Precise point positioning (PPP) has proved its capacity to provide centimetre-level position solutions in open sky environments. However, the technique still suffers from relatively long initial convergence times. Research has proved the potential of ambiguity resolution (AR) to reduce the convergence time and three main methods are used to perform AR: the fractional cycle bias method, the decoupled

The elliptical harmonic method for gravity forward computation of two-dimensional (2D) bodies with constant, polynomial and exponential density distributions is presented. This paper gives the elliptical harmonic expansions for the gravity field of 2D bodies mainly including the gravitational attractions and gradients, and the conversions from the surface integral expressions of the elliptical harmonic

Within this work, a new geodetic very long baseline interferometry (VLBI) scheduling approach inspired by evolutionary processes based on selection, crossover and mutation is presented. It mimics the biological concept “surviving of the fittest” to iteratively explore the scheduling parameter space looking for the best solution. Besides providing high-quality results, one main benefit of the proposed

The attempt to quantify the corrections of lunisolar nutation components was made after analysis of six sets of Earth’s orientation parameters (EOP). The deviations of the long-term nutation components about IAU2006/IAU2000A precession–nutation model are consistent with the uncertainties suggested by Mathews et al. (J Geophys Res Solid Earth, 2002. https://doi.org/10.1029/2001JB000390), but they exceed

We apply three spherical-harmonic-based techniques to deliver external gravitational field models of the asteroid (101955) Bennu within its circumscribing sphere. This region is known to be peculiar for external spherical harmonic expansions, because it may lead to a divergent series. The studied approaches are (i) spectral gravity forward modelling via external spherical harmonics, (ii) the least-squares

The intradecadal variations in length-of-day (LOD) and their time-varying characteristics still need to be further studied. Given that the corresponding signal periods on the intradecadal scales are quite close to each other and the span of currently observed ΔLOD data (i.e., 1962–2019, only 57 years) is not long enough, accurate detection of these signals depends on using effective mathematical method

We present results from observation, correlation and analysis of interferometric measurements between the three geodetic very long baseline interferometry (VLBI) stations at the Onsala Space Observatory. In total, 25 sessions were observed in 2019 and 2020, most of them 24 h long, all using X band only. These involved the legacy VLBI station ONSALA60 and the Onsala twin telescopes, ONSA13NE and ONSA13SW

This paper studies the contribution of airborne gravity data to improvement of gravimetric geoid modelling across the mountainous area in Colorado, USA. First, airborne gravity data was processed, filtered, and downward-continued. Then, three gravity anomaly grids were prepared; the first grid only from the terrestrial gravity data, the second grid only from the downward-continued airborne gravity

In the frame of the International Association of Geodesy Joint Working Group 2.2.2 “The 1 cm geoid experiment”, terrestrial and airborne gravity datasets along with GPS/leveling data were made available for the comparison of different geoid modeling methods and techniques in the wider area of Colorado, USA. We discuss the methods and procedures we followed for computing gravimetric quasi-geoid and

The next-generation, broadband geodetic very long baseline interferometry system, named VGOS, is developing its global network, and VGOS networks with a small size of 3–7 stations have already made broadband observations from 2017 to 2019. We made quality assessments for two kinds of observables in the 21 VGOS sessions currently available: group delay and differential total electron content (\(\delta

Spherical harmonic analysis is widely used in all aspects of geoscience. Exact quadrature methods are available for the spherical harmonic analysis of band-limited point values at the grid points of equiangular and Gaussian grids. However, no similarly exact quadrature methods are available for the spherical harmonic analysis of area mean values over the blocks delineated by these grids. In this study

The gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging

The Colorado geoid experiment was initiated and organized as a joint study by the Joint Working Group (JWG) 2.2.2 (1-cm geoid experiment) of the International Association of Geodesy (IAG) in 2017, and different institutions and research groups contributed to this study. The aim of this experiment was to clarify the repeatability of gravity potential values as International Height Reference System (IHRS)

Variations of marine gravity reflect mass changes in Earth’s interior, including magma motions during volcanic eruption, which manifest in submarine mass transports. Absolute gravimeters have been used to detect and study evolutions of magma mass motions, however, only for land volcanoes. Here for the first time, we used radar altimeter-derived time-varying marine gravity fields, corresponding to before

Ambiguity resolution of a single receiver is becoming more and more popular for precise GNSS (Global Navigation Satellite System) applications. To serve such an approach, dedicated satellite orbit, clock and bias products are needed. However, we need to be sure whether products based on specific frequencies and signals can be used when processing measurements of other frequencies and signals. For instance

Single-station PPP-RTK is a special case of PPP-RTK in that corrections are computed, instead of a network, by only one single GNSS receiver. The present contribution aims to develop a framework to generate multi-epoch, single-station corrections, thereby providing PPP-RTK users the capability to time-predict corrections that are subject to time delay or latency. By presenting analytical expressions

We have developed a broadband VLBI (very long baseline interferometry) system inspired by the concept of the VLBI Global Observing System (VGOS). The new broadband VLBI system was implemented in the Kashima 34 m antenna and in two transportable stations utilizing 2.4 m diameter antennas. The transportable stations have been developed as a tool for intercontinental frequency comparison but are equally

Different designs of receiver correlators and front ends will cause different biases in terms of the pseudorange. In this paper, we present an algorithm to derive GNSS receiver-dependent code biases by estimating an additional code bias for each satellite based on different orbit and clock products and apply the calibrated biases in user positioning. One-month data from 117 globally distributed multi-GNSS

A long-term drift in polar motion (PM) has been observed for more than a century, and Glacial Isostatic Adjustment (GIA) has been understood as an important cause. However, observed PM includes contributions from other sources, including contemporary climate change and perhaps others associated with Earth’s interior dynamics. It has been difficult to separate these effects, because there is considerable

In deformation analysis, invariant strain descriptors that are independent of the coordinate system are significant. An approach is proposed to determine the strain tensor and invariant strain quantities through the 3D retrieved co-event displacement of differential interferometric synthetic aperture radar (DInSAR). An optimal cell count is selected based on the proposed rule-of-thumb formula. This

We carry out a comprehensive analysis and assessment of degree-2 gravitational changes ΔC21, and ΔS21, estimated using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO), satellite laser ranging (SLR), Earth Orientation Parameters (EOP), and geophysical models over the period April 2002–February 2020. The four independent estimates of ΔC21 and ΔS21 variations agree well over

Water vapor plays an important role in Earth’s weather and climate processes and energy transfer. Plenty of techniques have developed to monitor precipitable water vapor (PWV), but joint use of different techniques has some problems, including systematic biases, different spatiotemporal coverages and resolutions among different datasets. To address the above problems and improve the data utilization

In 2015, the International Association of Geodesy defined the International Height Reference System (IHRS) as the conventional gravity field-related global height system. The IHRS is a geopotential reference system co-rotating with the Earth. Coordinates of points or objects close to or on the Earth’s surface are given by geopotential numbers C(P) referring to an equipotential surface defined by the

In 2017, the new generation satellite-based augmentation system (SBAS) test-bed was initiated by Australia and New Zealand, which supports the dual-frequency multi-constellation (DFMC) positioning with both GPS and Galileo signals. This new SBAS DFMC service allows the elimination of the first-order term of the ionospheric delays, and extends the service area to the entire footprint of the geostationary

Ionospheric scintillation refers to rapid and random fluctuations in radio frequency signal intensity and phase, which occurs more frequently and severely at high latitudes under strong solar and geomagnetic activity. As one of the most challenging error sources affecting Global Navigation Satellite System (GNSS), scintillation can significantly degrade the performance of GNSS receivers, thereby leading

Aside from the ionospheric total electron content (TEC) information, root-mean-square (RMS) maps are also provided as the standard deviations of the corresponding TEC errors in global ionospheric maps (GIMs). As the RMS maps are commonly used as the accuracy indicator of GIMs to optimize the stochastic model of precise point positioning algorithms, it is of crucial importance to investigate the reliability

With the development of multi-GNSS, the differential code bias (DCB) has been an increasing interest in the multi-frequency multi-GNSS community. Unlike code division multiple access (CDMA) mode used by GPS, BDS and Galileo etc., the GLONASS signals are modulated with frequency division multiple access (FDMA) mode. Up to now, the FDMA-aware GLONASS bias products are provided by two individual IGS analysis

Global pressure and temperature (GPT) models are widely available and easy-to-use in tropospheric delay estimation and GNSS water vapor retrieval, but cannot capture the diurnal and semidiurnal variations that add uncertainty to tropospheric delay determinations. This paper introduces an improved global pressure and temperature model (IGPT) established using 10 years hourly ERA5 dataset provided by

Global ionosphere maps (GIM) computed from dual-frequency GNSS measurements have been widely used for monitoring ionosphere as well as providing ionospheric corrections in Space Geodesy since 1998. This work focuses on a comprehensive study of the influence of time resolution on GIM performance. One and a half solar cycle of the IGS GIM with higher time resolution and accuracy (the UPC-IonSAT Quarter-of-an-hour

The new challenges related to the monitoring of Earth’s shape and motion have led the global geodetic observing system to set more stringent requirements on the precision and stability of the terrestrial reference frame (TRF). The achievement of this ambitious goal depends on the improvement of space geodesy techniques, satellite laser ranging (SLR) in particular, being the main instrument for TRF

Construction of a coseismic displacement grid model (hereafter referred to as the grid model) is a critical strategy for maintaining the precision of the semi-kinematic reference frame. However, no unequivocal criteria have yet been suggested for the timing of grid model construction. To clarify this timing, the observations of continuous global navigation satellite system in Taiwan were evaluated

Despite the high complexity of the real world, linear regression still plays an important role in estimating parameters to model a physical relationship between at least two variables. The precision of the estimated parameters, which can usually be considered as an indicator of the solution quality, is conventionally obtained from the inverse of the normal equations matrix for which intensive computation

Postglacial rebound in Fennoscandia causes striking trends in gravity measurements of the area. We present time series of absolute gravity data collected between 1976 and 2019 on 12 stations in Finland with different types of instruments. First, we determine the trends at each station and analyse the effect of the instrument types. We estimate, for example, an offset of 6.8 μgal for the JILAg-5 instrument

Laser altimeters are commonly used in planetary research for their high geodetic accuracy. A key procedure in processing of laser altimeter data is the geolocation. In this process, the time-of-flight measurements are converted to coordinates of laser pulse footprints on the surface of the target body. Here, we present a consistent and systematic formulation of three commonly used geolocation models

GNSS observations stochastic model influences all subsequent stages of data processing, from the possibility to reach the optimal parameters estimation, to the reliability and quality control of the solution. Nowadays, an uncontrolled use of GNSS stochastic models is common for both data processing and simulation missions, especially in commercial GNSS software packages. As a result, the variance–covariance

Understanding the noise content of the Global Positioning System (GPS) coordinate time series is a prerequisite for a realistic assessment and uncertainty of unknown parameters. Variance component estimation methods [e.g., restricted maximum likelihood estimator (REML)] are used to assess the noise content of GPS coordinate time series. For large-scale data, namely over a wide range of spatial and

Due to the lack of a natural reference for the absolute acceleration of free fall and gravity, absolute gravimeters are compared at international comparisons, where the gravity reference is realized based on a set of precise absolute measurements and the functional model for their processing. The main estimates of comparisons, specifically, the reference values, deviations of gravimeters (biases) and

Assessment of mass-induced sea level (MISL) variability in the Tropical Indian Ocean (TIO) was studied using observations from the Gravity Recovery and Climate Experiment (GRACE) during 2003–2017 in conjunction with the steric effects in the sea level anomaly as measured by satellite altimeters. Two steric sea levels were estimated from the ocean model analysis and Argo gridded temperature and salinity

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