For reasons mostly related to chip shape distortions, global navigation satellite system (GNSS) observations are corrupted by receiver-dependent biases. These are often stable in the long term, though numerically different depending on the signal frequency, satellite system and receiver manufacturer. Based on the mixed-differenced model combining undifferenced pseudorange with epoch-differenced carrier

For real-time precise orbit determination (POD) of low earth orbit (LEO) satellites, high-accuracy global navigation satellite system (GNSS) orbit and clock products are necessary in real time. Recently, the Japanese multi-GNSS advanced demonstration of orbit and clock analysis precise point positioning (PPP) service and the new generation of the Australian/New Zealand satellite-based augmentation

New GNSS signals have significantly augmented positioning service and promoted algorithmic innovations such as rapid PPP convergence. With the emerging of multifrequency signals, it becomes essential to thoroughly explore the contribution of third frequency pseudorange and carrier phase toward PPP. In this study, we research the role of the third frequency observations on accelerating PPP convergence

Precise positioning is a prerequisite for airborne high-quality magnetic data surveying. Modern airborne magnetic surveying platforms are usually composed of two parts: an aerial vehicle and a suspended magnetometer assembly. This configuration poses a challenge for georeferencing of data since the sensitivity of the magnetic sensors prohibits the placement of electronic positioning sensors directly

As a crucial parameter in the process of converting the zenith wet delay into precipitable water vapor at Global Navigation Satellite System (GNSS) stations, the weighted mean temperature (Tm) influences the accuracy of GNSS-based water vapor retrievals. We propose an improved atmospheric Tm modeling method by introducing sparse kernel learning to obtain high-accuracy and high-temporal-resolution Tm

As one of the leading technologies of real-time dynamic deformation monitoring, global navigation satellite system (GNSS) has been widely used in deformation monitoring. Multipath error is the primary error source that limits the application of GNSS high-precision deformation monitoring, which cannot be eliminated by the double-differenced technique. It is a problem to separate and mitigate multipath

The processing of cycle slip is one of the key techniques of carrier-phase-based high-precision positioning. As for the poor performance of the single-station inertial-aided cycle slip detection based on the tightly coupled integration system using pseudorange and Doppler measurements under inaccurate lever arm conditions, an improved real-time method based on ARIMA-GARCH (autoregressive integrated

Global Navigation Satellite Systems (GNSS) are enabled by atomic clocks, which provide the timing precision and accuracy required for the ranging measurements. Significant investments have been made and will continue to be made, to improve GNSS atomic clock technology and reduce the signal-in-space user range error. After providing a baseline by reviewing current GNSS satellite atomic clock technology

Based on the batch expectation–maximization (EM) and recursive least-squares algorithms, we develop a new recursive variance components estimation (Recursive-VCE) algorithm that applies a Kalman filter and validates it by a simulated kinematic precise point positioning (PPP) experiment and a PPP test on real-world data. The Recursive-VCE algorithm processes the observations in an epoch-by-epoch or

The signal-in-space ranging errors (SISREs), which are mainly dominated by clock errors, are computed for 18 BeiDou-3 (BDS-3) medium earth orbit satellites by comparing broadcast ephemeris values against precise values provided by Wuhan University from January 1 to December 31, 2019. For clock errors, a weighted least-square estimation method is carried out to eliminate the common clock error datum

Precise point positioning (PPP) using dual-frequency GNSS code and phase measurements has been the technique of choice for time and frequency transfer for more than a decade. Several analysis centers providing the satellite orbit and clock products used in PPP now make use of ambiguity resolution methods that preserve the integer nature of the carrier phase ambiguities, thus allowing the development

In the original article published, the references Wang et al. 2016a and Wang et al. 2016b are incorrect.

The occurrences of equatorial plasma bubble (EPB) irregularities over Asian and American sectors often show a different behavior due to significantly different geometries of the geomagnetic field. By using the GPS total electron content observations over equatorial and low latitudes sectors of Asian (about 120°E) and American (about 60°W) during 1997–2018, we present a comparative study of long-term

Precise Point Positioning Library (PPPLib) is a multi-GNSS data processing software designed to process multi-frequency data from GPS, BeiDou, Galileo, GLONASS, and QZSS. PPPLib is written in the C/C++ programming language. It can compile and run on both Linux and Windows operating systems. PPPLib mainly performs precise point positioning from single to triple frequency based on either ionospheric-free

EXtreme Gradient Boosting over Decision Trees (XGBoost or XGBDT) is a powerful tool to model a wide range of processes. We propose a new approach to create a global total electron content model, using machine-learning-based techniques, in particular, gradient boosting. The model is based on the Global Ionospheric Maps computed by Universitat Politècnica de Catalunya with a tomographic-kriging combined

The extended Kalman filter (EKF) is widely used for the integration of the global positioning system (GPS) and inertial navigation system (INS). It is well known that the EKF performance degrades when the system nonlinearity increases or the measurement covariance is not accurate. For the loosely coupled GPS/INS integration, accurate determination of the GPS measurement and its covariance is not a

We present a pure data-driven method to estimate vehicle dynamics from the measurements of sideslip and yaw rate in the use of GPS and inertial navigation system. The GPS and INS configuration provides vehicle position, velocity vector, vehicle orientation, and yaw rate observations. A new dynamic mode decomposition with control (DMDc) method denoises the state observations by adopting the total least-squares

The access to Android-based Global Navigation Satellite Systems (GNSS) raw measurements has become a strong motivation to investigate the feasibility of smartphone-based positioning. Since the beginning of this research, the smartphone GNSS antenna has been recognized as one of the main limitations. Besides multipath (MP), the radiation pattern of the antenna is the main site-dependent error source

The small-scale electron density irregularities in the ionosphere have a significant impact on the interruptions of Global Navigation Satellite System (GNSS) navigation and the accuracy of GNSS positioning techniques. The sporadic ionospheric E (Es) layer significantly contributes to the transient interruptions of signals (loss of lock) for GNSS tracking loops. These effects on the GNSS radio occultation

Modeling and understanding the statistical relationships between geophysical quantities is a crucial prerequisite for many geodetic applications. While these relationships can depend on multiple variables and their interactions, commonly used scalar methods like the (cross) correlation are only able to describe linear dependencies. However, particularly in regions with complex terrain, the statistical

Galileo satellites are equipped with laser retroreflector arrays for satellite laser ranging (SLR). In this study, we develop a methodology for the GNSS-SLR combination at the normal equation level with three different weighting strategies and evaluate the impact of laser observations on the determined Galileo orbits. We provide the optimum weighting scheme for precise orbit determination employing

Computerized ionospheric tomography (CIT) is an ill-posed inverse problem owing to insufficient data acquisition. Therefore, the ionospheric electron density (IED) distributions cannot be reconstructed accurately. Although many attempts have been made to deal with this issue, there is still a long way to go before it can be completely overcome. Specifically, the inverted IEDs of voxels without observational

The use of the GLONASS legacy signals for real-time kinematic positioning is considered. Due to the FDMA multiplexing scheme, the conventional CDMA observation model has to be modified to restore the integer estimability of the ambiguities. This modification has a strong impact on positioning capabilities. In particular, the ambiguity resolution performance of this model is clearly weaker than for

In computerized ionospheric tomography (CIT) with ground-based GNSS, the voxels without satellite-receiver ray traversing cannot be reconstructed directly. We present a CIT algorithm based on virtual reference stations (VRSs), called VRS–CIT, to decrease the number of unilluminated voxels and improve the precision of the estimated ionospheric electron density (IED). The VRSs are set at the nodes of

We present an improved clustering approach for grouping regional GPS stations with similar annual signals into four similarity levels. A newly introduced criterion, the annual phase difference among stations, reinforces the clustering process and resolves the discrepancy among the annual signals of stations classified into several clusters. Comparisons show that the improved method enhances the accuracy

Miniaturized atomic clocks with high frequency stability as local oscillators in global navigation satellite system (GNSS) receivers promise to improve real-time kinematic applications. For a number of years, such oscillators are being investigated regarding their overall technical applicability, i.e., transportability, and performance in dynamic environments. The short-term frequency stability of

Compared with the traditional GPS L1 C/A signal, the existing and emerging new-generation wideband GNSS signals suffer more severe distortions due to the nonlinear characteristics of a high-power amplifier (HPA) in the satellite transmitter. HPA nonlinearity can lead to in-band signal distortion and out-of-band spectral regrowth, which degrade the ranging performance of a GNSS receiver. Researchers

The GPS satellite transmitter antenna phase center offsets (PCOs) can be estimated in a global adjustment by constraining the ground station coordinates to the current International Terrestrial Reference Frame (ITRF). Therefore, the derived PCO values rest on the terrestrial scale parameter of the frame. Consequently, the PCO values transfer this scale to any subsequent GNSS solution. A method to derive

The reliability and performance of GPS receivers depend on the quality of the signal received, which can be largely affected by the interference caused by buildings, trees, and other obstacles. Since obstacles are always present in practical applications, several statistical representations have been developed along the years to measure, predict, and compensate errors induced by interferences. Two

The ionospheric gradient caused by spatial decorrelation is a crucial factor affecting the integrity of a ground-based augmentation system (GBAS). We processed GPS data from the Crustal Movement Observation Network of China from 2008 to 2018 with the long-term ionospheric anomaly monitoring method and then analyzed and verified a typical anomalous event. Compared with the wedge, plasma bubbles in the

The Global Navigational Satellite System (GNSS) technique is naturally sensitive to the geocenter motion, similar to all satellite techniques. However, the GNSS-based estimates of the geocenter used to contain more orbital artifacts than the geophysical signals, especially for the Z component of the geocenter coordinates. This contribution conveys a discussion on the impact of solar radiation pressure

The new global navigation satellite system real-time kinematic (RTK) receivers with tilt compensation extend the applicability of high-precision RTK positioning to previously restrictive environments since the pole is no longer required to be maintained vertically. The rapid and accurate initial alignment of the built-in low-cost inertial measurement unit (IMU) is a critical technical issue and currently

Precise estimation of satellite differential code biases (DCBs) plays a crucial role in precise ionospheric modeling, positioning, and timing. Due to the rank deficiency, a constraint or a datum is required in order to separate the satellite DCBs from the receiver DCBs. A common practice is to impose a zero-mean constraint on all the visible satellites. However, datum selection is affected by satellite

This investigation implements a least-squares methodology to fit a triaxial ellipsoid to a set of three-dimensional Cartesian coordinates obtained from present-day geospatial techniques, materializing the terrestrial frame ITRF2014. To approximate, as much as possible previous research on this topic, the original spatial values of the station coordinates were “reduced” to the surface of the EGM2008

In safety-critical applications, such as the Ground-Based Augmentation System for precision approaches in civil aviation, it is important to safeguard users under the case of ephemeris failures. For CAT II/III approaches, different ephemeris monitors with approaches for ambiguity resolution are proposed with the double differenced carrier phase as the test statistics. The continuity risks introduced

In the original version of this article, equation (9) was displayed incorrectly.

The realization of Coordinated Universal Time, one of the tasks of the International Bureau of Weights and Measures, relies on a network of international time links which currently is organized in a star-like scheme that links all contributing laboratories. GPS signal reception is the technique most widely employed by the laboratories. The PTB currently plays a unique role in the process due to its

The intra-system biases, including differential code biases (DCBs) and differential phase biases (DPBs), are generally defined as the receiver-dependent hardware delays between different frequencies in a single global navigation satellite system (GNSS) constellation. Likewise, the inter-system biases (ISBs) are the differential code and phase hardware delays between different GNSSs, which are of great

High-quality satellite orbits and clocks are necessary for multi-GNSS precise point positioning and timing. In undifferenced GNSS solutions, the quality of orbit and clock products significantly influences the resulting position accuracy; therefore, for precise positioning in real time, the corrections for orbits and clocks are generated and distributed to users. In this research, we assess the quality

A crucial issue of low earth orbit (LEO) navigation augmentation satellite constellation is to obtain a satellite clock of high medium–long stability (i.e., averaging time of 10–10,000 s) using a disciplined oscillator to reduce satellite size, weight, power consumption and cost, instead of using a large, heavy and expensive space atomic clock. To resolve this difficulty, we propose a new global navigation

Global Navigation Satellites Systems have been greatly developed in recent years, but receivers usually suffer the undesired measurement bias errors caused by multipath incidence in an urban area. We propose an effective subspace-based estimator cooperating with the conventional delay-locked loop (DLL) for Global Positioning System L1 C/A Signal. With the help of the multi-antenna, the incident rays

Integration of both global positioning system (GPS) and inertial navigation system (INS) assures a continuous and accurate navigation system. In low-cost low-precision micro-electromechanical system (MEMS)-based INS/GPS integration navigation systems, one of the major concerns is high-level stochastic noise and uncertainties existing in INS sensors and complex model of real noisy data. In such uncertainty-oriented

In the original article, some typos regarding Eq. (1) and respective sentence are corrected, and corrections are made to a sentence in section “Effect of the frequency difference on the PLL and DLL”.

The requirement for ARAIM continuity risk due to the monitor false alarm has been outlined in earlier works for ARAIM development (WG-C in ARAIM technical subgroup milestone 3 report, 2016). However, the expected continuity risk comes from an underlying conservative assumption that the correlation between multiple monitors for fault detection is negligible. Thus, we investigate the effect of the cross-correlation

Real-time users cannot carry out real-time precise point positioning (RT-PPP) because they cannot receive real-time service (RTS) products from the international GPS service (IGS) in the case of interrupted communication. We address this issue by introducing a stable particle swarm optimized wavelet neural network (PSOWNN) to predict the short-term satellite clock bias in real time accurately. The

The growing demand for positioning, navigation and timing services is boosting the development of new signal systems that are gradually being adopted by Global Navigation Satellite System (GNSS), such as the BDS, the Galileo and the modernized GPS. A common feature of these new signal systems is that they have longer pseudorandom noise (PRN) code lengths than the old ones, which greatly improves the

Global navigation satellite systems (GNSS) are widely used for safety-of-life positioning applications. Such applications require high integrity, availability, and continuity of the positioning service. Integrity is assessed by the definition of a protection level, which is an estimation of the maximum positioning error at extremely low probability levels. The emergence of multi-frequency civilian

The Tianping-1B is a 20-kg low earth orbit nanosatellite with a commercial multi-GNSS receiver based on a microelectromechanical system. This receiver collects concurrent code and phase dual-frequency measurements from the global positioning system (GPS) and the second and third generations of the BeiDou Global Navigation Satellite System (i.e., BDS-2 and BDS-3). However, BDS-3 signals with pseudorandom

Peak ground displacement (PGD) derived from high-rate Global Navigation Satellite System (GNSS) can be used to determine, i.e., the estimate or scale the earthquake magnitude in real time without magnitude saturation experienced by seismic sensors at large earthquakes. Compared with relative positioning or Precise Point Positioning (PPP), the variometric approach can calculate station velocity using

BDS-3 currently has 28 operational satellites in orbit, of which 27 IGSO/MEO satellites provide open services on five frequencies simultaneously. In particular, the linear combinations of the BDS-3 B1C/B1I/B2a signals have significant benefits in reducing the influence of ionospheric delay error as well as improving ambiguity estimation and positioning accuracy. The presented optimal ionosphere-free

Global navigation satellite system (GNSS) remote sensing of the troposphere, called GNSS meteorology, is already a well-established tool in post-processing applications. Real-time GNSS meteorology has been possible since 2013, when the International GNSS Service (IGS) established its real-time service. The reported accuracy of the real-time zenith total delay (ZTD) has not improved significantly over

The El Niño Southern Oscillation (ENSO) signatures interpreted in different tropical tropopause layer (TTL) parameters are investigated by using long-term Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC)-1 radio occultation temperature data from July 2006 to March 2019. The TTL parameters include the cold point tropopause height (CPT-H) and corresponding temperature

The length of the convergence time in Precise Point Positioning (PPP) is a result of unmodeled errors. The tropospheric delay error is considered a major error source that affects the PPP solution accuracy and convergence time, especially in the height coordinates. Recent research showed that Numerical Weather Models (NWM)-based tropospheric correction models are superior to traditional empirical tropospheric

One of the most significant advantages of multiple frequencies is that it can improve the success rate of ambiguity resolution, such as the three-frequency carrier ambiguity resolution (TCAR) method. So far, the global BeiDou-3 navigation satellite system already provides four frequencies. Hence, we systematically study the models and methods of four-frequency carrier ambiguity resolution (FCAR) by

In the original article, some typos regarding Eq. (3) and Table 9 are introduced.

Global Navigation Satellite System (GNSS) interferometric reflectometry, also known as the GNSS-IR, uses data from geodetic-quality GNSS antennas to extract information about the environment surrounding the antenna. Soil moisture monitoring is one of the most important applications of the GNSS-IR technique. This manuscript presents the main ideas and implementation decisions needed to write the Python

Fast ambiguity resolution is a major challenge for GLONASS phase-based applications. The integer-estimable frequency-division multiple-access (IE-FDMA) model succeeds in formulating a set of estimable GLONASS phase ambiguities and preserving the integer property, to which the classical integer ambiguity resolution, typically the least-squares ambiguity decorrelation adjustment (LAMBDA), becomes readily

We consider robotic calibrations of GNSS receiving antennas in an open field environment. At the newly built test range, the sky is unobstructed down to 10° elevation; an industrial robot with six degrees of freedom is employed. The antenna calibration algorithm uses single differences of carrier phases. Two types of antennas are tested, a common choke ring ground plane antenna and a rover-type antenna

GPS Block IIF satellites are able to redistribute the transmit power between the signal components. This ability is called flex power, and it has been developed as a remedy against jamming. Since it is operationally not possible to increase the transmit power for all signal components simultaneously, a redistribution between them is necessary under certain operational situations. Flex power has been

Based on a global GNSS tracking network, the B1I/B3I ionospheric-free phase center offsets (PCOs) are estimated for BeiDou Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. Peak-to-peak variations of up to several decimeters or even meters that depend on the solar radiation pressure (SRP) model and the sun elevation angle above the orbital plane (β angle) are found in the