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

In this work, we introduce a new way of improving the sligthly best performing global ionospheric model (GIM) within the International GNSS Service, the UQRG produced by UPC-IonSAT with the TOMION dual-layer voxel model solved with ground-based dual-frequency carrier phase GPS data combined with kriging interpolation. This is done by increasing its vertical resolution consistently with the heights

The Russian Global Navigation Satellite System (GLONASS) satellites have a stretched body shape and take a specific attitude mode inside the eclipse. Based on previous studies, the new Empirical CODE orbit model (ECOM2) performs better than the classical ECOM model if a satellite has elongated shape or does not maintain yaw-steering mode, and the use of an a priori box-wing (BW) model improves the

Quantum optical technology provides an opportunity to develop new kinds of gravity sensors and to enable novel measurement concepts for gravimetry. Two candidates are considered in this study: the cold atom interferometry (CAI) gradiometer and optical clocks. Both sensors show a high sensitivity and long-term stability. They are assumed on board of a low-orbit satellite like gravity field and steady-state

Ground-based Global Navigation Satellite System Reflectometry (GNSS-R) is quickly maturing toward the objective of becoming a viable alternative for operational coastal sea-level (SL) altimetry in a geocentric reference frame. SL has immense societal implications related to climate change. Of particular interest is the exploitation of existing coastal GNSS sites for reflectometry by means of signal-to-noise

To monitor temporal variations of the Earth’s gravity field and mass transport in the Earth’s system, data from gravity recovery and climate experiment (GRACE) satellite mission and its successor GRACE Follow-On (GFO) are used. To fill in the temporal gap between these missions, other satellites’ kinematic orbits derived from GPS-based high-low satellite-to-satellite tracking data may be considered

Several studies have recognized that Global Navigation Satellite System Reflectometry (GNSS-R) is subject to atmospheric propagation delays. Unfortunately, there is little information in the peer-reviewed literature about the methods and algorithms involved in correcting for this effect. We have developed an atmospheric ray-tracing procedure to solve rigorously the three-point boundary value problem

XGM2019e is a combined global gravity field model represented by spheroidal harmonics up to degree and order (d/o) 5399, corresponding to a spatial resolution of 2′ (~ 4 km). As data sources, it includes the satellite model GOCO06s in the longer wavelength range up to d/o 300 combined with a ground gravity grid which also covers the shorter wavelengths. The ground data consist over land and ocean of

The 2004 Sumatra, 2010 Maule, and 2011 Tohoku great earthquakes triggered tsunamis as large as a few decimeters over a few 100 km in the open ocean. The transient ocean mass redistribution propagating as tsunamis changed the Earth’s gravity field enough to perturb the GRACE satellites’ orbits at ~ 500 km above the surface. The on-board microwave ranging system detected inter-satellite acceleration

GPS has been used to estimate ocean tide loading (OTL) height displacement amplitudes to accuracies of within 0.5 mm at the M2 frequency, but such estimation has been problematic at luni-solar K2 and K1 frequencies because they coincide with the GPS orbital period and revisit period, leading to repeating multipath and satellite orbit errors. We therefore investigate the potential of using the GLONASS

China is currently focusing on the establishment of its BDS-3 system, and a BDS-3 constellation with 18 satellites in medium Earth orbit (MEO) and one satellite in geostationary Earth orbit (GEO) has been able to provide preliminary global services since the end of 2018. These BDS-3 satellites feature the inter-satellite link (ISL) and new high-quality onboard clocks. In this study, we present the

In geophysical and geodetic studies, gravity inversion is typically performed such that observed gravity values are first continued downward onto a regular (planar, spherical or spheroidal) surface by solving an inverse integral transform, which originates from a classical solution to the first boundary-value problem in potential theory. A typical example is continuing gravity observed at the topographic

The authors would like to apologize to the editor and readers for a bug in the numerical implementation of the formula for the initial guess on the regularization parameter 2013, as given in the second paragraph on page 1370, and repeated here for convenience.

The position of a seafloor geodetic station can be determined by combining Global Navigation Satellite System (GNSS) and acoustic technologies, called GNSS-acoustic positioning. The precision of GNSS-acoustic positioning, a technique that employs the distance intersection, is determined by the positioning geometry formed by the ship’s track lines with respect to the seafloor station and the errors

Ionospheric scintillation often occurs in equatorial and low-latitudes regions between ± 20° geomagnetic latitude and impacts GNSS performance on geodetic applications. In equatorial and low latitude regions, scintillation on the GNSS signal occurs mainly due to small-scale irregularities inside plasma bubbles that are magnetic field-aligned structures. We derived the propagation angle between GNSS

Lee’s exact method was developed to enable the Gauss–Krüger (GK) projection to be implemented without iterative procedures via the expansion of the intermediate mapping (Thompson projection) into series approximations in terms of isothermal coordinates \(\left( \psi , \lambda \right) \) for the forward mapping and GK coordinates \(\left( x, y \right) \) for the reverse mapping. The straightforward

The troposphere is considered as one of the major error sources in space geodetic techniques. Thus, accurate troposphere delay models are essential to provide high-quality products, such as reference frames, satellite orbits, or Earth rotation parameters. In this paper, a new troposphere delay model for satellite laser ranging, the Vienna Mapping Functions 3 for optical frequencies (VMF3o), is introduced

Recent efforts of tracking low Earth orbit and medium Earth orbit (MEO) satellites using geodetic very long baseline interferometry (VLBI) raise questions on the potential of this novel observation concept for space geodesy. Therefore, we carry out extensive Monte Carlo simulations in order to investigate the feasibility of geodetic VLBI for precise orbit determination (POD) of MEO satellites and assess

Doppler orbitography uses the Doppler shift in a transmitted signal to determine the orbital parameters of satellites including range and range rate (or radial velocity). We describe two techniques for atmospheric-limited optical Doppler orbitography measurements of range rate. The unstabilised technique determines the Doppler shift directly from a heterodyne measurement of the returned optical signal

The editors alerted the author to the editorial policy that ocean and sea areas should be named following agreed international standards.

We apply the AUSGeoid data processing and computation methodologies to data provided for the International Height Reference System (IHRS) Colorado experiment as part of the International Association of Geodesy Joint Working Groups 0.1.2 and 2.2.2. This experiment is undertaken to test a range of different geoid computation methods from international research groups with a view to standardising these

The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. https://doi.org/10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple

High-precision and high-resolution gravity fields can be derived from multi-source satellite altimeter data. A gravity anomaly model around the South China Sea (SCSGA) V1.0 on a 1′ × 1′ grid is established from sea surface heights (SSHs) of several geodetic missions (GMs) and exact repeat missions. Gridded deflections of the vertical are first calculated from SSHs by the least squares collocation (LSC)

Surface deformation measured by geodetic data is the sum of single-strain sources deforming at depth. A combination of volume changes from several analytical models (e.g. a point source or dislocation along a plane) can be used to model the different sources. However, solving for the best fit of volume variations, dislocations, position and orientation parameters of all sources is a nonlinear problem

Interferometric synthetic aperture radar (InSAR) technology can be used to observe high spatial resolution one-dimensional (1-D) deformation along the line-of-sight direction from a single-track synthetic aperture radar (SAR) dataset. With the aid of multi-track InSAR data or a prior model, InSAR can be extended to infer 3-D deformation information, but the temporal resolution is generally limited

Since 2015, the new generation global BDS system, i.e., BDS-3, has started its development with five experimental satellites demonstration system and has announced its initial global service officially on December 27, 2018. Among the various characteristics to be analyzed for the new generation BDS satellites, the differential code bias (DCB) is of special attention since that it has a direct dependence

Time series with strong periodicity and non-stationary character in terms of magnitude and frequency which are changing over measurement period can be decomposed into time-varying trend, seasonal and cyclical components by dynamic harmonic regression (DHR) modeling in the state-space framework. The time-variable parameters of the components are first associated with a generalized random walk process

For low Earth orbit (LEO) satellites, activities such as precise orbit determination, gravity field retrieval, and thermospheric density estimation from accelerometry require modeled accelerations due to radiation pressure. To overcome inconsistencies and better understand the propagation of modeling errors into estimates, we here suggest to extend the standard analytical LEO radiation pressure model

To remove atmospheric pressure loading (ATML) effect from GNSS coordinate time series, surface pressure (SP) models are required to predict the displacements. In this paper, we modeled the 3D ATML surface displacements using the latest MERRA-2 SP grids, together with four other products (NCEP-R-1, NCEP-R-2, ERA-Interim and MERRA) for 596 globally distributed GNSS stations, and compared them with ITRF2014