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

Airborne gravimetry with strapdown inertial sensors has been a valuable tool for many years to fill in the gravity data gaps on the areas not accessible by land. Accuracies of 1 mGal level with off-the-shelf navigation-grade inertial measurement units (IMU) can only be achieved provided that the accelerometer drifts mainly caused by the temperature variations inside the IMU housing are separated from

In the original publication of the articles, “Methodology and consistency of slant and vertical assessments for ionospheric electron content models” and “Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle”, a common typo affecting the text only (not the computations) has been recently noticed. It compromised the definition of the scaling factor from Global

The International Laser Ranging Service (ILRS) provides weekly solutions for coordinates of Satellite Laser Ranging (SLR) stations coordinates, geocenter coordinates, as well as Earth rotation parameters with a daily resolution. The ILRS standard solution is an important contribution to the International Terrestrial Reference Frame (ITRF). As of today, it is derived from SLR observations to the pairs

Recent studies have indicated a correlation between Earth’s free core nutation (FCN) and geomagnetic jerks (GMJs). However, some uncertainties still need to be resolved before their relationship can be confirmed. The variations in the amplitude and phase of the FCN result from the comprehensive influence of the surface fluid layer and core–mantle couplings, which makes its correlation with GMJs difficult

The proper choice of stochastic model is of great importance to global navigation satellite system (GNSS) data processing. Whereas extensive investigations into stochastic modeling are mainly based on the relative (or differential) method employing zero and/or short baselines, this work proposes an absolute method that relies upon a stand-alone receiver and works by applying the least-squares variance

Triple-frequency observations will introduce an inter-frequency clock bias (IFCB) between the new frequency and the original dual-frequency observations. It has been verified that satellite IFCB can reach dozens of centimeters and several centimeters for GPS Block IIF satellite and BDS satellite, respectively. The existence of satellite IFCB will significantly affect undifferenced triple-frequency

Correction to: Journal of Geodesy (2020) 94:22

With the successful completion of European Space Agency (ESA)’s PolarGAP campaign, ground gravity data are now available for both polar regions. Therefore, it is now possible to solve the GOCE polar gap problem in satellite-only gravity field recovery by using additional polar ground gravity data instead of some regularization methods. However, ground gravimetry data need to be filtered to remove the

Benefiting from global multi-frequency and multi-constellation GNSS measurements provided by the experimental International GNSS real-time service (IGS RTS), a predicting-plus-modeling approach employed by Chinese Academy of Sciences (CAS) for the routine generation of real-time global ionospheric maps (RT-GIM) is first reported. Along with RT-GIMs generated by Universitat Politècnica de Catalunya

A novel approach for the computation of the spherical harmonic coefficients of the gravity field of a constant density polyhedron is presented. The proposed method is based on the expression of these coefficients as the volume integral of solid harmonics. It is well known that the divergence theorem leads to an expression of these volume integrals as surface integrals. We show that these surface integrals

This paper develops a robust M estimation approach applied for three-dimensional (3D) correlated vector observations. A modified bifactor reduction model is constructed, where the weight shrinking factor of the 3D vector observation is determined by a new test statistic that coincides with the estimated direction of the outlier vector and thus is more sensitive to vector-type outliers than the standardized

In this contribution, we propose a method for statistically evaluating the risk in a deformation monitoring system. When the structure under monitoring moves beyond tolerance, the monitor system should issue an alert. Only a very small probability is acceptable of the system telling us that no change beyond a critical threshold has taken place, while in reality it has. This probability is referred

It has been recognized since the early days of interplanetary spaceflight that accurate navigation requires taking into account changes in the Earth’s rotation. In the 1960s, tracking anomalies during the Ranger VII and VIII lunar missions were traced to errors in the Earth orientation parameters. As a result, Earth orientation calibration methods were improved to support the Mariner IV and V planetary

Two widely used scintillation indexes \( S_{4} \) and \( \sigma_{\varphi } \) are generated by dedicated ionospheric scintillation monitoring receivers (ISMRs), which typically have 50-Hz temporal resolution and thus require substantial memory capabilities. Taking into consideration the huge number of common Global Navigation Satellite System (GNSS) receivers, the derivation of a GNSS receiver-based

Abstract The establishment of the terrestrial laser scanner changed the analysis strategies in engineering geodesy from point-wise approaches to areal ones. During recent years, a multitude of developments regarding a laser scanner-based geometric state description were made. However, the areal deformation analysis still represents a challenge. In this paper, a spatio-temporal deformation model is

Accurate, short-term predictions of Earth orientation parameters (EOP) are needed for many real-time applications including precise tracking and navigation of interplanetary spacecraft, climate forecasting, and disaster prevention. Out of the EOP, the LOD (length of day), which represents the changes in the Earth's rotation rate, is the most challenging to predict since it is largely affected by the

Abstract This study presents a new method, called the Radial Interpolation Method, to interpolate data characterized by an approximately radial pattern around a relatively constrained central zone, such as the ground deformation patterns shown in many active volcanic areas. The method enables the fast production of short-term deformation maps on the base of spatially sparse ground deformation measurements

The Analysis Centers (ACs) of the International GNSS Service (IGS) have reprocessed a large global network of GPS tracking data from 1994.0 until 2014.0 or later. Each AC product time series was extended uniformly till early 2015 using their weekly operational IGS contributions so that the complete combined product set covers GPS weeks 730 through 1831. Three ACs also included GLONASS data from as

In this contribution, we present and analyze datasnooping in the context of the DIA method. As the DIA method for the detection, identification and adaptation of mismodelling errors is concerned with estimation and testing, it is the combination of both that needs to be considered. This combination is rigorously captured by the DIA estimator. We discuss and analyze the DIA-datasnooping decision probabilities

Incorrect modeling of troposphere delays is one of the major error sources for space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). Over the years, many approaches have been devised which aim at mapping the delay of radio waves from zenith direction down to the observed elevation angle, so-called mapping functions. This paper contains

We present an efficient and flexible alternative method to connect islands and offshore tide gauges with the height system on land. The method uses a regional, high-resolution hydrodynamic model that provides total water levels. From the model, we obtain the differences in mean water level (MWL) between tide gauges at the mainland and at the islands or offshore platforms. Adding them to the MWL relative

Time-varying Stokes coefficients estimated from GRACE satellite data are routinely converted into mass anomalies at the Earth's surface with the expression proposed for that purpose by Wahr et al. (J Geophys Res 103(B12):30,205-30,229, 1998). However, the results obtained with it represent mass transport at the spherical surface of 6378 km radius. We show that the accuracy of such conversion may be

Missing or incorrect consideration of azimuthal asymmetry of troposphere delays is a considerable error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). So-called horizontal troposphere gradients are generally utilized for modeling such azimuthal variations and are particularly required for observations at low elevation

The possibility of observing satellites with the very long baseline interferometry (VLBI) technique has been discussed for several years in the geodetic community, with observations of either existing satellites of the global navigation satellite systems or of satellites dedicated to realise a space tie. Such observations were carried out using the Australian telescopes in Hobart and Ceduna which,

A new methodology is proposed to estimate changes in the Earth's dynamic oblateness ([Formula: see text] or equivalently, [Formula: see text]) on a monthly basis. The algorithm uses monthly Gravity Recovery and Climate Experiment (GRACE) gravity solutions, an ocean bottom pressure model and a glacial isostatic adjustment (GIA) model. The resulting time series agree remarkably well with a solution based

The increasing accuracy and growing time span of Very Long Baseline Interferometry (VLBI) observations allow the determination of seasonal signals in station positions which still remain unmodelled in conventional analysis approaches. In this study we focus on the impact of the neglected seasonal signals in the station displacement on the celestial reference frame and Earth orientation parameters.

In connection with the work for the next generation VLBI2010 Global Observing System (VGOS) of the International VLBI Service for Geodesy and Astrometry, a new scheduling package (Vie_Sched) has been developed at the Vienna University of Technology as a part of the Vienna VLBI Software. In addition to the classical station-based approach it is equipped with a new scheduling strategy based on the radio

A method for validating the calibration parameters of the six accelerometers on board the Gravity field and steady-state Ocean Circulation Explorer (GOCE) from star tracker observations that was originally tested by an end-to-end simulation, has been updated and applied to real data from GOCE. It is shown that the method provides estimates of scale factors for all three axes of the six GOCE accelerometers

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum