International GNSS Service Research Articles

Real-Time BDS-3 Clock Estimation with a Multi-Frequency Uncombined Model including New B1C/B2a Signals

The global system of BDS (BeiDou Navigation Satellite System), i.e., BDS-3, is characterized with a multi-frequency signal broadcasting capability, which was demonstrated as beneficial for GNSS (Global Navigation Satellite System) data processing. However, research on real-time BDS-3 clock estimation with multi-frequency signals is quite limited, especially for the new B1C and B2a signals. In this study, we developed models for BDS-3 multi-frequency real-time data processing, including the uncombined model for clock estimation and the GFIF (Geometry-Free Ionosphere-Free) combined model for IFCB (Inter-Frequency Clock Bias) determination. Based on the models, simulated real-time numerical experiments with about 80 global IGS (International GNSS Service) network stations are conducted for validation and analysis. The results indicate that: (1) the uncombined model with multi-frequency signals can achieve comparable accuracy with the traditional dual-frequency IF model in terms of clock estimation, and the double-differenced clock STDs (Standard Deviations) are generally less than 0.05 ns with post-processed clocks as a reference; (2) unlike the B1C and B1I/B3I signals, the satellite IFCBs generated from multi-frequency clock estimation show apparent temporal variations for B2a and B1I/B3I signals, further investigation with GFIF models confirm the variations mainly result from the errors of receiver antenna corrections. Therefore, we addressed the feasibility of the uncombined model and the importance of accurate antenna information in the multi-frequency data processing.

Validation of regional and global ionosphere maps from GNSS measurements versus IRI2016 during different magnetic activity

Abstract This manuscript explores the divergence of the Vertical Total Electron Content (VTEC) estimated from Global Navigation Satellite System (GNSS) measurements using global, regional, and International Reference Ionosphere (IRI) models over low to high latitude regions during various magnetic activity. The VTEC is estimated using a territorial network consisting of 7 GNSS stations in Egypt and 10 GNSS stations from the International GNSS Service (IGS) Global network. The impact of magnetic activity on VTEC is investigated. Due to the deficiency of IGS receivers in north Africa and the shortage of GNSS measurements, an extra high interpolation is done to cover the deficit of data over North Africa. A MATLAB code was created to produce VTEC maps for Egypt utilizing a territorial network contrasted with global maps of VTEC, which are delivered by the Center for Orbit Determination in Europe (CODE). Thus we can have genuine VTEC maps estimated from actual GNSS measurements over any region of North Africa. A Spherical Harmonics Expansion (SHE) equation was modelled using MATLAB and called Local VTEC Model (LVTECM) to estimate VTEC values using observations of dual-frequency GNSS receivers. The VTEC calculated from GNSS measurement using LVTECM is compared with CODE VTEC results and IRI-2016 VTEC model results. The analysis of outcomes demonstrates a good convergence between VTEC from CODE and estimated from LVTECM. A strong correlation between LVTECM and CODE reaches about 96 % and 92 % in high and low magnetic activity, respectively. The most extreme contrasts are found to be 2.5 TECu and 1.3 TECu at high and low magnetic activity, respectively. The maximum discrepancies between LVTECM and IRI-2016 are 9.7 TECu and 2.3 TECu at a high and low magnetic activity. Variation in VTEC due to magnetic activity ranges from 1–5 TECu in moderate magnetic activity. The estimated VTEC from the regional network shows a 95 % correlation between the estimated VTEC from LVTECM and CODE with a maximum difference of 5.9 TECu.

Evaluation of QZSS orbit and clock products for real-time positioning applications

Abstract The Quasi-Zenith Satellite System (QZSS) is the recent Japanese satellite positioning system to enhance the positioning accuracy in Japan’s urban areas. Additionally, they provide precise orbit and clock corrections and can be obtained through their experimental signals (LEX), streaming access, and published site. Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) is one of the precise products offered in QZSS services that can be obtained on a global scale. In this study, we evaluated the performance of MADOCA orbit and clock corrections, particularly for real-time positioning applications using LEX signals. Based on the simulation, we predict that 16 countries in the East Asia and Oceania regions will gain the maximum benefit of the LEX signals. However, we stress that one may have difficulties decoding the LEX signals at regions where only one QZSS satellite is observed. During our sailing expedition at Sumatran Sea, we could only decode up to 37 % LEX signals for the observation period. It profoundly increased up to 95 % at Sulawesi Strait where at least three QZSS satellites with an elevation angle of, at its minimum, 40° were observed. The orbit and clock accuracy is estimated to be 5.2 cm and 0.6 ns with respect to International GNSS Service (IGS) final products. Our simulation of using the Real-Time Precise Point Positioning (RTPPP) method revealed that the accuracy of the corresponding positioning applications was less than one decimeter. Further, we compared the MADOCA products for RTPPP applications with Apex5 positioning solutions in static field observations. The positioning accuracy for MADOCA-RTPPP during the field observations was estimated to be centimeter to decimeter level and is slightly worse than Apex5 positioning solutions. Nevertheless, we highlight vast positioning applications using MADOCA-RTPPP, e. g., survey and mapping, smart agriculture, and offshore engineering navigation.

Machine learning regression models for prediction of multiple ionospheric parameters

• Machine learning regression models to predict multiple ionospheric parameters. • Forecasting of f0F2, hmF2 and TEC parameters up to 1 h in the mid-latitude region. • Performance comparison of DT, RF and SVM regression models. • A novel approach as a dataset of digisonde and GNSS stations in close proximity. The variation of the ionospheric parameters has a crucial role in space weather, communication, and navigation applications. In this research, we analyze the prediction performance of three machine learning (ML) regression models, decision trees, random forest and support vector machine algorithms for the F2-layer critical frequency (f0F2), F2-layer height of the peak electron density (hmF2), and total electron content (TEC). The hourly f0F2 and hmF2 values of ROME (RO041) digisonde and hourly TEC values of a close by International GNSS Service (IGS) station (site code M0SE00ITA) were obtained for the period between January 1, 2012 and 31 December 2013. The inputs to be trained in the proposed methods are the observation periods of the data (sine and cosine of the day of year and hour of the day), hourly values of solar index F10.7 and geomagnetic index Ap, the present values of f0F2(t), hmF2(t), TEC(t), and their values at t − 23 h. The outputs are the predicted values of f0F2, hmF2, TEC at t + 1. The 2012 values of these parameters were used to train the models and they were predicted 1 h in advance during 2013. The root mean square error (RMSE) values between observed and predicted data were compared for the whole year, summer, winter, and equinox periods. The results showed that proposed ML regression models were successful in the prediction of multiple ionospheric parameters, but random forest regression provides more accurate prediction results than support vector machine and decision trees.

A novel hybrid Machine learning model to forecast ionospheric TEC over Low-latitude GNSS stations

Understanding the ionospheric variability caused by the solar and geomagnetic space weather can be achieved using the ionospheric Total Electron Content (TEC) parameter. Developing a novel artificial intelligence-based machine learning model that can forecast the TEC parameter would primarily benefit Global Positioning System (GPS) users. This paper holds one such a novel hybrid empirical model that exploits nonlinear autoregressive neural network with external input (NARX) for a one hour in advance TEC forecasting over the Hyderabad (17.45°N,78.47°E) and Bengaluru (12.95°N, 77.68°E) GPS stations. The 11-year GPS data spans from 2009 to 2019 corresponding to the 24th solar cycle obtained over these GPS stations operated by the International GNSS Service (IGS) center. The performance of this multiple input data model, which accepts TEC, Ap index, Solar flux index, time of the day, geographical coordinates, and others, have been evaluated during both High Solar Activity (HSA) year 2014 and Low Solar Activity (LSA) period 2019. A comprehensive evaluation of the proposed model has been carried out in comparison with the International Reference Ionosphere 2016 (IRI-2016) model, NeQuick-G model, Auto Regressive Moving Average (ARMA), Neural Network (NN), and combined NN with ARMA models. Results reveal that the proposed hybrid ML model could forecast the ionospheric well. The proposed hybrid ML model's root-mean-square error (RMSE) ranges in 0.5–1 TECU during the LSA period and 1.63–2.2 TECU during the HSA period. The proposed model's Maximum Absolute Percentage Error (MAPE) is between 1.6% and 4.5%, with a 0.99 correlation coefficient (R 2 ) value consistently. Thus, the proposed ML model provides promising ionospheric TEC forecasting results.

Analysis and improvement of the Bancroft algorithm for GNSS satellite orbit determination

Satellite orbit information is crucial for ensuring that global navigation satellite systems (GNSSs) provide appropriate positioning, navigation and timing services. Typically, users can obtain access to orbit information of a specific accuracy level from navigation messages or precise ephemeris products. Without this information, a system will not be able to provide normal service. In response to this problem, initial orbit information of a certain level of precision must be obtained to support subsequent applications, such as broadcasting or precise ephemeris calculations, thereby ensuring the successful subsequent operation of the navigation system. One of two ways to calculate the initial orbit of a GNSS satellite is to utilize ground tracking stations to observe satellite vector information in the geocentric inertial system; the second way is to utilize GNSS range observations and known orbit information from other satellites. For the second approach, some researchers use the Bancroft algorithm combined with receiver clock offset to determine the initial orbit of GNSS satellites. Because this method requires an additional known receiver clock offset, we study the dependence of the Bancroft algorithm on clock offset in GNSS orbit determination. By assessing the impact of errors of different magnitude on the accuracy of the orbit results, we obtain experimental conclusions. After comprehensively analyzing various errors, we determine the accuracy level that the Bancroft algorithm can achieve for orbit determination without considering receiver clock correction. Dual-frequency and single-frequency pseudorange data from International GNSS Service stations are used in orbit determination experiments. When a small receiver clock offset is considered and no correction is made, the deviations in the calculated satellite positions in three dimensions are approximately 979.3 and 1118.1 m (dual and single frequency); with a satellite clock offset, these values are approximately 928.8 and 1062.7 m (dual and single frequency).

Ionospheric–Thermospheric Responses in South America to the August 2018 Geomagnetic Storm Based on Multiple Observations

The ionospheric storm time responses during August 2018 are investigated over South American region using multiple observables, for example, Global Navigation Satellite System (GNSS) derived vertical total electron content (VTEC) from International GNSS Service, magnetic field data, geomagnetic indices, global ionospheric maps, thermospheric mass density (TMD), and [O/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ] ratio measurement. Strong-ionospheric and upper-atmospheric disturbances affected the ionospheric variables with long duration during the storm recovery phase and following after. First, daytime VTEC (9:00–20:00 UT) presented variations of >15 TECU during days 25 to 30 of August 2018 in low and middle latitudes of South America, this after sudden storm commencement (SSC). Furthermore, nighttime (21:00–24:00 and 00:00–05:00 UT) VTEC presented low values (5<TECU<7) in mid-latitude region after SSC event during the main phase, followed by high values (>8 TECU) in the recovery phase. Second, the ionospheric values during the storm main phase and following after, at low- and mid-latitudes, caused the equatorial ionization anomaly to expand due to prompt penetration electric field. Furthermore, VTEC enhancements are likely to occur few hours after the SSC of 25 August 2018, while enhancements of TMD and [O/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ] ratio started to appear later on 26 and 27 of August 2018.

Real-Time Precise GPS Orbit and Clock Estimation With a Quasi-Orbit-Fixed Solar Radiation Pressure Model

<h3>Abstract</h3> Real-time precise global navigation satellite system (GNSS) orbit and clock products play a key role for real-time GNSS-based applications, both in the scientific and industrial communities. Different from the typical two-step procedure to generate orbit and clock solutions separately, we estimate the real-time orbit and clock products simultaneously using a Kalman filter. For this purpose, we developed a GNSS data processing software that can run in pseudo-real-time mode with RINEX files and is ready to run in real-time mode once given the real-time observation stream. Meanwhile, a quasi-orbit-fixed solar radiation pressure (SRP) model is developed. In order to verify the performance of the software and the new SRP model, several experiments with a global network of 60 tracking stations over a time span of three months were conducted to generate real-time Global Positioning System (GPS) orbit and clock products. Then, the results were assessed in terms of accuracy and efficiency, both critical for real-time precise GNSS applications. Compared to the International GNSS Service (IGS) final orbits, the real-time GPS orbit accuracy was 2.82 cm, 5.45 cm, and 5.47 cm in the radial, along-track, and cross-track components, respectively. The precision of the clock product in terms of standard deviation (STD) value was about 0.1 ns. Moreover, the average execution time per epoch was usually less than 1.0 s, which ensures the high efficiency of the processing.

A Method to Mitigate the Effects of Strong Geomagnetic Storm on GNSS Precise Point Positioning

AbstractGeomagnetic storm can affect the performance of Global Navigation Satellite System (GNSS) precise positioning services. To mitigate the adverse effects of strong geomagnetic storms, we propose to establish the geometry‐free (GF) cycle slip threshold model based on ionospheric disturbance index rate of total electron content index to reduce the false detection rate of cycle slip in GNSS precise point positioning (PPP) during strong storm periods, thus improving the accuracy and reliability of GNSS PPP. The performance of our proposed model is validated by using 171 International GNSS Service (IGS) tracking stations data on 8 September 2017. The analysis indicates that compared with conventional PPP scheme, the proposed model can improve the positioning accuracy by approximately 14.0% (36.8%) and 23.1% (51.5%) in the horizonal and vertical components for global (high latitudes) stations. Furthermore, the availability of our proposed model is also validated by PPP experiments using 379 IGS tracking stations data during another strong storm occurred on 26 August 2018.

An Analysis of Spatio-Temporal Water Vapor Variation in the East Java using Ground Based GPS Receivers

Water vapor plays a critical role in the global/regional scale of weather and climate changes. Traditionally, the water vapor measurement uses radiosonde balloons which are very sparse in the distribution. The utilization of GPS as a new method for studying water vapor has been studied in several publications. This research analyzed the precipitable water vapor (PWV) based on ground-based GPS receivers in the East Java region. In the first part, the datasets are compared. The Zenith Total Delay (ZTD) from GPS processing will be compared with the Zenith Path Delay from the International GNSS Service (IGS) results. The comparison of ZTD and ZPD shows a good agreement. The comparison of GPS PWV and Radiosonde shows a good agreement. The spatio-temporal of GPS PWV is correlated with the Monsoon Asian-Australian cycles that affect weather and climate in Indonesia. The result indicates that GPS data provide valuable information in meteorology and climatology.

Analysis on the performances of the GNSS tropospheric delay correction models

Tropospheric delay is one of the important factors affecting GNSS positioning accuracy, and there are different ways to deal with the multiple measurement situations. In short baseline measurements, the difference method is commonly used to eliminate tropospheric errors. However, it cannot be used in long baseline measurements or complex weather since it still has great influences on precision measurement after difference calculation. Therefore, modelling method is usually used to reduce tropospheric delay. As it is well known, there are three types of commonly used tropospheric delay correction models, which are suitable for different situations. When any model is used to solve the tropospheric delay in a large scale, there is always an error between the model value and the actual one. In order to investigate the applicability of the three models in different atmospheric conditions, we actually used the measured meteorological data provided by IGS (International GNSS Service) stations as a reference, and then calculated the ZTD (Zenith Tropospheric Delay) with the different models, including Hopfield model, Saastamoinen model and Black model. The calculation results indicate that Saastamoinen model is the most robust and practical model.

A new climatological electron density model for supporting space weather services

The ionosphere is the ionized part of the Earth’s atmosphere, ranging from about 60 km up to several Earth radii, whereas the upper part above about 1000 km height up to the plasmapause is usually called the plasmasphere. We present a new three-dimensional electron density model to support space weather services and mitigate propagation errors for trans-ionospheric signals. The model is developed by superposing the Neustrelitz Plasmasphere Model (NPSM) to an ionosphere model composed of separate F and E-layer distributions. It uses the Neustrelitz TEC model (NTCM), Neustrelitz Peak Density Model (NPDM), and the Neustrelitz Peak Height Model (NPHM) for the total electron content (TEC), peak ionization, and peak height information. These models describe the spatial and temporal variability of the key parameters as a function of local time, geographic/geomagnetic location, solar irradiation, and activity. The model is developed to calculate the electron concentration at any given location and time in the ionosphere for trans-ionospheric applications and named the Neustrelitz Electron Density Model (NEDM2020). A comprehensive validation study is conducted against electron density in-situ data from DMSP and Swarm, Van Allen Probes and ICON missions, and topside TEC data from COSMIC/FORMOSAT-3 mission, bottom side TEC data from TOPEX/Poseidon mission, and ground-based TEC data from International GNSS Service (IGS) covering both high and low solar activity conditions. Additionally, the model performance is compared with the 3D electron density model NeQuick2. Our investigation shows that the NEDM2020 performs better than the NeQuick2 compared with the in-situ data from Van Allen Probes and ICON satellites and TEC data from COSMIC and TOPEX/Poseidon missions. When compared with DMSP and IGS TEC data, both NEDM2020 and NeQuick2 perform very similarly.

BDS/GNSS multipath reflectometry (BDS/GNSS-MR) based altimetry with new signals: Initial assessment and comparison

The BeiDou Navigation Satellite System with global coverage (BDS-3) was officially launched on July 31, 2020. In addition to the legacy B1I and B3I signals from the regional system (BDS-2), BDS-3 provides several new signals, i.e., B1C, B2a, B2b and B2a + b, with advanced technologies and global availability, which brings new opportunities for ground-based BDS multipath reflectometry (BDS-MR) altimetry. Previous studies focused on the MR altimetry performance of the legacy signals using signal-to-noise ratio (SNR) observations, but the new BDS signals have not been investigated. In this contribution, all types of BDS-3 SNR data collected from seven International GNSS Service (IGS) stations are analyzed signal by signal in terms of SNR quality and altimetry performance, while the legacy BDS B2I and Global Positioning System (GPS) L2C signals are also selected for comparison. Seven globally distributed IGS stations are first investigated for the quality of SNR observations, and then two optimally selected land stations are used to assess BDS-MR based altimetry performance, while a coastal station is used to assess BDS-MR for sea level retrieval performance. It is found that the quality of SNR observations varied site by site due to the differences in environment and equipment, but in general, the new signals except B1C show a higher level of SNR. Then, no detectable biases among each signal are found for land altimetry, while new signals could yield higher amplitude when performing spectral analysis. In coastal sea level altimetry, only two new signals B1C and B2a are available at the selected IGS station, and it is observed that the retrieval performance of BDS B2a is comparable to that of B2I, B3I and GPS L2C with root-mean-square errors (RMSEs) of about 21 cm, while that for B1I and B1C is slightly poorer with RMSEs of 29.68 cm and 26.66 cm respectively.

ГЕОДИНАМІКА

The study analyzes the coordinate time series of five permanent International GNSS Service (IGS) stations located in New Zealand. It also considers their annual movement from 2009 to 2018. The raw data in the form of Receiver Independence Exchange (RINEX) files were taken from IGS database and processes by means of online processing service AUSPOS. Using coordinate time series, horizontal and vertical displacement rates were calculated covering the ten-year study period. According to the results, stations located at the North Island of New Zealand revealed an uplift of 31-32 mm/yr. At the same time, stations placed on the South Island showed the 21-22 mm/yr of positive vertical displacement. Regarding the horizontal displacements, their rates increase in North-South direction over the study region. In particular, two stations of North Island, located at the North-Western part, appeared in 24-25 mm/yr displacement, and one station at the Southern part of North Island showed the 35 mm/yr displacement rate. Stations, established at South Island, showed the horizontal displacement rates of 41-56 mm/yr. This research confirms the main contribution made to the field of crustal deformation studies, including the updated values of displacements along with their directions over the recent years. The results of this study can be used for further geodynamics investigations as well as for finding the most likely earthquake locations of the current study area.

Method for Forecasting Ionospheric Electron Content Fluctuations Based on the Optical Flow Algorithm

We present the optical flow algorithm for forecasting the rate of total electron content index (OFROTI). It consists of a method for predicting maps of rapid fluctuations of ionospheric electron content in terms of global navigation satellite system (GNSS) dual-frequency phase measurements of the rate of change of total electron content index (ROTI). The forecast is made in space and time, at horizons up to more than 6 h. These forecast maps will consist of the ROTI spatial distribution in the northern hemisphere above 45&#x00B0; latitude. The prediction method models the ROTI spatial distribution as a pseudoconservative flux, i.e., exploiting the inertia of the flux of ROTI to determine the future position. This idea is implemented as a modification of the optical flow image processing technique. The algorithm has been modified to deal with the nonconservation of the ROTI quantity in time. We show that the method can predict both, the local value of ROTI and also the regions with ROTI above a given level, better than the prediction using the current map as forecast, i.e., predicting by a current map from horizons of 15 min up to 6 h. The method was tested on 11 representative active and calm days during 2015 and 2018 from the multi-GNSS (GPS, GLONASS, Galileo, and Beidou) multifrequency measurements of more than 250 multi-GNSS receivers above 45&#x00B0;N latitude, including the high rate (1 Hz) measurements of Greenland geodetic network (GNET) network among the International GNSS Service network.

Ground GNSS Station Selection to Generate the Global Ionosphere Maps Using the Information Content

AbstractMore and more satellite constellations and ground receivers are available all over the world, and they can provide rich ionospheric remote sensing data sources. Due to the fact that different analysis centers use different generation techniques and different ground stations, their routinely released Global Ionosphere Maps (GIMs) have some differences. To study the problems of how many stations and which stations should be optimally chosen to generate the GIMs, a step‐by‐step iterative method based on the information content is proposed under the framework of 3DVAR data assimilation. This method adopts the information content to qualitatively evaluate the information contribution of a measurement to the reconstructed GIM, and selects the ground station with a maximum information content in every iteration. About 500 ground receivers from the International GNSS Services networks and Multi‐GNSS Experiment networks are collected from DOY 001 to DOY 120 in 2018 to demonstrate the feasibility of this method. The results show that the information contribution from the first 100 selected stations is over 70%, and the information contribution from the first 200 chosen stations is up to 87%. When the station selection criterion is taken as 95% of the total information content, nearly 300 stations are needed to reconstruct each GIM. Moreover, the quantitative information contribution from GPS, GLONASS, GALILEO, and BEIDOU satellite constellations is preliminarily analyzed.

Integrity monitoring for precise orbit determination of LEO satellites

Due to an increasing requirement for high accuracy orbital information for low Earth orbit (LEO) satellites, precise orbit determination (POD) of LEO satellites is a topic of growing interest. To assure the safety and reliability of the applications requiring high accuracy LEO orbits in near-real-time, integrity monitoring (IM) is an essential operation of the POD process. In this contribution, the IM strategy for LEO POD in both the kinematic and reduced-dynamic modes is investigated. The overbounding parameters of the signal-in-space range error are investigated for the GPS products provided by the International GNSS Service’s Real-Time Service and the Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis service. Benefiting from the dynamic models used and the improved model strength, the test results based on the data of the LEO satellite GRACE FO-1 show that the average-case mean protection levels (PLs) can be reduced from about 3–4 m in the kinematic mode to about 1 m in the reduced-dynamic mode in the radial, along-track and cross-track directions. The overbounding mean values of the SISRE play the dominant role in the final PLs. In the reduced-dynamic mode and average-case projection, the IM availabilities reach above 99% in the radial, along-track and cross-track directions with the alert limit (AL) set to 2 m. The values are still above 98% with the AL set to 4 m, when the duty cycle of tracking is reduced to 40%, e.g., in the case of power limits for miniature satellites such as CubeSats.

Estimation of the ocean tide loading displacements by GPS and GLONASS kinematic Precise Point Positioning

Ocean Tide Loading Displacement (OTLD) parameters, derived by Global Positioning System (GPS) approach, need more time to converge to a stable state and show poor precision of K1 and K2 constituents. Combining multi-system Global Navigation Satellite System (GNSS) data can greatly improve the positioning accuracy and significantly reduce the convergence time compared to single GPS PPP, combined GPS+GLONASS with ambiguity resolved in kinematic Precise Point Positioning (PPP) is improved on the basis of the algorithm of GPS kinematic PPP. We collected eight years of continuous observations of 11 worldwide sites from International GNSS Service to generate three dimensional OTLD parameters of eight constituents using GPS with ambiguity fixed, GLONASS with ambiguity free and combined GPS+GLONASS with ambiguity fixed kinematic PPP approach. The results show the eight constituents derived by GPS_FX and GPS+GLONASS_FX solution need four years and three years to converge to stable values, respectively. GLONASS can significantly improve the convergence rate of K1 and K2 constituents which needs only two years to converge to stable values, and S2 and P1 constituents which need three years to stable values. The results also show the GPS+GLONASS/reference misfits are the smallest for the most constituents in three components (less than 2mm) except for K2 and K1 in vertical and north directions. GLONASS can improve more than 40% in vertical and north components over GPS and GPS+GLONASS for K2 and K1 constituents and show very close agreement with GPS_FX solution in vertical and north component for S2 and P1 constituents. Ambiguity resolved in OTLD estimation can significantly accelerate the convergence and improve the accuracy for eight constituents, especially for combined GPS+GLONASS kinematic PPP mode, but no single constellation mode solution for all eight major constituents exists.

Improve real-time GNSS orbit with epoch-independent undifferenced ambiguity resolution

AR (Ambiguity Resolution) is one of the critical issues in high-accuracy GNSS (Global Navigation Satellite System) applications. Commonly, the double-difference AR technique is employed in GNSS network data processing. With the demand of high-accuracy, low-latency and high-integrity GNSS orbit, the orbit estimation in sequential mode becomes a candidate of that in batch mode. Unlike orbit estimation with double-difference AR in either batch or sequential mode, researches on real-time orbit estimation with undifferenced AR in sequential mode is still limited. In this study, real-time orbit determination with epoch-independent undifferenced AR in sequential mode is assessed. With one-week observation data from about 100 global distributed IGS (International GNSS Service) network stations, simulated real-time Galileo orbit determination are conducted with GFZ post-processed solution as reference for validation. Numerical results indicate that, first, the 3D error RMS (Root Mean Square) of fixed orbit is about 30% smaller than that of float orbit; second, the Galileo orbit error RMS reach 3.66, 3.60 and 3.09 cm for the radial, tangential and normal directions respectively for the fixed solution; third, small jumps exist in the real-time orbit and may be attributed to the temporal variations of UPD (Uncalibrated Phase Delay) and wrongly fixed ambiguities. In summary, the orbit quality is comparable to that of IGS real-time solutions, and further improvements may be achieved with improved AR constraint strategy and background orbit model.

A multi‐frequency method to improve the long‐term estimation of GNSS clock corrections and phase biases

<h3>Abstract</h3> The space segment of the Global Navigation Satellite System (GNSS) is equipped with highly stable atomic clocks. In order to use these clocks as references, their time offsets must be estimated from ground measurements as accurately as possible. This work presents a multi-frequency and multi-constellation method for estimating satellite and receiver clock corrections, starting from unambiguous, uncombined, and undifferenced carrier-phase measurements. A byproduct of the estimation process is phase biases (i.e., the hardware delays of the carrier-phase measurements occurring at receivers and satellites). The stability and predictability of our clock estimates for receivers and satellites (GPS and Galileo) are compared with those obtained by the International GNSS Service (IGS), whereas the phase biases are assessed against two independent determinations involving combinations of carrier-phase measurements. We conclude that the method reduces day boundary discontinuities in the clock corrections, and that the estimated phase biases reproduce variabilities already observed by other authors.