Analysis Center Research Articles

The Zenith Total Delay Combination of International GNSS Service Repro3 and the Analysis of Its Precision

Currently, ground-based global navigation satellite system (GNSS) techniques have become widely recognized as a reliable and effective tool for atmospheric monitoring, enabling the retrieval of zenith total delay (ZTD) and precipitable water vapor (PWV) for meteorological and climate research. The International GNSS Service analysis centers (ACs) have initiated their third reprocessing campaign, known as IGS Repro3. In this campaign, six ACs conducted a homogeneous reprocessing of the ZTD time series spanning the period from 1994 to 2022. This paper primarily focuses on ZTD products. First, the data processing strategies and station conditions of six ACs were compared and analyzed. Then, formal errors within the data were examined, followed by the implementation of quality control processes. Second, a combination method is proposed and applied to generate the final ZTD products. The resulting combined series was compared with the time series submitted by the six ACs, revealing a mean bias of 0.03 mm and a mean root mean square value of 3.02 mm. Finally, the time series submitted by the six ACs and the combined series were compared with VLBI data, radiosonde data, and ERA5 data. In comparison, the combined solution performs better than most individual analysis centers, demonstrating higher quality. Therefore, the advanced method proposed in this study and the generated high-quality dataset have considerable implications for further advancing GNSS atmospheric sensing and offer valuable insights for climate modeling and prediction.

Effect of WHU/GFZ/CODE satellite attitude quaternion products on the GNSS kinematic PPP during the eclipse season

To ensure high-precision Global Navigation Satellite System (GNSS) applications, many analysis centers (ACs) have begun to provide satellite attitude products, which affect the modeling of phase variations and phase wind-up. Despite several studies having demonstrated the importance of providing attitude products, particularly eclipsing products, the performance of satellite attitude models for different ACs has not been further investigated. This study compared the satellite attitude models provided by Wuhan university (WHU), German Research Centre of Geosciences (GFZ), and Center for Orbit Determination in Europe (CODE), and investigated the impact of satellite attitude products on high-rate GNSS data processing (i.e., 1HZ). The satellite attitudes of most satellite blocks were consistent well with each other, except for the BDS-2 inclined geostationary orbit (IGSO), BDS-3 medium earth orbit (MEO), GPS IIIA, and GLONASS-M satellites. The differences in the yaw angle between the different ACs ranged as 10–180°. Compared to the good consistency of the wum and com products, gbm exhibited significant differences from the former for most constellations. Following the application of the satellite attitude products, the average 3D RMS value of the single-kinematic PPP was improved by 11% and 10% for the 30-s and 1-s sampling rate observations, respectively. Thus, these eclipsing satellites with inaccurate attitude models can be deleted while integrating more satellites into the GNSS data processing.

An effective method for improving GNSS precise point positioning performance at the day boundary

Abstract Aiming to address poor self-consistency of the satellite clock and orbit interpolations at the day boundary, which is caused by the discontinuities of their International GNSS Service (IGS) products for two consecutive days, an effective method is proposed to improve the precise point positioning (PPP) performances at the day boundary. According to different orders of Lagrange interpolator and different IGS Analysis Centers products of Center for Orbit Determination in Europe (CODE), GeoForschungsZentrum (GFZ) and Wuhan University (WUH), biases at the day boundaries are estimated and analyzed using a 4 day (DOY 94-97, 2022) data set of GPS, BDS-3 and Galileo from 123 IGS stations. These estimated biases show the time-varying characteristics. The differences in biases across 9th-11th orders of Lagrange interpolator are minimal, and these variances have a negligible impact on positioning. The results show that this poor self-consistency at the day boundary has an obvious influence on the kinematic PPP positioning, especially there is a centimeter-level variation at time of 24:00:00/00:00:00. This influence on the Up direction of kinematic PPP positioning is more serious than other directions. When the bias is estimated and corrected, the kinematic PPP positioning accuracies at the day boundary have a mean improvement of 0.043, 0.064 and 0.027 m for WUH, GFZ and CODE, respectively. The mean improvements for GPS, BDS-3 and Galileo are 0.021, 0.062 and 0.051 m. Additionally, the static PPP performances at the day boundary show the convergence times are shortened by 3.2, 6.2, and 2.5 min for WUH, GFZ and CODE, respectively, when the poor self-consistency of the satellite clock and orbit interpolations is estimated and corrected. Meanwhile, its 0.5 and 1 h positioning accuracies are improved.

SLR Validation and Evaluation of BDS-3 MEO Satellite Precise Orbits

Starting from February 2023, the International Laser Ranging Service (ILRS) began releasing satellite laser ranging (SLR) data for all BeiDou global navigation satellite system (BDS-3) medium earth orbit (MEO) satellites. SLR data serve as the best external reference for validating satellite orbits, providing a basis for comprehensive evaluation of the BDS-3 satellite orbit. We utilized the SLR data from February to May 2023 to comprehensively evaluate the orbits of BDS-3 MEO satellites from different analysis centers (ACs). The results show that, whether during the eclipse season or the yaw maneuver season, the accuracy was not significantly decreased in the BDS-3 MEO orbit products released from the Center for Orbit Determination in Europe (CODE), Wuhan University (WHU), and the Deutsches GeoForschungsZentrum (GFZ) ACs, and the STD (Standard Deviation) of SLR residuals of those three ACs are all less than 5 cm. Among these, CODE had the smallest SLR residuals, with 9% and 12% improvement over WHU and GFZ, respectively. Moreover, the WHU precise orbits exhibit the smallest systematic biases, whether during non-eclipse seasons, eclipse seasons, or satellite yaw maneuver seasons. Additionally, we found some BDS-3 satellites (C32, C33, C34, C35, C45, and C46) exhibit orbit errors related to the Sun elongation angle, which indicates that continued effort for the refinement of the non-conservative force model further to improve the orbit accuracy of BDS-3 MEO satellites are in need.

Analysis and diagnosis of abnormal SLR validation results for BeiDou-3 SECM-B MEO C225 and C226 satellite orbits

Satellite laser ranging (SLR) is the only stand-alone and external tool for verifying the accuracy of microwave-based GNSS orbits. On February 2, 2023, the International Laser Ranging Service initiated the SLR global tracking campaign for the complete BeiDou-3 medium Earth orbit (MEO) constellation. This initiative provides an opportunity to unveil the potential issue for BeiDou-3 MEO orbit modeling. An examination of the SLR validation results of precise BeiDou-3 MEO orbits across different IGS/Multi-GNSS Experiment (MGEX) analysis centres (ACs) reveals that the SLR residual standard deviation for BeiDou-3 SECM-B MEOs C225 and C226 orbits reaches 18 cm. This figure is approximately four to nine times those for other BeiDou-3 MEOs. This contradicts the fact that the orbit quality of C225 and C226 is comparable to other satellites. By analyzing the correlation between SLR residuals and de-trend clock residuals, detector-specific bias performance, and the distribution characteristics of SLR residuals relative to satellite azimuth and nadir angles, we diagnose that abnormal SLR validation results for C225 and C226 originate from a large deviation in the official horizontal offsets for the laser retroreflector arrays (LRAs) in the satellite reference frame. LRA horizontal offsets for C225 and C226 are estimated based on SLR residuals. With our adjusted LRA offset estimates, the SLR residual metrics for C225 and C226 orbits (across various IGS/MGEX ACs) are comparable to the results obtained for other BeiDou-3 MEOs. Additionally, our adjustments enable the identification of their orbit modeling errors across different IGS/MGEX ACs according to the pattern of SLR residual variation. From the study, spacecraft manufacturers should be encouraged to conduct a comprehensive review of ground calibrations for BeiDou LRA offsets. This is crucial for optimizing BeiDou orbit model and enhancing its applications in high-precision geosciences.

Comprehensive Analysis on GPS Carrier Phase under Various Cutoff Elevation Angles and Its Impact on Station Coordinates’ Repeatability

When processing the carrier phase, the global navigation satellite system (GNSS) grants the highest precision for geodetic measurements. The analysis centers (ACs) from the International GNSS Service (IGS) provide different data such as precise clock data, precise orbits, reference frame, ionosphere and troposphere data, as well as other geodetic products. Each individual AC has its own strategy for delivering the abovementioned products, with one of the key elements being the cutoff elevation angle. Typically, this angle is arbitrarily chosen using generic values without studying the impact of this choice on the obtained results, in particular when very precise positions are considered. This article addresses this issue. To this end, the article has two key sections, and the first is to evaluate the impact of using the two different cutoff elevation angles that are most widely used: (a) 3 degrees cutoff and (b) 10 degrees cutoff elevation angle. This analysis is completed in two major parts: (i) the analysis of the root mean square (RMS) for the carrier phase and (ii) the analysis of the station position in terms of repeatability. The second key section of the paper is a comprehensive carrier phase analysis conducted by adopting a new approach using a mean of the 25-point average RMS (A-RMS) and the single-point RMS and using an ionosphere-free linear combination. By using the ratio between the 25-point average RMS and the single-point RMS we can define the type of scatter that dominates the phase solution. The analyzed data span a one-year period. The tested GNSS stations belong to the EUREF Permanent Network (EPN) and the International GNSS Service (IGS). These comprise 55 GNSS stations, of which only 23 GNSS stations had more than 95% data availability for the entire year. The RMS and A-RMS are analyzed in conjunction with the precipitable water vapor (PWV), which shows clear signs of temporal correlation. Of the 23 GNSS stations, three stations show an increase of around 50% of the phase RMS when using a 3° cutoff elevation angle, and only four stations have a difference of 5% between the phase RMS when using both cutoff elevation angles. When using the A-RMS, there is an average improvement of 37% of the phase scatter for the 10° cutoff elevation angle, whereas for the 3° cutoff elevation angle, the improvement is around 33%. Based on studying this ratio, four stations indicate that the scatter is dominated by the stronger-than-usual dominance of long-period variations, whereas the others show short-term noise. In terms of station position repeatability, the weighted root mean square (WRMS) is used as an indicator, and the results between the differences of using a 3° and 10° cutoff elevation angle strategy show a difference of −0.16 mm for the North component, −0.21 mm for the East component and a value of −0.75 mm for the Up component, indicating the importance of using optimal cutoff angles.

Combination and SLR validation of IGS Repro3 orbits for ITRF2020

In preparation for the International Terrestrial Reference Frame 2020, the International GNSS Service analysis centers released the results of the third reprocessing campaign (IGS Repro 3) of all the GNSS network solutions backwards starting from 1994. For the first time, the IGS reprocessing products included not just GPS and GLONASS, but also the Galileo constellation. In this study, we describe the methodology and results of the orbit combination provided by the IGS Analysis Center Coordinator (IGS ACC) at Geoscience Australia. The quality of the combined orbit products was cross-checked with the individual IGS Repro3 Analysis Center (AC) contributions. The internal consistency of the individual Analysis Center (AC) solutions with the combined orbits was assessed based on the root mean square of the 3D orbit differences. In 2020, the mean consistency of the combination is at the level of 9, 23, and 15 mm for GPS, GLONASS, and Galileo, respectively. The external validation of the orbits was performed using Satellite Laser Ranging (SLR). We proposed a novel approach to handling detector-specific biases in the results of SLR validation, which reduced the standard deviation of SLR residuals by up to 13% for Galileo FOC satellites. This method is based on bias aligning the offsets to single-photon SLR stations that were treated as a reference. The proposed approach increased the internal consistency of the SLR dataset, facilitating the detection of orbit modeling issues. The standard deviation of SLR residuals of the best individual solution versus the combined solution equals 13/13, 15/17, 17/17, 18/19 mm for Galileo-FOC, -IOV, GLONASS-K1B, -M, respectively. Therefore, the combined solution can be considered equal in quality compared to the best individual AC solutions. Searching for patterns in SLR residuals for different satellite-Sun-Earth geometries revealed that some orbit modeling issues are not fully diminished for individual ACs. Eventually, our findings suggest that the delivered combined orbit product may be considered the best solution overall, as it benefits from the best individual solutions for each satellite type.

Reference clock impact on GNSS clock outliers

Abstract With the advent of the Global Navigation Satellite System (GNSS), the need for precise and highly accurate orbit and clock products becomes crucial in processing GNSS data. Clocks in GNSS observations form the basis of positioning. Their high quality and stability enable high accuracy and the reliability of the obtained results. The clock modelling algorithms are continuously improved; thus, the accuracy of the clock products is evolving. At present, 8 Analysis Centers (ACs) contribute to the International GNSS Service final clock products. These products are based on GNSS observations on a network of reference stations, where for a given day one of the reference station clocks is the reference clock. In this paper, the authors determined the impact of the reference clock on the quality of clock product, especially outliers, for the first time. For this purpose, the multi-GNSS final clock products provided by the Center for Orbit Determination in Europe (CODE) for the period 2014–2021 (1773–2190 GPS week, 2921 days) were analysed. Analysis shows that by applying the Median Absolute Deviation (MAD) algorithm for outlier detection, the Passive Hydrogen Maser (PHM) clock installed on board the GALILEO satellites have the lowest level of noise, whereas the Block IIR GPS satellite launched in 1999 appears to have the highest levels of noise. Furthermore, the GNSS station OHIE3, when used as a reference clock, generates an increase in the level of noise, especially noticeable on the G09 and E03 satellites.

Centimeter-Level Orbit Determination of GRACE-C Using IGS-RTS Data

GNSS real-time applications greatly benefit from the International GNSS Service’s (IGS) real-time service (RTS). This service does more than provide for terrestrial precise point positioning (PPP); it also brings more possibilities for space-borne technology. With this service, the State-Space Representation (SSR) product, which includes orbit corrections and clock corrections, is finally available to users. In this paper, the GPS real-time orbit and clock corrections provided by 11 analysis centers (ACs) from the day of the year (DOY) 144 to 153 of 2022 are discussed from 3 perspectives: integrity, continuity, and accuracy. Moreover, actual observation data from the GRACE-C satellite are processed, along with SSR corrections from different ACs. The following can be concluded: (1) In terms of integrity and continuity, the products provided by CNE, ESA, and GMV perform better. (2) CNE, ESA, and WHU are the most accurate, with values of about 5 cm for the satellite orbit and 20 ps for the satellite clock. Additionally, the clock accuracy is related to the Block. Block IIR and Block IIR-M are slightly worse than Block IIF and Block IIIA. (3) The accuracy of post-processing reduced-dynamic precise orbit determination (POD) and kinematic POD are at the centimeter level in radius, and the reduced-dynamic POD is more accurate and robust than the kinematic POD.

Performance of Galileo satellite products determined from multi-frequency measurements

Each Galileo satellite provides coherent navigation signals in four distinct frequency bands. International GNSS Service (IGS) analysis centers (ACs) typically determine Galileo satellite products based on the E1/E5a dual-frequency measurements due to the software limitation and the limited tracking capability of other signals in the early time. The goal of this contribution is to evaluate the quality of Galileo satellite products determined by using different dual-frequency (E1/E5a, E1/E5b, E1/E5, E1/E6) and multi-frequency (E1/E5a/E5b/E5/E6) measurements based on different sizes of ground networks. The performance of signal noise, the consistency of frequency-specific satellite phase center offsets and the stability of satellite phase biases are assessed in advance to confirm preconditions for multi-frequency processing. Orbit results from different dual-frequency measurements show that orbit precision determined from E1/E6 is clearly worse (about 35%) than that from other dual-frequency solutions. In view of a similar E1, E5a, E5b and E6 measurement quality, the degraded E1/E6 orbit performance is mainly attributed to the unfavorable noise amplification in the respective ionosphere-free linear combination. The advantage of using multi-frequency measurements over dual-frequency for precise orbit determination is clearly visible when using small networks. For instance, the ambiguity fixing rate is 80% for the multi-frequency solution while it is less than 40% for the dual-frequency solution if 150 s data sampling is employed in a 15-station network. Higher fixing rates result in better (more than 30%) satellite orbits and more robust satellite clock and phase bias products. In general, satellite phase bias products determined from a 20-station (or more) network are precise enough to conduct precise point positioning with ambiguity resolution (PPP-AR) applications. Multi-frequency kinematic PPP-AR solutions always show 5–10% precision improvement compared to those computed from dual-frequency observations.

MADOCA: Japanese precise orbit and clock determination tool for GNSS

The Japan Aerospace Exploration Agency (JAXA) has developed Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA). This tool estimates orbits and clock offsets of multiple GNSS systems (Multi-GNSS), namely GPS, GLONASS, QZSS, Galileo, and BeiDou. The orbit and clock offsets are estimated in both post-processing with iterative weighted least squares and real-time processing with extended Kalman filter (EKF) using observation data collected from the International GNSS Service (IGS) network and our monitoring station network (MGM-net). Since we began the development in 2011, we have improved the MADOCA’s performance by adopting the precise force and measurement models, the original empirical solar radiation pressure (SRP) model, and processing algorithms for stability and reduction of processing time. In the latest annual evaluation of MADOCA products in 2021, the orbit comparison with the IGS final product for the GPS and GLONASS were 2.8 and 8.0 cm (median value of daily 3D-root mean square (RMS)), respectively, and the results of satellite laser ranging (SLR) residual evaluation for the BeiDou and Galileo were 14.6 and 4.9 cm (RMS), respectively, a performance comparable to the products of the IGS Analysis Centers (ACs). QZSS products, in particular, have achieved the world’s highest level of accuracy as 6.4, 10.1, 9.0, and 10.5 cm (RMS) for the QZS-1, -2, -3, and -4 respectively in the SLR residual evaluation. This was achieved by improving and fine-tuning for the original empirical SRP models. Consequently, the position difference in those products’ static precise point positioning (PPP) reached 1.2 cm (3D-RMS). JAXA has made post-processing and real-time MADOCA products publicly available to users and is promoting experiments using MADOCA products in Japan and abroad.

Comprehensive Assessment of BDS-2 and BDS-3 Precise Orbits Based on B1I/B3I and B1C/B2a Frequencies from iGMAS

The BeiDou Global Navigation Satellite System (BDS), including the second generation (BDS-2) and the third generation (BDS-3), has been widely used in areas of positioning, navigation, and timing (PNT). One of the essential prerequisites for accurate PNT service is the precise satellite orbits of multi-frequency and multi-constellation BDS-2 and BDS-3 satellites. As usual, the precise orbit products can be obtained from analysis centers (ACs) of the international GNSS Service (IGS). The precise orbits can also be downloaded from the international GNSS Monitoring and Assessment System (iGMAS). Compared with the IGS ACs, the iGMAS can provide featured services such as satellite orbits based on the new B1C/B2a BDS signals. Considering the indispensability of the new signals, the performance of all BDS precise orbits from iGMAS needs to be known. However, there is no comprehensive assessment of BDS-2 and BDS-3 precise orbits based on B1I/B3II and B1C/B2a frequencies from iGMAS, especially for the period after the BDS entered the stable operation stage. In this paper, BDS-2/BDS-3 final (ISC), rapid (ISR), and ultra-rapid (ISU) products based on B1I/B3I and B1C/B2a frequencies from iGMAS are all assessed comprehensively. Specifically, at first, the precise orbits from iGMAS are compared with the ones from the IGS ACs. Based on this, the satellite laser ranging inspects the precise orbits from iGMAS. Finally, the orbit errors are discussed systematically by considering the beta and elongation angles. Using one year of data, the orbit accuracy of geostationary orbit, inclined geosynchronous orbit, and medium earth orbit (MEO) satellites can almost reach meter to decimeter level, decimeter to sub-decimeter level, and centimeter level, respectively, where the ISC products are the best. The ISC, ISR, and ISU products based on B1I/B3I frequencies are generally better than the ones based on B1C/B2a frequencies. Additionally, according to the SLR data, the results show that the accuracy of precise orbits of BDS-3 is better than that of BDS-2. The mean values of orbit biases of BDS-3 MEO satellites are approximately 2.88 cm. In addition, the orbit errors are related to the beta angle and elongation angle to some extent, and the manufacturers may also have an influence on the orbit errors.

Using Various Analysis Center Products to Assess the Time-Frequency Transfer Performance of GPS/Galileo/BDS PPPAR Methods

Numerous organizations and Analysis Centers (AC) currently offer various Ambiguity Resolution (AR) products using various methodologies. However, there are no associated studies on their use for time-frequency transfer. This paper examines 16 Multi-GNSS Experiment (MGEX) stations with external high-precision atomic clocks to constitute 15 international time comparison links, and uses AR products data from CNES, SGG, CODE, and PRIDE laboratories, using three ambiguity-fixed strategies, to thoroughly evaluate the effects of various strategies and AR products for high-precision time-frequency transfer. We reach the following results by using the IGS final clock product as a reference and comparing it to ambiguity-float. With various ambiguity-fixed procedures, the time stability Standard Deviation (STD) of time transfer is increased for a single GPS, and the improvement ranges from 10 to 40%. The frequency stability has barely improved; up to 40%, the most notable improvement comes from FCB with GRM products. The time stability STD of combinations has improved after the addition of the Galileo system compared to the single GPS, and the improvement ranges from 2 to 9%. Most strategies have been improved, while a few techniques have been weakened with the GEC (GPS + Galileo + BDS) combination. We feel that the stability has not significantly increased with the systems’ increase in terms of short-term stability after comparing multiple groups of linkages.

Combination of GNSS orbits using least-squares variance component estimation

Over the past years, the International GNSS Service (IGS) has been putting efforts into extending its service by setting up and running the Multi-GNSS experiment and pilot project (MGEX). Several MGEX analysis centers (ACs) contribute by providing solutions containing not only GPS and GLONASS but also Galileo, BeiDou, and QZSS. As the current IGS combination software can only handle the orbits of one constellation at a time, it requires substantial modifications to obtain a consistent MGEX orbit product. In this contribution, we present a least-squares framework for a Multi-GNSS orbit combination, where the weights used to combine the ACs’ orbits are determined by least-squares variance component estimation. We introduce and compare two weighting strategies, where either AC-specific weights or AC and constellation-specific weights are used. An automated Z-score test is implemented yielding a common set of core satellites that are used to determine the weights. Both strategies are tested using MGEX orbit solutions for a period of two and a half years. They yield similar results with an agreement with the ACs’ orbits at the one centimeter level for GPS and up to a few centimeters for the other constellations. The 3D-RMS is generally slightly better with the AC and constellation weighting. A comparison of our combination approach with the official IGS combination using three years of GPS and GLONASS orbits shows an agreement of better than 5 mm and 12 mm for GPS and GLONASS, respectively, while the agreement of the official IGS combination with the ACs’ GPS solutions is only around 15,textrm{mm}. An external validation using satellite laser ranging shows that the mean residuals of our combined products are around -3,textrm{mm} for Galileo, 6,textrm{mm} for GLONASS, -8,textrm{mm} for BeiDou, and -31,textrm{mm} for QZSS.

Observable-specific phase biases of Wuhan multi-GNSS experiment analysis center’s rapid satellite products

Precise Point Positioning (PPP) with Ambiguity Resolution (AR) is an important high-precision positioning technique that is gaining popularity in geodetic and geophysical applications. The implementation of PPP-AR requires precise products such as orbits, clocks, code, and phase biases. As one of the analysis centers of the International Global Navigation Satellite System (GNSS) Service (IGS), the Wuhan University Multi-GNSS experiment (WUM) Analysis Center (AC) has provided multi-GNSS Observable-Specific Bias (OSB) products with the associated orbit and clock products. In this article, we first introduce the models and generation strategies of WUM rapid phase clock/bias products and orbit-related products (with a latency of less than 16 h). Then, we assess the performance of these products by comparing them with those of other ACs and by testing the PPP-AR positioning precision, using data from Day of the Year (DOY) 047 to DOY 078 in 2022. It is found that the peak-to-peak value of phase OSBs is within 2 ns, and their fluctuations are caused by the clock day boundary discontinuities. The associated Global Positioning System (GPS) orbits have the best consistency with European Space Agency (ESA) products, and those of other systems rank in the medium place. GLObal NAvigation Satellite System (GLONASS) clocks show slightly inconsistency with other ACs’ due to the antenna thrust power adopted, while the phase clocks of other GNSSs show no distortion compared with legacy clocks. With well-estimated phase products for Precise Orbit Determination (POD), the intrinsic precision is improved by 14%, 17%, and 24% for GPS, Galileo navigation satellite system (Galileo), and BeiDou-3 Navigation Satellite System (BDS-3), respectively. The root mean square of PPP-AR using our products in static mode with respect to IGS weekly solutions can reach 0.16 cm, 0.16 cm, and 0.44 cm in the east, north, and up directions, respectively. The multi-GNSS wide-lane ambiguity fixing rates are all above 90%, while the narrow-lane fixing rates above 80%. In conclusion, the phase OSB products at WUM have good precision and performance, which will benefit multi-GNSS PPP-AR and POD.

Multi-GNSS clock combination with consideration of inconsistent nonlinear variation and satellite-specific bias

As part of the International GNSS Service (IGS) multi-GNSS Pilot Project (MGEX), precise orbit and clock products for multi-GNSS constellations have been submitted by several analysis centers (ACs) since 2012. Based on the 30 s satellite clocks from 6 MGEX ACs, the multi-GNSS clocks are combined and the consistency of the AC clocks is assessed in this study. Usually, a linear transformation between the combined and AC solution is used for clock combination, and the clock residuals of the AC solution w.r.t the combined solution are used to determine the weights of the AC. However, any inconsistent satellite-specific bias or nonlinear variations in the clocks induced by the AC’s processing strategy can contaminate the linear transformation as well as the determination of the weight. In this study, the analysis center and satellite-specific bias (ASB) of the MGEX AC clock solutions is first identified and estimated by using observations from globally distributed stations. Moreover, the clock solutions with nonlinear variations induced by the reference clock or nonconstant intersystem bias (ISB) are corrected by aligning the clocks to the selected reference solution before clock combination. With the correction of the ASB, the root-mean-square of the clock residuals decreases significantly and reaches 14-26, 37-91, 33-48 and 12-44 ps for GPS, GLONASS, BDS-2 and Galileo, respectively. In general, the consistency of AC solutions w.r.t the combination reaches 8-16, 27-58, 13-27 and 9-36 ps for GPS, GLONASS, BDS-2 and Galileo in terms of the standard deviation. Finally, the individual AC and combined orbit as well as clock solutions of different constellations are assessed by precise point positioning, and the combined multi-GNSS solutions show competitive performance with the best AC solution in terms of both the positioning accuracy and stability of the reference frame parameters. However, inconsistent scale parameters of both the AC and combined solutions are identified and require more investigation.Graphical

Accounting for BDS-2/BDS-3 inter-system biases in PPP and RTK models

Inter-system Biases (ISBs) between BDS-2 and BDS-3 is of great importance for BDS-2/BDS-3 joint processing, which is meaningful to make full use of BDS observations and improves PNT (positioning, navigation, timing) performance. In this contribution, we derive ISBs models with undifferenced ionospheric-free (IF) combination and double-differenced model, corresponding to the IF-PPP and RTK technologies respectively. To analyze code ISB in PPP, we processed data from 55 multi-GNSS experimental (MGEX) stations including 7 receiver types and conduct a detailed analysis on the effect of frequency, receiver types and precise products from 4 IGS Analysis Centers (ACs). It is concluded that both the overlapping frequency and the non-overlapping frequency of BDS-2/BDS-3 exist code ISB. The code ISB of overlapping frequency is within 10 ns, and that of the non-overlapping frequency can reach 100 ns. Moreover, code ISB is influenced by receiver types as well as satellite geometry. The average ISB of stations with the same manufactures tend to be the same while that of stations from different manufactures are different. Affected by the satellite geometry, the ISB characteristics exhibit periodicity and correlation with the location of stations. By comparing ISB calculated by different precise clock products from the GeoForschungsZentrum (GFZ), European Space Agency (ESA), Center for Orbit Determination in Europe (CODE) and Wuhan University (WHU), the results show that the daily STD of ISBCOD, ISBWHU,ISBESA and ISBGFZ is about 0.2 ns, which means that ISB can be calibrated by constant estimation when these products are used. As for Differential Inter-system Biases (DISBs) in RTK, it is discovered that the BDS-2/BDS-3 joint differenced system has a Differential Inter-system Code Bias (DISCB) that exceeds 3.4 ns when the rover and base receivers are made by different manufactures and the hardware delay characteristics for BDS-2 and BDS-3 are different. However, the Differential Inter-system Phase Bias (DISPB) doesn’t exist and can be neglected in RTK.

Validation of Multi-Year Galileo Orbits Using Satellite Laser Ranging

Satellite laser ranging (SLR) observations provide an independent validation of the global navigation satellite system (GNSS) orbits derived using microwave measurements. SLR residuals have also proven to be an important indicator of orbit radial accuracy. In this study, SLR validation is conducted for the precise orbits of eight Galileo satellites covering four to eight years (the current longest span), provided by multiple analysis centers (ACs) participating in the multi-GNSS experiment (MGEX). The purpose of this long-term analysis (the longest such study to date), is to provide a comprehensive evaluation of orbit product quality, its influencing factors, and the effect of perturbation model updates on precise orbit determination (POD) processing. A conventional ECOM solar radiation pressure (SRP) model was used for POD. The results showed distinct periodic variations with angular arguments in the SRP model, implying certain defects in the ECOM system. Updated SRP descriptions, such as ECOM2 or the Box-Wing model, led to significant improvements in SLR residuals for orbital products from multiple ACs. The standard deviation of these residuals decreased from 8–10 cm, before the SRP update, to about 3 cm afterward. The systematic bias of the residuals was also reduced by 2–4 cm and the apparent variability decreased significantly. In addition, the effects of gradual SRP model updates in the POD were evident in orbit comparisons. Orbital differences between ACs in the radial direction were reduced from the initial 10 cm to better than 3 cm, which is consistent with the results of SLR residual analysis. These results suggest SLR validation to be a powerful technique for evaluating the quality of POD strategies in GNSS orbits. Furthermore, this study has demonstrated that perturbation models, such as SRP, provide a better orbit modeling for the Galileo satellites.

BDS-2/BDS-3 combined precise time-frequency transfer with different inter-system bias estimation strategies and different analysis centres products

BeiDou-3 global navigation satellite system (BDS-3) has officially provided positioning, navigation, and timing (PNT) services on 31 July 2020. The difference between BDS-2 and BDS-3 in signal modulation mode, signal characteristics, and satellite clock datum leads to the possible existence of inter-system bias (ISB) between BDS-2 and BDS-3, which becomes the key to affect the time-frequency transfer of BDS. In this contribution, taking the observations of BRUX, CEBR, USUD, WTZZ, and YEL2 stations as an example, five analysis centres (ACs) precise products (for instance, CNT, COM, ESA, GBM, and WUM) are used to evaluate the BDS-2 BII/B3I combined BDS-3 B1I/B3I, B1I/B2a, B1C/B2a, and B1C/B2a time-frequency transfer performance with ignore ISB (ISBNO), estimating ISB as constant (ISBCT), estimating ISB as a random walk (ISBRW) and estimating ISB as white noise (ISBWN) four kinds of estimation strategies. The results show that the ISBCT estimation strategy has the better performance than ISBNO, ISBRW, and ISBWN estimation strategies in BDS-2/BDS-3 combined time-frequency transfer; compared with ignoring ISB strategy, the standard deviation and frequency instability of ISBCT estimation strategy is decreased by 9.16% and 12.83% on average, respectively. Meanwhile, an ISBCT estimation strategy is recommended when using CNT, COM, ESA, and WUM precision products for BDS-2/BDS-3 combined time-frequency transfer.

Earth’s Time-Variable Gravity from GRACE Follow-On K-Band Range-Rates and Pseudo-Observed Orbits

During its science phase from 2002–2017, the low-low satellite-to-satellite tracking mission Gravity Field Recovery And Climate Experiment (GRACE) provided an insight into Earth’s time-variable gravity (TVG). The unprecedented quality of gravity field solutions from GRACE sensor data improved the understanding of mass changes in Earth’s system considerably. Monthly gravity field solutions as the main products of the GRACE mission, published by several analysis centers (ACs) from Europe, USA and China, became indispensable products for quantifying terrestrial water storage, ice sheet mass balance and sea level change. The successor mission GRACE Follow-On (GRACE-FO) was launched in May 2018 and proceeds observing Earth’s TVG. The Institute of Geodesy (IfE) at Leibniz University Hannover (LUH) is one of the most recent ACs. The purpose of this article is to give a detailed insight into the gravity field recovery processing strategy applied at LUH; to compare the obtained gravity field results to the gravity field solutions of other established ACs; and to compare the GRACE-FO performance to that of the preceding GRACE mission in terms of post-fit residuals. We use the in-house-developed MATLAB-based GRACE-SIGMA software to compute unconstrained solutions based on the generalized orbit determination of 3 h arcs. K-band range-rates (KBRR) and kinematic orbits are used as (pseudo)-observations. A comparison of the obtained solutions to the results of the GRACE-FO Science Data System (SDS) and Combination Service for Time-variable Gravity Fields (COST-G) ACs, reveals a competitive quality of our solutions. While the spectral and spatial noise levels slightly differ, the signal content of the solutions is similar among all ACs. The carried out comparison of GRACE and GRACE-FO KBRR post-fit residuals highlights an improvement of the GRACE-FO K-band ranging system performance. The overall amplitude of GRACE-FO post-fit residuals is about three times smaller, compared to GRACE. GRACE-FO post-fit residuals show less systematics, compared to GRACE. Nevertheless, the power spectral density of GRACE-FO and GRACE post-fit residuals is dominated by similar spikes located at multiples of the orbital and daily frequencies. To our knowledge, the detailed origin of these spikes and their influence on the gravity field recovery quality were not addressed in any study so far and therefore deserve further attention in the future. Presented results are based on 29 monthly gravity field solutions from June 2018 until December 2020. The regularly updated LUH-GRACE-FO-2020 time series of monthly gravity field solutions can be found on the website of the International Centre for Global Earth Models (ICGEM) and in LUH’s research data repository. These operationally published products complement the time series of the already established ACs and allow for a continuous and independent assessment of mass changes in Earth’s system.