The strength of the GNSS precise positioning model degrades in cases of a lack of visible satellites, poor satellite geometry or uneliminated atmospheric delays. The least-squares solution to a weak GNSS model may be unreliable due to a large mean squared error (MSE). Recent studies have reported that Tikhonov’s regularization can decrease the solution’s MSE and improve the success rate of integer

The paper presents a coherent, original theory and an effective algorithm to calculate the surface area of a geodesic polygon, i.e. the area on an ellipsoid of revolution limited by geodesics, connecting pairs of subsequent vertices of known geographical coordinates. Using the cylindrical coordinate system and introducing an equatorial geodesic triangle, the novel strict recursive formulas were derived

We propose a novel dictionary learning add-on for the Inverse Problem Matching Pursuit (IPMP) algorithms for approximating spherical inverse problems such as the downward continuation of the gravitational potential. With the add-on, we aim to automatize the choice of dictionary and simultaneously reduce the computational costs. The IPMP algorithms iteratively minimize the Tikhonov–Phillips functional

In this study, we compare six commonly used methods for the downward continuation of airborne gravity data. We consider exact and noisy simulated data on grids and along flight trajectories and real data from the GRAV-D airborne campaign. We use simulated and real surface gravity data for validation. The methods comprise spherical harmonic analysis, least-squares collocation, residual least-squares

In this paper, the methods retrieving tide and SWH using reflected BeiDou GEO satellite signals are proposed, and a data-driven method is proposed to calibrate sea state bias of the retrieved tide. In addition, an estimator combining multi-satellite observation based on linear unbiased minimum variance (LUMV) is developed to improve the retrieved precision. The B1I signal experiments in Qingdao and

Least-squares collocation (LSC) is a widely used method applied in physical geodesy to separate observations into a signal and noise part but has received only little attention when interpolating velocity fields. The advantage of the LSC is the possibility to filter and interpolate as well as extrapolate the observations. Here, we will present several extensions to the traditional LSC technique, which

Efficient Variance Component Estimation (VCE) is significant to optimal data combination in large-scale least-squares problems as those encountered in satellite geodesy, where millions of observations are jointly processed to estimate a huge number of unknown parameters. In this paper, an efficient VCE algorithm with rigorous trace calculation is proposed based on the local–global parameters partition

An unwritten rule to resolve GNSS ambiguities in precise point positioning (PPP-AR) is that users should follow faithfully the frequency choices and observable combinations mandated by satellite clock and phase bias providers. Switching to other frequencies of measurements requires that the satellite clocks be converted, albeit in a roundabout way, to agree with the new frequencies of code biases.

Customary confidence regions do not truly reflect in the majority of our geodetic applications the confidence one can have in one’s produced estimators. As it is common practice in our daily data analyses to combine methods of parameter estimation and hypothesis testing before the final estimator is produced, it is their combined uncertainty that has to be taken into account when constructing confidence

In recent years, numerous low earth orbit (LEO) satellites have been launched for different scientific tasks such as the Earth’s magnetic field, gravity recovering and ocean altimetry. The LEO satellites can cover the ocean area and are less affected by atmospheric delays and multipath errors, which provides new opportunities for calibrating the phase biases of the Global Navigation Satellite System

Although modern global geometric reference frames (GRFs) such as the International Terrestrial Reference Frame (ITRF) can be used anywhere on Earth, regional reference frames (RRFs) are still used to densify geodetic control and optimize solutions for continental-scale areas and national purposes. Such RRFs can be formed by densifying the ITRF, utilizing GPS / GNSS stations common to both the ITRF

Due to high computation demand, slant total delays (STDs) determined by 3D ray tracing cannot be widely used in geodetic analysis. This study proposes a novel fast 3D ray tracing approach, named APM-3D, based on piecewise algorithm and strictly matched step size. It can produce more than 1000 rays per second with a single core PC, which satisfies the operational applications of slant delays in mapping

Carrier-phase integer ambiguity resolution (AR) is the key to improving the positioning accuracy of precise point positioning (PPP). However, in theory, the integer property of ambiguities in PPP are destroyed due to the absorption of phase biases. In this study, we analyzed a set of clock products consisting of a code clock, phase clock and wide-lane (WL) bias based on the decoupled clock (DCK) model

The precise estimation of geodetic parameters using single- and double-differenced SLR observations is investigated. While the differencing of observables is a standard approach for the GNSS processing, double differences of simultaneous SLR observations are practically impossible to obtain due to the SLR basic principle of observing one satellite at a time. Despite this, the availability of co-located

The best integer equivariant (BIE) estimator for the multivariate t-distribution was introduced in Teunissen (J Geod, 2020. https://doi.org/10.1007/s00190-020-01407-2), where it was shown that the BIE-weights will be different from that of the normal distribution. In this contribution, we analyze these BIE estimators while making use of multi global navigation satellite system (GNSS) data. The BIE-estimators

To deal with inconsistency between Global Navigation Satellite System (GNSS) multi-frequency data and International GNSS Service (IGS) clock product, we propose a unified model for GNSS satellite inter-frequency clock bias (IFCB) estimation and correction based on the IGS clock datum. The proposed model is rigorously derived by three sequential steps. First, by means of accurate modeling of the time-variant

Ocean tide aliasing is one of the largest error sources in satellite gravimetry. Despite its importance, the aliasing mechanism of ocean tides in satellite gravimetry is only partially understood. This paper explains tidal aliasing as a two-step mechanism. The primary aliasing is caused by orbit undersampling of original tidal signals. The secondary aliasing is due to undersampling of the primary aliasing

In order to fully exploit the advantages of both precise point positioning (PPP) and real-time kinematic (RTK), a PPP–RTK method has been proposed to achieve centimeter-level positioning by applying the rapid integer ambiguity resolution, which is now widely implemented in some commercial systems such as Trimble RTX-Fast and NavCom StarFire. Nevertheless, the performance of PPP–RTK faces with restrictions

Global navigation satellite systems (GNSS) can provide high-accuracy positioning services in the open environment, while they have poor performance in shadowed regions. Pseudolite (PL) systems, with flexible deployment, can carry on the role of GNSS to provide high-accuracy positioning services in the case of GNSS failure. Ground-based precise point positioning (gPPP) for pseudolite systems allows

The establishment of a national gravity standard based on international metrological standards is a high priority for the Estonian geodetic, geophysical, and metrological community. With the presently available gravimetric instruments and models, geoscientific research at the level of \(10^{-9}\) g is possible and requires a homogeneous performance of the definition of gravity standards and of measurements

The Galileo High Accuracy Service (HAS) is a new capability of the European Global Navigation Satellite System that is currently under development. The Galileo HAS will start providing satellite orbit and clock corrections (i.e. non-dispersive effects) and soon it will also correct dispersive effects such as inter-frequency biases and, in its full capability, ionospheric delay. We analyse here an ionospheric

Accurate three-dimensional (3D) atmospheric water vapor distribution, which plays a crucial role in understanding the meteorological phenomena and hazards, has been successfully retrieved using Global Navigation Satellite System (GNSS) tomography technique. Presently, the problem of the ill-posed tomography system, that results from poor GNSS acquisition geometry, remains a vital issue to be solved

The primary objective of the 1-cm geoid experiment in Colorado (USA) is to compare the numerous geoid computation methods used by different groups around the world. This is intended to lay the foundations for tuning computation methods to achieve the sought after 1-cm accuracy, and also evaluate how this accuracy may be robustly assessed. In this experiment, (quasi)geoid models were computed using

The primary goal of the geodetic Very Long Baseline Interferometry (VLBI) technique is to provide highly accurate terrestrial and celestial reference frames as well as Earth orientation parameters. In compliance with the concept of VLBI, additional parameters reflecting relative offsets and variations of the atomic clocks of the radio telescopes have to be estimated. In addition, reality shows that

Global navigation satellite system (GNSS) velocity fields generally contain outliers due to environmental interference, local crustal activities, or strong seismic activities, which significantly affect the parameter estimation of the crustal deformation model. The robust M estimation can be used to improve the accuracy of the parameter estimation while retaining as much GNSS observation information

The main climatological features of the ionospheric equivalent slab thickness (τ) for the Northern hemisphere midlatitudes are analyzed. F2-layer peak electron density values recorded at three midlatitude ionospheric stations (Chilton 51.5° N, 0.6° W, U.K.; Roquetes 40.8° N, 0.5° E, Spain; Wallops Island 37.9° N, 75.5° W, USA) and vertical total electron content values from colocated ground-based Global