the high-precision performance of GNSS real-time kinematic (RTK) in many cases, large noises in pseudo-range measurements or harsh signal environments still impact float ambiguity estimation in kinematic localization, which leads to ambiguity-fixed failure and worse positioning results. To improve RTK ambiguity resolution (AR) performance further, multi-sensor fusion technique is a feasible

The precise orbit determination (POD) of Global Navigation Satellite System (GNSS) satellites and low Earth orbiters (LEOs) are usually performed independently. It is a potential way to improve the GNSS orbits by integrating LEOs onboard observations into the processing, especially for the developing GNSS, e.g., Galileo with a sparse sensor station network and Beidou with a regional distributed operating

This study presents a solution of the ‘1 cm Geoid Experiment’ (Colorado Experiment) using spherical radial basis functions (SRBFs). As the only group using SRBFs among the fourteen participated institutions from all over the world, we highlight the methodology of SRBFs in this paper. Detailed explanations are given regarding the settings of the four most important factors that influence the performance

The determination of the gravimetric geoid is based on the magnitude of gravity observed at the topographic surface of the Earth. In order to satisfy Laplace’s equation, the masses between the surface of the Earth and the geoid must be removed or shifted inside the geoid. Then the gravity values have to be reduced to the geoid, forming the boundary values on the boundary surface. Gravity reduction

The C-band Sentinel-1 A/B satellites in TOPS mode provide unprecedented opportunities for continuous radar mapping of the earth with enhanced revisit frequency. The reliability for routine operational services relies on a very stringent azimuth co-registration accuracy. However, while the enhanced spectral diversity (ESD) technique achieves a co-registration accuracy of better than 0.001 pixels, the

The reference frame of a global terrestrial network is defined by the origin, the orientation and the scale. The origin of the ITRF2014 is defined by the ILRS long-term solution, the orientation by no-net rotation conditions w.r.t. the previous reference frame (ITRF2008), and the scale by the mean values from global VLBI and SLR solution series (Altamimi et al. in J Geophys Res Solid Earth 121:6109–6131

As the KTH method for geoid determination by combining Stokes integration of gravity data in a spherical cap around the computation point and a series of spherical harmonics suffers from a bias due to truncation of the data sets, this method is based on minimizing the global mean square error (MSE) of the estimator. However, if the harmonic series is increased to a sufficiently high degree, the truncation

The key to precise global navigation satellite system (GNSS) positioning is carrier phase integer ambiguity resolution with a high success rate. On the other hand when the success rate is too low, the user will normally prefer the float solution. The alternative can be to use the best integer equivariant (BIE) estimator, since it is optimal in the minimum mean squared error (MMSE) sense. Low-cost receiver

In the analysis of very long baseline interferometry (VLBI) observations, many geophysical models are used for correcting the theoretical signal delay. In addition to the conventional models described by Petit and Luzum (eds) (IERS Conventions, 2010), we are applying different parts of non-tidal site loading, namely the atmospheric, oceanic, and hydrological ones. To investigate their individual contributions

One of the more common methods of observation of variability of the Earth’s ionosphere is based on total electron content (TEC) estimated from ground-based dual-frequency Global Positioning System (GPS) receivers. Variations in solar, geomagnetic and seismic activity cause depletions or enhancements in the ionospheric electron concentrations that can be detected as disturbances. Some of these disturbances

Global navigation satellite system-reflectometry (GNSS-R) has great potential to be a novel technique for altimetry, which can be used to derive sea surface heights (SSH). Shipborne altimetry is an important method to measure local SSH with high spatial resolution. In order to test the feasibility of shipborne dual-antenna GNSS-R reflector height retrieval, we developed a GNSS-R receiver system and

Interferometric synthetic aperture radar (InSAR) time series technique has been widely applied to map the ground deformation over the past two decades. One of the key steps of InSAR time series approach is to select appropriate measurement scatterer (MS) pixels to build the triangulated irregular network (TIN). In order to build a stable TIN, there are four criteria need to be satisfied: (1) working

In this paper, we present an approach to generating a global topside ionospheric map (GTIM) using dual-frequency global positioning system (GPS) data from multiple low Earth orbit (LEO) satellites at different orbital altitudes. NeQuick2 is employed to normalize LEO data to the same observation range, and 13 LEO satellites from 2015/01/01 to 2015/09/27 are used to generate GTIM-500 (with an ionospheric

The gravity recovery and climate experiment follow-on (GRACE-FO) satellites, launched in May of 2018, are equipped with geodetic quality GPS receivers for precise orbit determination (POD) and gravity recovery. The primary objective of the GRACE-FO mission is to map the time-variable and mean gravity field of the Earth. To achieve this goal, both GRACE-FO satellites are additionally equipped with a

Models for postseismic transient displacements can be formulated using logarithmic and exponential decay formulas with single or multiple timescales. The logarithmic form is associated with rate and state friction theory and afterslip, while the exponential form is associated with bulk viscoelastic relaxation of coseismic stresses. It is now quite widely understood that one can model GPS/GNSS time

This paper combines gravity data collected from airborne, shipborne and terrestrial surveys and those derived from satellite altimetry to determine a high-resolution gravimetric and hybrid geoid model (on a 30” × 30″ grid) in and around Taiwan. Some 6000 new land gravity values at a 0.03-mGal precision make a notable contribution to the geoid modeling. Shipborne gravity data in waters 20 km offshore

This contribution extends the theory of integer equivariant estimation (Teunissen in J Geodesy 77:402–410, 2003) by developing the principle of best integer equivariant (BIE) estimation for the class of elliptically contoured distributions. The presented theory provides new minimum mean squared error solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions

The Gravity Recovery and Climate Experiment (GRACE) satellite mission has profoundly advanced our knowledge of contemporary sea level change. Owing to the coarse spatial resolution and leakage issue across the land–ocean boundary, it is challenging (even impossible) for GRACE to detect mass changes over a region smaller than its spatial resolution, especially a semi-enclosed basin (e.g., the Bohai

Ten-year worth of absolute gravity (AG) campaigns at Onsala Space Observatory (OSO), Sweden, are simultaneously reduced using synchronous data from a superconducting gravimeter (SG). In this multi-campaign adjustment, the a priori models commonly applied for each setup in AG-alone experiments are sidestepped in favour of SG records and a model to estimate its drift. We obtain a residual (hourly samples)

Real-time precise point positioning (PPP) based on open-access real-time service (RTS) of the international GNSS service (IGS) has attracted increasing attention in recent years. For offshore applications, the receiving of RTS corrections becomes a major obstacle due to lack of internet-based infrastructures. Short-message communication (SMC) is a particular technique of BeiDou navigation satellite

The Argentinean–German Geodetic Observatory (AGGO) is a fundamental geodetic observatory located close to the city of La Plata, Argentina. Two high-precision gravity meters are installed at AGGO: the superconducting gravimeter SG038, which is in operation since December 2015, and the absolute gravimeter FG5-227, which has provided absolute gravity measurements since January 2018. By co-location of

Low-pass filters are commonly used for the processing of airborne gravity observations. In this paper, for the first time, we include the resulting correlations consistently in the functional and stochastic model of residual least-squares collocation. We demonstrate the necessity of removing high-frequency noise from airborne gravity observations, and derive corresponding parameters for a Gaussian

A near real-time troposphere tomography system (WATS-NRT) based on Global Positioning System (GPS) slant wet delays (SWD) was developed to reconstruct three-dimensional wet refractivity fields over a wide area. The NCEP Global Forecast System (GFS) short-range forecast products (GFS-FC) were taken as the tomography background to tackle the ill-condition issue, and the Adaptive Simultaneous Iterative

Different from differential code biases, the observable-specific code biases (OSBs) directly describe the biases of individual pseudorange measurements, which provide full flexibilities for multi-GNSS code biases handling. We present the method for the parameterization, computation and alignment of multi-GNSS OSBs as part of the local ionospheric modeling. As a representative example, GPS L1/L2/L5