International GNSS Service Analysis Centers Research Articles

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.

A method to assess the quality of GNSS satellite phase bias products

As part of the International GNSS Service (IGS), several analysis centers provide GPS and Galileo satellite phase bias products to support precise point positioning with ambiguity resolution (PPP-AR). Due to the high correlation with satellite orbits and clock offsets, it is difficult to assess directly the precision of satellite phase bias products. Once outliers exist in satellite phase biases, PPP-AR results are no longer reliable and the combination of satellite phase bias products from IGS analysis centers also gets difficult. In this contribution, we propose a method independent of ground measurements to detect outliers in satellite phase biases by computing the total Difference of satellite Orbits, Clock offsets and narrow-lane Biases at the midnight epoch between two consecutive days. Results over 180 days show that about 0.2, 1.1, 2.0 and 0.1% of the total DOCB values for GPS satellites exceed 0.15 narrow-lane cycles for CODE final, CODE rapid, CNES/CLS final and WUHN rapid satellite products, respectively, while the same outlier-ratios for Galileo satellites are 0.1, 0.9, 0.4 and 0.1%, respectively. As an important contribution to the orbit, clock and bias combination task, we check the consistency of satellite phase bias products between two analysis centers before and after removing these detected outliers from individual analysis centers. It is convincing that the number of large differences of satellite phase biases between two analysis centers is notably reduced.

Impacts of satellite clock errors on GPS/BDS/Galileo real-time PPP time transfer

By utilizing the real-time precise orbit and clock products provided by International GNSS Service (IGS), it is feasible to calculate real-time PPP (RTPPP) time and frequency transfer. The quality of these real-time precise products has a significant effect on the performance of clock comparisons and time transfer. This paper focuses on real-time clock comparisons with IGS real-time multi-GNSS precise products, which tries to explore the potential of GNSS RTPPP time transfer in time and frequency community. By using real-time precise satellite orbit and clock products from two IGS analysis centers, i.e. CNES and WHU, the clock comparisons and time transfer performance of four time links are comprehensively investigated. It is shown that the statistical uncertainty of real-time clock comparison based on multi-GNSS is within 0.15 ns, and GPS RTPPP provides time transfer results with better performance than BDS-3 and Galileo. In addition, the deviations occur in remote time links results of BDS-3 and Galileo-only between using CNES and WHU, the maximum difference can reach up to 1.10 ns. It is shown that real-time BDS-3 and Galileo satellite products of CNES and WHU are inconsistent, and will affect the time transfer performance. The paper also investigates the receiver clock offset solutions determined by using different available satellites. The results show that there are significant satellite-related biases between different satellites, especially for BDS-3 and Galileo. Thus, the reference time scales determined by using different satellites are inconsistent, and further, the time transfer for long baseline time links will be affected as there are few common view satellites for remote stations.

Modeling the Differences between Ultra-Rapid and Final Orbit Products of GPS Satellites Using Machine-Learning Approaches

The International GNSS Service analysis centers provide orbit products of GPS satellites with weekly, daily, and sub-daily latency. The most frequent ultra-rapid products, which include 24 h of orbits derived from observations and 24 h of orbit predictions, are vital for real-time applications. However, the predicted part of the ultra-rapid orbits is less accurate than the estimated part and has deviations of several decimeters with respect to the final products. In this study, we investigate the potential of applying machine-learning (ML) and deep-learning (DL) algorithms to further enhance physics-based orbit predictions. We employed multiple ML/DL algorithms and comprehensively compared the performances of different models. Since the prediction errors of the physics-based propagators accumulate with time and have sequential characteristics, specific sequential modeling algorithms, such as Long Short-Term Memory (LSTM), show superiority. Our approach shows promising results with average improvements of 47% in 3D RMS within the 24-hour prediction interval of the ultra-rapid products. In the end, we applied the orbit predictions improved by LSTM to kinematic precise point positioning and demonstrated the benefits of LSTM-improved orbit predictions for positioning applications. The accuracy of the station coordinates estimated based on these products is improved by 16% on average compared to those using ultra-rapid orbit predictions.

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.

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.

Preliminary Analysis of Intersystem Biases in BDS-2/BDS-3 Precise Time and Frequency Transfer

The Chinese BeiDou global satellite system (BDS-3) and regional system (BDS-2) are predicted to coexist over the next decade. Intersystem biases (ISBs) in BDS-2/BDS-3 play a key role in maintaining the consistency and continuity from the BDS-2 to BDS-3 time transfer. Here, we discuss the temporal characteristics, parameter composition, generation mechanism, and the effect of ISBs in BDS-2/BDS-3 on time and frequency transfer. The satellite orbits and clock products from three international GNSS service analysis centers, namely Wuhan University (WUM, China), GeoForschungsZentrum Potsdam (GFZ, Germany), and the Center for Orbit Determination in Europe (CODE), were employed to investigate the time-transfer stability of ISBs when BDS-2 and BDS-3 were used in combination. We analyzed the intrinsic characteristics of ISBs, the receiver types, antennas, and frequency standards. Our first results showed that ISBs are stable for different analysis center products, although the mean values of daily results differed markedly for the three analysis centers. With respect to the relationship between station attribution and ISB difference for a time link, the receiver type, antenna, and frequency standard influence the ISB differences in time and frequency transfer. The effect of three ISB stochastic models was evaluated with respect to time and frequency transfer. The “walk” and “constant” schemes were slightly superior to “noise”, with the improvement in their frequency stability being approximately 5% compared with that of “noise”.

Exchanging satellite attitude quaternions for improved GNSS data processing consistency

The orientation of GNSS satellites in space is a key quantity in GNSS data processing. It is required to correctly apply several force models and observation corrections. Incorrect or insufficient modeling of satellite attitude can lead to inconsistencies both among providers of GNSS products and between providers and users, which negatively affects the quality of combined products and positioning solutions. Exchanging satellite attitude information in the form of quaternions helps to eliminate or reduce those inconsistencies. This study presents the first systematic exchange of attitude data in a common format (called ORBEX) within the International GNSS Service (IGS). A comparison of attitude auxiliary data from seven IGS analysis centers over a one-year period shows significant differences for GPS and GLONASS satellites, but not for Galileo. These differences are mostly confined to eclipse periods but can reach up to 180°. Considering the attitude differences between analysis center solutions in an experimental clock combination significantly improved the consistency of analysis center solutions during eclipse periods. A kinematic PPP analysis covering ten globally distributed stations over one week resulted in an almost unanimous improvement when using the provided satellite attitude instead of a nominal model, with an average RMS reduction of 50% in the east and up components. The results presented in this study show that satellite attitude is important GNSS auxiliary data and making it available benefits both providers and users.

Evaluation of BDS-2 real-time orbit and clock corrections from four IGS analysis centers

Real-time precise orbit/clock product is fundamental to BeiDou Navigation Satellite System (BDS) real-time precise point positioning (PPP). In order to explore achievable performance of BDS real-time orbit/clock products and thus offer usage recommendations for BDS real-time PPP users, this paper studies BDS real-time orbit/clock corrections provided by four International GNSS Service (IGS) Analysis Centers (ACs), i.e. Wuhan University (WHU), Deutsches Zentrum für Luft- und Raumfahrt (DLR), GeoForschungsZentrum Potsdam (GFZ) and Centre National d’ Etudes Spatiales (CNE) for seven consecutive days staring from day of year (DOY) 324, 2019. Firstly, the availability of BDS-2 real-time orbit/clock corrections is studied. Larger than 85% availabilities are identified for all ACs. During the test period, DLR does not provide all Geosynchronous Earth Orbit (GEO) satellites’ corrections, whereas CNE does not provide C14/C16′s corrections. Secondly, the BDS real-time orbit accuracy is analyzed. Results indicate that the real-time orbit accuracy of GEO satellites is at meter level, and those of Inclined Geosynchronous Satellite Orbit (IGSO)/Medium Earth Orbit (MEO) satellites are at decimeter level. Among all ACs, the accuracy of CNE’s three-dimensional (3D) orbit correction is the best, which is 2.391/0.278/0.271 m for GEO/IGSO/MEO satellites, respectively. DLR has the largest orbit errors of 1.116/0.504 m for IGSO/MEO satellites. Thirdly, the BDS real-time clock offset precision is investigated. On the one hand, CNE’s real-time corrections still perform best with 1.19/0.28/0.32 ns clock offset precision for GEO/IGSO/MEO satellites, respectively. On the other hand, DLR’s real-time clock is the worst with 2.61/1.91 ns IGSO/MEO clock offset precision. Finally, all corrections are applied to estimate 47 Multi-GNSS Experiment (MGEX) station’s BDS-2 real-time PPP on DOY 330, 2019. Results show an average of 0.53–1.46 h convergence time and 8.8–10.9 cm positioning accuracy in the static mode. In the meantime, the average convergence time in the kinematic mode is 2.11–9.84 h, much longer than the static counterpart. The corresponding converged positioning accuracy is 30.7–68.0 cm. To sum up, WHU/GFZ/CNE’s real-time corrections are proven with satisfied orbit/clock performance, thus are recommended for BDS-2 real-time PPP.

Performance evaluation of real-time global ionospheric maps provided by different IGS analysis centers

With the development of real-time precise clock and orbit products, high-precision real-time ionospheric products have become one of the most critical resources for real-time single-frequency precise point positioning. Fortunately, there are several international GNSS service (IGS) analysis centers, e.g., UPC, WHU, and CAS, that are providing real-time global ionospheric maps (RT-GIMs). We evaluate these maps in detail over 2 years for different aspects. First, the RT-GIMs and 1-day predicted ionospheric products (C1PG GIM) differenced with the IGS final GIMs (IGSG GIM) are performed. Second, ionospheric vertical total electron content from Jason-2/3 data is set as a reference to evaluate the quality of RT-GIMs over oceanic regions. Third, 22 stations, which are not used in the generation of RT-GIMs, C1PG GIM, and IGSG GIM, are selected and the difference of slant total electron content (dSTEC) method is used to assess the accuracy and consistency of RT-GIMs over continental regions. Finally, the performance of RT-GIMs in the position domain is demonstrated based on SF-PPP solutions. The results show that the accuracy of the RT-GIMs is slightly worse than that of C1PG GIM and IGSG GIM. All RT-GIMs and the C1PG GIM have a smaller mean difference compared to the IGSG GIM by (−0.97, − 0.90, − 0.77, − 0.80) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM). Over oceanic regions, the RT-GIMs perform nearly the same as the C1PG GIM, but a slightly worse than IGSG GIM. The STDs are (3.96, 3.05, 3.25, 3.12, 2.54) TECU relative to Jason-2 and (4.94, 3.24, 3.38, 3.24, 2.65) TECU relative to Jason-3 for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM), respectively. Comparing with dSTEC values observed from the selected ground stations over continental regions, the RMS is (4.02, 2.16, 2.29, 1.86, 1.49) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM). In the position domain, the positioning accuracy of SF-PPP solution corrected by the RT-GIMs and C1PG GIM can reach decimeter level in the horizontal direction and meter level in the vertical direction, which is worse than obtained by IGSG GIM. Meanwhile, the positioning accuracy of SF-PPP corrected by RT-GIMs is almost the same as that obtained using C1PG GIM. For RT-GIMs, the accuracy of the CAS RT-GIM is slightly better than that of the other two RT-GIMs.

Comparative analysis of MGEX products for post-processing multi-GNSS PPP

In recent years, the precise products generated by the International GNSS Service (IGS) as a part of the Multi-GNSS Experiment (MGEX) project have been increasingly used for multi-GNSS applications. Nowadays, six IGS Analysis Centers (ACs) have been providing GNSS products with different features. However, there is still neither a combined solution nor a standard accuracy definition for MGEX products, unlike the standard IGS products. For the GNSS techniques that are directly dependent on precise products, such as Precise Point Positioning (PPP), the quality of these products is a very crucial point in positioning performance. In this context, this study aims to investigate the impact of MGEX products provided by different IGS ACs on post-processing PPP performance in terms of accuracy, availability, and consistency. For this purpose, an experimental test was performed including all possible multi-GNSS combinations of GPS, GLONASS, Galileo, and BeiDou. 24-hour observation datasets collected at ten IGS stations during the 1-month period of May 1–31 were processed with twelve PPP modes using all available precise products. As a first step, an analysis of product availability was carried out for the related MGEX precise products within the test period to be able to assess the impact of the availability on the test results. PPPH software was used to perform the test and the results were statistically assessed as regards positioning error, RMS error and convergence time. The results indicate that the PPP performance may considerably differ depending on the precise products utilized in the PPP process. For the test period, PPP solutions utilizing the precise products generated by GFZ (GeoForschungsZentrum Potsdam) and WU (Wuhan University) agencies have relatively better positioning performance for nearly all processing modes compared to other solutions. The quality and availability of precise products are significant factors which lay behind the better PPP performance. On the other hand, while the integration of two or more systems significantly strength the PPP performance, GPS is still the dominant system for PPP and the solutions that do not include GPS constellation have very poor performance. The results also show that MGEX products have different impacts on the PPP performance as varying with the constellation involved in PPP solution and the geographical location of the station.

An Optimum Strategy for Producing Precise GPS Satellite Orbits using Double-Differenced Observations

Both the double-differenced and zero-differenced GNSS positioning strategies have been widely used by the geodesists for different geodetic applications which are demanded for reliable and precise positions. A closer inspection of the requirements of these two GNSS positioning techniques, the zero-differenced positioning, which is known as Precise Point Positioning (PPP), has gained a special importance due to three main reasons. Firstly, the effective applications of PPP for geodetic purposes and precise applications depend entirely on the availability of the precise satellite products which consist of precise satellite orbital elements, precise satellite clock corrections, and Earth orientation parameters. Secondly, the PPP processing strategy has been employed by the International GNSS Service (IGS) and IGS analysis centers to evaluate their products in terms of homogeneity and precision over a long period of time. Thirdly, the precise positions, which are determined using PPP technique, and are referenced directly to the geodetic reference frame of the satellite orbital parameters. Thus, the definition of the geodetic datum of the site coordinates using different strategies plays an enormous role in the process of generation satellite orbital parameters which have to be compatible with the corresponding satellite clock corrections and the Earth orientation parameters. This study focuses on producing uninterrupted series of satellite orbit and clock products using different criteria and assesses these products using PPP. The double-difference processing technique was used to achieve the goal of this study by Bernese GPS software version 5.0. Twenty-two globally distributed IGS stations were selected to run PPP based on the generated products and then compare the results with corresponding PPP results which were created based on the IGS rapid products. The comparison pointed to a significant improvement in the generated precise products which have considerably increased the precision of positions. What is more, this study stated that there is an observable agreement between the horizontal positions accuracies which are generated using different techniques for modeling the reference frame.

Evaluation and analysis of real-time precise orbits and clocks products from different IGS analysis centers

To meet the increasing demands from the real-time Precise Point Positioning (PPP) users, the real-time satellite orbit and clock products are generated by different International GNSS Service (IGS) real-time analysis centers and can be publicly received through the Internet. Based on different data sources and processing strategies, the real-time products from different analysis centers therefore differ in availability and accuracy. The main objective of this paper is to evaluate availability and accuracy of different real-time products and their effects on real-time PPP. A total of nine commonly used Real-Time Service (RTS) products, namely IGS01, IGS03, CLK01, CLK15, CLK22, CLK52, CLK70, CLK81 and CLK90, will be evaluated in this paper. Because not all RTS products support multi-GNSS, only GPS products are analyzed in this paper. Firstly, the availability of all RTS products is analyzed in two levels. The first level is the epoch availability, indicating whether there is outage for that epoch. The second level is the satellite availability, which defines the available satellite number for each epoch. Then the accuracy of different RTS products is investigated on nominal accuracy and the accuracy degradation over time. Results show that Root-Mean-Square Error (RMSE) of satellite orbit ranges from 3.8 cm to 7.5 cm for different RTS products. While the mean Standard Deviations of Errors (STDE) of satellite clocks range from 1.9 cm to 5.6 cm. The modified Signal In Space Range Error (SISRE) for all products are from 1.3 cm to 5.5 cm for different RTS products. The accuracy degradation of the orbit has the linear trend for all RTS products and the satellite clock degradation depends on the satellite clock types. The Rb clocks on board of GPS IIF satellites have the smallest degradation rate of less than 3 cm over 10 min while the Cs clocks on board of GPS IIF have the largest degradation rate of more than 10 cm over 10 min. Finally, the real-time kinematic PPP is carried out to investigate the effects of different real-time products. The CLK90 has the best performance and mean RMSE of 26 globally distributed IGS stations in three components are 3.2 cm, 6.6 cm and 8.5 cm. And the second-best positioning results are using IGS03 products.

GLONASS pseudorange inter-channel biases considerations when jointly estimating GPS and GLONASS clock offset

GLONASS clock offset estimation is affected by the inter-channel biases (ICBs) caused by frequency division multiple access technique. The effect of ICBs on joint GPS/GLONASS clock offset estimation is analyzed. An efficient approach for joint estimation of GPS/GLONASS satellite clock offset is applied to the generation of 30-s clock offset products. During the estimation, the following three ICB handling strategies were tested: calculating ICBs for each GLONASS signal channel, calculating ICBs for each GLONASS satellite and neglecting ICBs. The behavior of ICBs under different strategies was statistically stable. Subsequently, the clock offset products using different ICB strategies were evaluated. The evaluation shows that consideration of the ICB is important when estimating the clock offset. Furthermore, estimating one ICB for each GLONASS satellite is better than estimating one for each GLONASS signal channel because, with the former strategy, the clock offset products behave more smoothly and have higher accuracy compared with products from the International GNSS Service Analysis Center. In addition, precise point positioning, using clock offsets based on one ICB for each GLONASS satellite, has the highest positioning accuracy.

Robust combination of IGS analysis center GLONASS clocks

The International GNSS Service (IGS) Analysis Centers (ACs) generate precise GNSS products by integrating tracking data from globally distributed IGS stations. The ACs’ products are further processed and combined for the positioning, navigation and timing users. We propose a robust least squares estimation for combining GLONASS clock products. Besides the difference in clock reference, systematic errors exist in the clock differences between different ACs, which show a linear trend and are completely removed. The clock combinations utilizing the final, rapid and ultra-rapid products of the IGS ACs were implemented in this study. The results of clock validation show that the agreement and stability of the newly generated combination products are better than those of most ACs. Furthermore, the impact of the different clock combination products on precise point positioning (PPP) is analyzed. Compared to the results of PPP using the products generated by the traditional combination strategy, the repeatability of GLONASS static PPP using the new clock combinations is 2.31, 2.95, and 5.62 mm, an improvement by 26.7, 28.9 and 20.6% in N, E and U respectively. The average RMS of GLONASS kinematic PPP using the new clock combinations is 1.20, 1.47 and 3.01 cm, an improvement by 67.5, 71.9 and 70.3% in N, E and U respectively. The improvement of the proposed strategy on PPP results is significant.

Applications of two-way satellite time and frequency transfer in the BeiDou navigation satellite system

A two-way satellite time and frequency transfer (TWSTFT) device equipped in the BeiDou navigation satellite system (BDS) can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination (MPOD) method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service (IGS) analysis centers (ACs) show that the reference time difference between BeiDou time (BDT) and golbal positoning system (GPS) time (GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10−12, which is similar to the GPS IIR.

Comparación de la metodología utilizada para el cálculo de los parámetros orbitales en los Centros de Análisis del Servicio GNSS Internacional (IGS)

The orbital information given in the form of Ultra-Rapid Orbits (IGA and IGU), Rapid Orbits (IGR), and Final Orbits (IGS), as well as the Earth rotational parameters and the clock offset provided by the International GNSS Service plays an important role in supporting the Global Navigation Satellite Systems GPS and GLONASS. In this paper, we compare the observables, the force models, the adjustment methods and the numerical integration procedures applied by the different International GNSS Service Analysis Centers for the orbital parameter determination.

Development of Precise Point Positioning Method Using Global Positioning System Measurements

Precise point positioning (PPP) is increasingly used in several parts such as monitoring of crustal movement and maintaining an international terrestrial reference frame using global positioning system (GPS) measurements. An accuracy of PPP data processing has been increased due to the use of the more precise satellite orbit/clock products. In this study we developed PPP algorithm that utilizes data collected by a GPS receiver. The measurement error modelling including the tropospheric error and the tidal model in data processing was considered to improve the positioning accuracy. The extended Kalman filter has been also employed to estimate the state parameters such as positioning information and float ambiguities. For the verification, we compared our results to other of International GNSS Service analysis center. As a result, the mean errors of the estimated position on the East-West, North-South and Up-Down direction for the five days were 0.9 cm, 0.32 cm, and 1.14 cm in 95% confidence level.

An evaluation of solar radiation pressure strategies for the GPS constellation

The subtle effects of different Global Positioning System (GPS) satellite force models are becoming apparent now that mature processing strategies are reaching new levels of accuracy and precision. For this paper, we tested several approaches to solar radiation pressure (SRP) modeling that are commonly used by International GNSS Service (IGS) analysis centers. These include the GPS Solar Pressure Model (GSPM; Bar-Sever and Kuang in The Interplanetary Network Progress Report 42-160, 2005) and variants of the so-called DYB model (Springer et al. in Adv Space Res 23:673–676, 1999). Our results show that currently observed differences between GPS orbit solutions from the various IGS analysis centers are in large part explained by differences between their respective approaches to modeling SRP. DYB-based strategies typically generate orbit solutions that have the smallest differences with respect to the IGS final combined solution, largely because the DYB approach is most commonly used by the contributing analysis centers. However, various internal and external metrics, including ambiguity resolution statistics and satellite laser ranging observations, support continued use of the GSPM-based approach for precise orbit determination of the GPS constellation, at least when using the GIPSY-OASIS software.

Further Characterization of the Time Transfer Capabilities of Precise Point Positioning (PPP): The Sliding Batch Procedure

In recent years, many national timing laboratories have installed geodetic Global Positioning System receivers together with their traditional GPS/GLONASS Common View receivers and Two Way Satellite Time and Frequency Transfer equipment. Many of these geodetic receivers operate continuously within the International GNSS Service (IGS), and their data are regularly processed by IGS Analysis Centers. From its global network of over 350 stations and its Analysis Centers, the IGS generates precise combined GPS ephemeredes and station and satellite clock time series referred to the IGS Time Scale. A processing method called Precise Point Positioning (PPP) is in use in the geodetic community allowing precise recovery of GPS antenna position, clock phase, and atmospheric delays by taking advantage of these IGS precise products. Previous assessments, carried out at Istituto Nazionale di Ricerca Metrologica (INRiM; formerly IEN) with a PPP implementation developed at Natural Resources Canada (NRCan), showed PPP clock solutions have better stability over short/medium term than GPS CV and GPS P3 methods and significantly reduce the day-boundary discontinuities when used in multi-day continuous processing, allowing time-limited, campaign-style time-transfer experiments. This paper reports on follow-on work performed at INRiM and NRCan to further characterize and develop the PPP method for time transfer applications, using data from some of the National Metrology Institutes. We develop a processing procedure that takes advantage of the improved stability of the phase-connected multi-day PPP solutions while allowing the generation of continuous clock time series, more applicable to continuous operation/monitoring of timing equipment.