Global Navigation Satellite System Constellations Research Articles

High-Rate Attitude Determination of Moving Vehicles With GNSS: GPS, BDS, GLONASS, and Galileo

We investigate the long-term performance and improvement of high-rate multiconstellation Global Navigation Satellite System (GNSS) or multi-GNSS attitude determination in a dynamical environment and evaluate how much each GNSS contributes to such an improvement with applications to land vehicle navigation. We build a multiantenna GNSS system with three nondedicated receivers and conduct two experiments with quad-constellations in GNSS-friendly and GNSS-challenged environments on January 19 and 23, 2018, respectively. A high-grade inertial measurement unit (IMU) provides a reference of comparison for dynamic attitude solutions. In the static case, the global positioning system (GPS), BeiDou navigation satellite system (BDS), and GLObal NAvigation Satellite System (GLONASS) single-constellation solutions have basically the same performance for both experiments. In the dynamic case, GPS achieves the best accuracy in the experiment on January 19, while on January 23, GPS and GLONASS achieve very similar accuracy and significantly outperform BDS in the pitch and roll components. The different dynamic performances of these single constellations are primarily attributed to their differences in observation noise level and satellite geometry strength. By combining GPS, BDS, GLONASS, and Galileo, the multi-GNSS solution performs significantly better than any single-constellation solution. The average improvements in the dynamic cases are 26.2%, 40.7%, and 36.0% on January 19 and 19.2%, 30.0%, and 36.2% on January 23 in the yaw, pitch, and roll components, respectively. The attitude solutions on January 19 are always better determined than on January 23 in the dynamic cases, which should clearly indicate the importance of combining multiple GNSS constellations and the benefit of more observed satellites and a stronger satellite geometry in GNSS-challenged environments. We also introduce the concept of “influence rate” and quantitatively analyze the contribution of each GNSS system to the combined attitude solution.

Electron Density Reconstruction by Ionospheric Tomography From the Combination of GNSS and Upcoming LEO Constellations

AbstractComputerized ionospheric tomography (CIT) based on Global Navigation Satellite System (GNSS) data is a worthwhile project. However, predominant issues like unevenly distributed stations, lack of data, and high‐elevation GNSS signals could affect the precise information about the ionosphere. To address this problem, many previous studies were mainly improving tomographic algorithms, rather than incorporating multisource data such as data from rapidly developed upcoming Low‐Earth‐Orbit (LEO) satellites. In this paper, the potential improvements of GNSS‐based ionospheric tomography at a global scale by combining the upcoming LEO constellations is investigated. On this basis, some numerical experiments were conducted to evaluate the performances of LEO‐augmented GNSS ionospheric tomography. Specifically, the slant total electron contents (STEC) required for ionospheric tomography from ground receivers to GNSS (including GPS, GLONASS, BDS, and Galileo) and LEO satellites are simulated by the international reference ionosphere (IRI‐2016) model during low and high solar activity in 2018 and 2014, respectively. The simulated STEC values from single‐, double‐ and quad systems of GNSS constellations were first used for ionospheric tomography. Afterward, the GNSS‐based STEC values were combined with the LEO‐based simulated STEC values. The STEC values directly derived from the IRI‐2016 model that have not been used in ionospheric tomography were used as independent references. The results showed that the GNSS + LEO solutions outperform the GNSS‐only solutions overall, the STEC values obtained by GNSS + LEO solutions are more consistent with the STEC references during both high and low years of solar activity. In comparison with the STEC references, the RMS values of the CIT‐derived STEC for GNSS‐only solutions can be decreased by 15% and 20.3% at most during low and high years of solar activity, respectively.

Multi-GNSS Software Receiver Design Optimization for Accuracy Improvement

Abstract: Recently, tremendous research has been conducted on Global navigation satellite systems (GNSS) software receivers to better serve the current challenging environments that suffers from multipath fading. Therefore, the development of GNSS receivers has seen a new rush toward a multi-GNSS as a solution for fading problems. In this paper, a multi-GNSS software receiver is designed, optimized, and its performance is presented. The implemented software receiver covers three different signals from two GNSS constellations, namely GPS L1, GPS L2, and Galileo E1. In this paper. the fundamentals of stages of GNSS signal reception (acquisition, tracking, and navigation) are discussed where each stage is customized and optimized for each considered signal and the stage of mutli-GNSS data combination is optimized afterword. The performance of the optimized multi-GNSS software receiver is examined under different combination scenarios where the Least-Square Estimation (LSE) method using precise positioning (PP) algorithms is adopted. Results showed that using multi-GNSS receiver enhances the accuracy of Position, Velocity, and Timing (PVT) solution. Keywords: GNSS, PVT, GPS, Galileo, and accuracy

Precision-Aided Partial Ambiguity Resolution Scheme for Instantaneous RTK Positioning

The use of carrier phase data is the main driver for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). However, carrier phase observations are ambiguous by an unknown number of cycles, and their use in RTK relies on the process of mapping real-valued ambiguities to integer ones, so-called Integer Ambiguity Resolution (IAR). The main goal of IAR is to enhance the position solution by virtue of its correlation with the estimated integer ambiguities. With the deployment of new GNSS constellations and frequencies, a large number of observations is available. While this is generally positive, positioning in medium and long baselines is challenging due to the atmospheric residuals. In this context, the process of solving the complete set of ambiguities, so-called Full Ambiguity Resolution (FAR), is limiting and may lead to a decreased availability of precise positioning. Alternatively, Partial Ambiguity Resolution (PAR) relaxes the condition of estimating the complete vector of ambiguities and, instead, finds a subset of them to maximize the availability. This article reviews the state-of-the-art PAR schemes, addresses the analytical performance of a PAR estimator following a generalization of the Cramér–Rao Bound (CRB) for the RTK problem, and introduces Precision-Driven PAR (PD-PAR). The latter constitutes a new PAR scheme which employs the formal precision of the (potentially fixed) positioning solution as selection criteria for the subset of ambiguities to fix. Numerical simulations are used to showcase the performance of conventional FAR and FAR approaches, and the proposed PD-PAR against the generalized CRB associated with PAR problems. Real-data experimental analysis for a medium baseline complements the synthetic scenario. The results demonstrate that (i) the generalization for the RTK CRB constitutes a valid lower bound to assess the asymptotic behavior of PAR estimators, and (ii) the proposed PD-PAR technique outperforms existing FAR and PAR solutions as a non-recursive estimator for medium and long baselines.

GROOPS: A software toolkit for gravity field recovery and GNSS processing

The Gravity Recovery Object Oriented Programming System (GROOPS) is a software toolkit written in C++ that enables the user to perform core geodetic tasks. Key features of the software include gravity field recovery from satellite and terrestrial data, the determination of satellite orbits from global navigation satellite system (GNSS) measurements, and the computation of GNSS constellations and ground station networks. Next to raw data processing, GROOPS is capable to operate on time series and spatial data to directly analyze and visualize the computed data sets. Most tasks and algorithms are (optionally) parallelized through the Message Passing Interface, thus the software enables a smooth transition from single-CPU desktop computers to large distributed computing environments for resource intensive tasks. For an easy and intuitive setup of complex workflows, GROOPS contains a graphical user interface to create and edit configuration files. The source code of the software is freely available on GitHub (https://github.com/groops-devs/groops) together with documentation, a cookbook with guided examples, and step-by-step installation instructions.

Analysis of multi‐constellation GNSS receiver performance utilizing 1‐st side‐lobe signal on the use of SSV for KPS satellites

A numerical analysis is conducted for assessing the feasibility on the use of Global Navigation Satellite System (GNSS) receivers for Korea Positioning System (KPS) satellites in space service volume (SSV). KPS is planned to provide a navigation and timing service by constructing seven satellites over the Korean Peninsula, which will orbit above the GNSS constellation in SSV. The major problems caused by such orbital characteristics include reduced satellite visibility due to poor geometric diversity and weak signals, causing an increase in the user range error (URE). To address these constraints, this study considers multi-GNSS and 1-st side-lobe signal utilization scenarios. More specifically, the GNSS satellite visibility, geometric dilution of precision, carrier-to-noise ratio, URE, and navigation error for KPS satellites in SSV are analysed through a numerical simulation. A trade-off between visibility and received signal power as well as their effects on positioning accuracy is analysed to describe the utility of side-lobe signals. Finally, based on numerical analysis of the simulation results, this verifies the applicability of GNSS SSV for KPS satellites through multi-GNSS and side-lobe utilization scenarios.

First spaceborne demonstration of BeiDou-3 signals for GNSS reflectometry from CYGNSS constellation

The full constellation of Chinese Global Navigation Satellite System (GNSS) BeiDou-3 has been deployed completely and started fully operational service. In addition to providing global Positioning, Navigation and Timing (PNT) services, the BeiDou-3 satellites transmissions can also be used as the sources of illumination for Earth Observation (EO) with a bistatic radar configuration. This innovative EO concept, known as GNSS reflectometry (GNSS-R), allows to measure the Earth surface characteristics at high resolution via the reflected L-band radar signals collected by a constellation of small, low cost and low Earth orbiting satellites. For the first time in orbit, earth reflected BeiDou-3 signal has been detected from the limited sets of raw data collected by the NASA’s Cyclone GNSS (CYGNSS) constellation. The feasibility of spaceborne BeiDou-3 reflections on two typical applications, including sea surface wind and flooding inundation detection, has been demonstrated. The methodology and results give new strength to the prospect of new spaceborne GNSS-R instruments and missions, which can make multi-GNSS reflectometry observations available to better capture rapidly changing weather systems at better spatio-temporal scales.

Flight Trial Demonstration of Secure GBAS via the L-band Digital Aeronautical Communications System (LDACS)

The ground-based augmentation system (GBAS) is the cornerstone for enabling automated landings without the instrument landing system (ILS). Currently, GBAS is evolving to GBAS approach service type-D (GAST-D) for category III landings. This development toward GBAS GAST-D extends GBAS via the use of multiple frequencies (L1/L2 and L5) and the use of multiple global navigation satellite system constellations. GBAS requires correction data to be broadcast to aircraft, which is currently handled via the VHF data broadcast (VDB) datalink. However, VDB has several known shortcomings: 1) low throughput, 2) small area of operation, and 3) no cyber-security measures. In this article, we propose the use of the L-band digital aeronautical communications system (LDACS) for broadcasting GBAS correction data to address these shortcomings. In flight experiments conducted in 2019, we set up an experimental GBAS installation using LDACS. Broadcast data are secured using the timed efficient stream loss-tolerant authentication (TESLA) broadcast authentication protocol. Our results indicate that cryptographically secured GBAS data via LDACS can provide GAST-C and GAST-D services with high availability if cryptographic parameters are chosen appropriately.

Availability analysis of GNSS signals above GNSSs constellation

AbstractIn view of many problems associated with the availability of global navigation satellite system (GNSS) signals in high-altitude space, this paper presents a comprehensive and systematic analysis. First, the coverage and strength characteristics of GNSS signals in high-altitude space (i.e., space above the GNSS constellation) are presented, and the visibility of GNSS signals is evaluated by combining these two factors. Second, the geometric configuration and geometric dilution of precision (GDOP) of visible GNSS satellites are analysed. Then, the Doppler shift range of the GNSS signals is deduced based on the dynamic performance of high-altitude spacecraft. Finally, taking GaoFen-4 (GF-4) as the application object, the availability of GNSS signals is simulated and evaluated. GNSS signals in high-altitude space are generally weak, and the visible GNSS satellites are concentrated in the high-elevation range. The combination of main and side lobe signals and compatibility of multiple constellations can increase the number of visible satellites, improve the geometry configuration, reduce GDOP, and thus improve the availability of GNSS signals. The results of this research can provide technical support for the design and development of GNSS receivers suitable for high-altitude space.

Reference system origin and scale realization within the future GNSS constellation \u201cKepler\u201d

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 innovative key features of optical inter-satellite links (ISL) delivering highly precise range measurements and of optical frequency references enabling a perfect time synchronization within the complete constellation. In this study, the potential improvements of the Kepler constellation on the TRF origin and scale are assessed by simulations. The fully developed Kepler system allows significant improvements of the geocenter estimates (realized TRF origin in long-term). In particular, we find improvements by factors of 43 for the Z and of 8 for the X and Y component w. r. t. a contemporary MEO-only constellation. Furthermore, the Kepler constellation increases the reliability due to a complete de-correlation of the geocenter coordinates and the orbit parameters related to the solar radiation pressure modeling (SRP). However, biases in SRP modeling cause biased geocenter estimates and the ISL of Kepler can only partly compensate this effect. The realized scale enabling all Kepler features improves by 34% w. r. t. MEO-only. The dependency of the estimated satellite antenna phase center offsets (PCOs) upon the underlying TRF impedes a scale realization by GNSS. In order to realize the network scale with 1 mm accuracy, the PCOs have to be known within 2 cm for the MEO and 4 mm for the LEO satellites. Independently, the scale can be realized by estimating the MEO PCOs and by simultaneously fixing the LEO PCOs. This requires very accurate LEO PCOs; the simulations suggest them to be smaller than 1 mm in order to keep scale changes below 1 mm.

A scheduling strategy to inter-satellite links assignment in GNSS

By introducing inter-satellite link (ISL), the dependence of the global navigation satellite system (GNSS) on ground infrastructure can be reduced and its performance enhanced via inter-satellite ranging and communication. Owing to platform restrictions, there are usually fewer onboard Ka-band ISL antennas than the number of visible satellites, which poses a problem when optimizing the inter-satellite links assignment of the GNSS. In this study, to optimize inter-satellite ranging and communication, a multi-objective optimization model is built and a scheduling strategy is proposed for the inter-satellite links assignment scheduling problem. The position dilution of precision (PDOP) of links and the transmission time-delay of telemetry data are set as the ranging performance and communication metrics, respectively. We regard the links assignment in each slot as a general graph-matching problem, and apply the Blossom algorithm to obtain the maximum matching. We then generate and optimize the satellite sequences for whole slots using non-dominated sorting genetic algorithm II (NSGA-II). The simulation scenes include 10,080 epochs of GNSS constellation, and the simulation results show that the performance of the proposed strategy is better than that of other methods published recently, and can provide various solutions to meet the different preferences of system managers.

Performance Analysis of Static Precise Point Positioning Using Open-Source GAMP

Abstract In addition to Global Positioning System (GPS) constellation, the number of Global Navigation Satellite System (GLONASS) satellites is increasing; it is now possible to evaluate and analyze the position accuracy with both the GPS and GLONASS constellation. In this article, statistical analysis of static precise point positioning (PPP) using GPS-only, GLONASS-only, and combined GPS/GLONASS modes is evaluated. Observational data of 10 whole days from 10 International GNSS Service (IGS) stations are used for analysis. Position accuracy in east, north, up components, and carrier phase/code residuals is analyzed. Multi-GNSS PPP open-source package is used for the PPP performance analysis. The analysis also provides the GNSS researchers the understanding of the observational data processing algorithm. Calculation statistics reveal that standard deviation (STD) of horizontal component is 3.83, 13.80, and 3.33 cm for GPS-only, GLONASS-only, and combined GPS/GLONASS PPP solutions, respectively. Combined GPS/GLONASS PPP achieves better positioning accuracy in horizontal and three-dimensional (3D) accuracy compared with GPS-only and GLONASS-only PPP solutions. The results of the calculation show that combined GPS/GLONASS PPP improves, on an average, horizontal accuracy by 12.11% and 60.33% and 3D positioning accuracy by 10.39% and 66.78% compared with GPS-only and GLONASS-only solutions, respectively. In addition, the results also demonstrate that GPS-only solutions show an improvement of 54.23% and 62.54% compared with GLONASS-only PPP mode in horizontal and 3D components, respectively. Moreover, residuals of GLONASS ionosphere-free code observations are larger than the GPS code residuals. However, phase residuals of GPS and GLONASS phase observations are of the same magnitude.

MULTI-GNSS PPP: An Alternative Positioning Technique for Establishing Ground Control Points

Traditionally, ground control points (GCPs) are utilized to determine absolute image orientations indirectly in aerial triangulation. For a long time, differential and relative GNSS (Global Navigation Satellite System) positioning techniques have been extensively used to establish GCPs. In our country, the establishment and measurement of GCPs are instructed in the related regulation based on differential GNSS techniques. One of the two methods described in the related regulation is based on establishing, at least, C3 level networks with maximum base length of 10 km and with minimum 35-minute observation time. In an alternative method, without base length restriction, GCP coordinates can be determined being connected to at least 3 TUSAGA-Active stations and with minimum 120-minute static observation. The expected precision for the coordinates of GCPs are described to be better than 5 cm in horizontal and 6 cm in vertical within the regulation. Although differential techniques can provide highly accurate positioning solutions, they are required at least two receivers to mitigate GNSS error sources. Additionally, positioning accuracy obtained from these techniques are strictly dependent on the distance from reference stations. It is clear that all these raise the operational cost and system complexity of differential GNSS techniques. In recent years, Precise Point Positioning (PPP), which enables centimeter- or millimeter-level positioning accuracy with only one receiver on a global scale, has emerged as an alternative positioning method. Over the last decade, PPP has attracted considerable attention within the GNSS community due to its exceptional benefits such as operational simplicity, cost-effectiveness, elimination of base station requirement. However, the main drawback of PPP is relatively long observation period required to achieve a specific positioning accuracy, for example, nearly 50 min to reach 10 cm or better horizontal accuracy with 30 seconds sampling rate. On the other hand, the completion of GLONASS constellation and the emergence of new satellite systems, such as Galileo and BeiDou, offers considerable opportunities to improve the PPP performance. The combinations of different GNSS constellations, namely multi-GNSS, strength the number and geometry of visible satellites, and therefore, reduces the convergence time significantly. Additionally, the new generation GNSS receivers make possible to collect more observations (even up to 100Hz), which provides abundant data for PPP processing. Taking all these into account, the principal objective of this study is to investigate the usability of PPP in establishing GCPs for aerial triangulation. For this purpose, an experimental test was conducted to evaluate the positioning performance of multi-GNSS PPP with high-frequency GNSS receivers (1 Hz). The results indicate that 5 cm or better horizontal and vertical positioning accuracy can be achieved by multi-GNSS PPP process within approximately 30 minutes using high-frequency GNSS receivers. Considering these results and its operational simplicity, it can be said that PPP is a robust alternative for the establishment of GCPs.

Machine Learning-Based CYGNSS Soil Moisture Estimates over ISMN sites in CONUS

Soil moisture (SM) derived from satellite-based remote sensing measurements plays a vital role for understanding Earth’s land and near-surface atmosphere interactions. Bistatic Global Navigation Satellite System (GNSS) Reflectometry (GNSS-R) has emerged in recent years as a new domain of microwave remote sensing with great potential for SM retrievals, particularly at high spatio-temporal resolutions. In this work, a machine learning (ML)-based framework is presented for obtaining SM data products over the International Soil Moisture Network (ISMN) sites in the Continental United States (CONUS) by leveraging spaceborne GNSS-R observations provided by NASA’s Cyclone GNSS (CYGNSS) constellation alongside remotely sensed geophysical data products. Three widely-used ML approaches—artificial neural network (ANN), random forest (RF), and support vector machine (SVM)—are compared and analyzed for the SM retrieval through utilizing multiple validation strategies. Specifically, using a 5-fold cross-validation method, overall RMSE values of 0.052, 0.061, and 0.065 cm3/cm3 are achieved for the RF, ANN, and SVM techniques, respectively. In addition, both a site-independent and a year-based validation techniques demonstrate satisfactory accuracy of the proposed ML model, suggesting that this SM approach can be generalized in space and time domains. Moreover, the achieved accuracy can be further improved when the model is trained and tested over individual SM networks as opposed to combining all available SM networks. Additionally, factors including soil type and land cover are analyzed with respect to their impacts on the accuracy of SM retrievals. Overall, the results demonstrated here indicate that the proposed technique can confidently provide SM estimates over lightly-vegetated areas with vegetation water content (VWC) less than 5 kg/m2 and relatively low spatial heterogeneity.

GNSS-RO LEO satellite orbit optimization for Egypt and the Middle East region

The “Radio Occultation (RO)” method is one from the simple, accurate and high resolution methods that produces a complete atmosphere model. Each region/country optimizes a “Low Earth Orbiter (LEO)” satellite orbit that covers its climate requirements by processing the “Global Navigation Satellite System (GNSS)” received signal. Orbit optimization includes the six Keplerian parameters that define the orbit shape. The optimum values of the Keplerian parameters are based up on the number and the distribution of the observations located in the country or the case study region. In the present research, a GNSS-LEO orbit optimization is made for Egypt and the Middle East region. The research objective is to feed the case study region by an adequate and uniform distributed number of observations. Both of time and spatial distributions are taken in consideration in deferent orbits comparison. Two GNSS constellations, “Global Positioning System (GPS)” (29 satellites) and “Global Navigation Satellite System (GLONASS)” (24 satellites), data are used in the analysis. More than hundred orbit cases are used for analysis to find the optimum one.Research demonstrated that the proposed orbit parameters for Egypt area are: altitude = 1500 km, inclination = 0°, initial value of mean anomaly = 300° and the other parameters are set to 0 values. The average expected number of observations due to this orbit is 8 observations per day in Egypt. Results also showed that the proposed orbit parameters for Middle East region are: altitude = 1500 km, inclination = 0°, initial value of mean anomaly = 330° and the other parameters are set to 0 values. The average expected number of observations due to this orbit is 854 observations per day in the Middle East region. These orbits insure obtaining the maximum number of observations with the best spatial and time distribution. The only deference between the two orbits is the angle of the initial value of the mean anomaly. If it is set to 300°, the observations distribution is expected to be distorted over the Middle East region by a small value. And if it is set to 330°, the number of observations through Egypt will be reduced to 7 instead of 8 observations per day.

Assessment of L5 frequency on real-time GPS orbit and clock estimation

Real-time precise Global Navigation Satellite System (GNSS) satellite orbit and clock products are the prerequisite of real-time GNSS-based applications. With the modernization of Global Positioning System (GPS) constellation and construction of other GNSS constellations, the number of GNSS satellites transmitting multi-frequency signals is increasing rapidly. While the benefit of multi-frequency to Precise Point Positioning (PPP) and Precise Clock Estimation (PCE) has been evaluated by many researchers, the impact of multi-frequency on orbit and clock estimation is still limited, especially in real-time mode. Different from the dual-frequency model, the Inter-Frequency Clock Bias (IFCB) must be treated carefully in the triple-frequency model. In this contribution, the triple-frequency model for real-time GPS satellite orbit and clock estimation is derived and the influence of L5 frequency observations on real-time GPS satellite orbit and clock are analyzed. With observation data from globally distributed stations spanning January 1 to 14 of 2018, real-time GPS orbit and clock are estimated with both dual-frequency and triple-frequency observations. Numerical experiments indicate that, compared to the International GNSS Service (IGS) final orbit, the L5 frequency observations improve the consistency of the normal component with about 0.2 cm, however lead to a decrease of consistency in the radial component with about 0.6 cm; the influence on the tangential direction varies with different number of stations. The potential reason for this phenomenon may partly be attributed to the absence of accurate antenna information for L5 frequency. However, due to the tight constraint of dynamic force model on orbit, the overall differences for each component is less than 1.0 cm, which means the contribution of the third frequency observation on the orbit is limited.

Characterizing Background Signals and Noise in Spaceborne GNSS Reflection Ocean Observations

This letter analyzes the background signals and thermal noise received over ocean scenes in spaceborne global navigation satellite system (GNSS)-reflectometry (GNSS-R) remote sensing using observations from the cyclone GNSS (CYGNSS) constellation. The measured noise floor contains a stable and predictable radiometric thermal noise component and a more variable background signal component from unintended specular reflections within the CYGNSS receive antenna pattern from all GNSS satellite constellations (GPS, Galileo, GLONASS, Beidou, and all SBAS). The presence of SBAS reflections, in particular, is evident in the noise floor measurements, especially the U.S. wide area augmentation system (WAAS) satellites. The results show that the impact is negligible, since background signal contributions by other GNSS transmitters affect both the “signal” and “noise” portions of CYGNSS’s delay Doppler map measurements, and therefore cancel when the measured noise floor is subtracted from the desired signal. The potential increase in measurement uncertainty introduced by any residual background signal to the CYGNSS calibration is analyzed.

Sensitivity of GNSS tropospheric gradients to processing options

Abstract. An analysis of processing settings impacts on estimated tropospheric gradients is presented. The study is based on the benchmark data set collected within the COST GNSS4SWEC action with observations from 430 Global Navigation Satellite Systems (GNSS) reference stations in central Europe for May and June 2013. Tropospheric gradients were estimated in eight different variants of GNSS data processing using precise point positioning (PPP) with the G-Nut/Tefnut software. The impacts of the gradient mapping function, elevation cut-off angle, GNSS constellation, observation elevation-dependent weighting and real-time versus post-processing mode were assessed by comparing the variants by each to other and by evaluating them with respect to tropospheric gradients derived from two numerical weather models (NWMs). Tropospheric gradients estimated in post-processing GNSS solutions using final products were in good agreement with NWM outputs. The quality of high-resolution gradients estimated in (near-)real-time PPP analysis still remains a challenging task due to the quality of the real-time orbit and clock corrections. Comparisons of GNSS and NWM gradients suggest the 3∘ elevation angle cut-off and GPS+GLONASS constellation for obtaining optimal gradient estimates provided precise models for antenna-phase centre offsets and variations, and tropospheric mapping functions are applied for low-elevation observations. Finally, systematic errors can affect the gradient components solely due to the use of different gradient mapping functions, and still depending on observation elevation-dependent weighting. A latitudinal tilting of the troposphere in a global scale causes a systematic difference of up to 0.3 mm in the north-gradient component, while large local gradients, usually pointing in a direction of increasing humidity, can cause differences of up to 1.0 mm (or even more in extreme cases) in any component depending on the actual direction of the gradient. Although the Bar-Sever gradient mapping function provided slightly better results in some aspects, it is not possible to give any strong recommendation on the gradient mapping function selection.

Multi-GNSS inter-system biases: estimability analysis and impact on RTK positioning

Inter-system biases (ISB) are of great relevance for the combined processing of the code and phase data of multiple global navigation satellite systems (GNSSs). Calibrating the ISB makes it possible to enhance the interoperability among different GNSS constellations and thus benefits multi-GNSS-based positioning, navigation and timing applications. Initial investigations of the characteristics of ISB have been carried out, usually making use of overlapping frequencies and adopting the double-differenced (DD) model. However, this approach seems inapplicable when dealing with ISB for non-overlapping frequencies. We identify the estimability of the ISB by using the ionospheric-float, ionospheric-fixed and ionospheric-weighted models formulated on the basis of between-receiver single-differenced (SD) multi-GNSS observation equations, resulting in the so-called SD method, which is capable of estimating the ISB in case of both overlapping and non-overlapping frequencies. Using dual-frequency data for short and medium baselines, we analyze 30-s epoch-by-epoch estimates of the GPS–Galileo and GPS–BDS ISB. The quantitative results indicate that the same conclusion is reached using either the SD method or the customary method based on DD observations (called the DD method); that is, the code and phase ISB time series are both approximately constant on a time scale of a few days from a statistical perspective. However, the SD method has the advantage that it can be used to flexibly estimate ISB for both overlapping and non-overlapping frequencies and thus can be better applied for real-time kinematic positioning than the DD method. Furthermore, the multi-GNSS positioning accuracy using inter-system differencing can be improved by 20–35%, as compared to the SD classical differencing in which S-basis is selected per constellation, thanks to the reasonable calibration of the ISB.

Rapid displacement determination with a stand-alone multi-GNSS receiver: GPS, Beidou, GLONASS, and Galileo

Global Navigation Satellite System (GNSS) is an effective tool to retrieve displacement with high precision. Relative positioning and precise point positioning (PPP) are two basic techniques. We present a multi-GNSS dynamic PPP model considering the parameters of velocity and acceleration to determine high-precision displacement rapidly. The performance evaluations of dynamic PPP are conducted in terms of convergence time and positioning repeatability. The mean convergence time of GPS-only, Beidou-only, GPS?+?Beidou, GPS?+?GLONASS, GPS?+?Galileo, and quad-constellation dynamic PPP are 49.4, 104.5, 45.3, 39.9, 47.3, and 35.1?s, respectively. The Beidou-only dynamic PPP has poorer positioning repeatability than the GPS-only solution and the integration of multi-GNSS will enhance the positioning repeatability. The usability of multi-GNSS dynamic PPP for kinematic application is demonstrated by a vehicle-borne kinematic experiment and seismic waves capture data at station LASA during the 2015 Mw 7.8 Nepal earthquake. The dynamic PPP for the kinematic test will be improved in terms of positioning precision with more GNSS constellations and does not suffer the long convergence time compared with kinematic solutions.