Contribution analysis of QZSS to single-frequency PPP of GPS/BDS/GLONASS/Galileo

The Quasi-Zenith Satellite System (QZSS) established by the Japan Aerospace Exploration Agency mainly serves the Asia-Pacific region and its surrounding areas. Currently, four in-orbit satellites provide services. Most users of GNSS in the mass market use single-frequency (SF) receivers owing to the low cost. Therefore, it is meaningful to analyze and evaluate the contribution of the QZSS to SF precise point positioning (PPP) of GPS/BDS/GLONASS/Galileo systems with the emergence of GNSS and QZSS. This study compares the performances of three SF PPP models, namely the GRoup and PHase Ionospheric Correction (GRAPHIC) model, GRAPHIC with code observation model, and an ionosphere-constrained model, and evaluated the contribution of the QZSS to the SF PPP of GPS/BDS/GLONASS/Galileo systems. Moreover, the influence of code bias on the SF PPP of the BDS system is also analyzed. A two-week dataset (DOY 013–026, 2019) from 10 stations of the MGEX network is selected for validation, and the results show that: (1) For cut-off elevation angles of 15, 20, and 25°, the convergence times for the static SF PPP of GLONASS + QZSS are reduced by 4.3, 30.8, and 12.7%, respectively, and the positioning accuracy is similar compared with that of the GLONASS system. Compared with the BDS single system, the convergence times for the static SF PPP of BDS + QZSS under 15 and 25° are reduced by 37.6 and 39.2%, the horizontal positioning accuracies are improved by 18.6 and 14.1%, and the vertical components are improved by 13.9 and 21.4%, respectively. At cut-off elevation angles of 15, 20, and 25°, the positioning accuracy and precision of GPS/BDS/GLONASS/Galileo + QZSS is similar to that of GPS/BDS/GLONASS/Galileo. And the convergence times are reduced by 7.4 and 4.3% at cut-off elevation angles of 20 and 25°, respectively. In imitating dynamic PPP, the QZSS significantly improves the positioning accuracy of BDS and GLONASS. However, QZSS has little effect on the GPS-only, Galileo-only and GPS/BDS/GLONASS/Galileo. (2) The code bias of BDS IGSO and MEO cannot be ignored in SF PPP. In static SF PPP, taking the frequency band of B1I whose multipath combination is the largest among the frequency bands as an example, the vertical component has a systematic bias of approximately 0.4–1.0 m. After correcting the code bias, the positioning error in the vertical component is lower than 0.2 m, and the positioning accuracy in the horizontal component are improved accordingly. (3) The SF PPP model with ionosphere constraints has a better convergence speed, while the positioning accuracy of the three models is nearly equal. Therefore the GRAPHIC model can be used to get good positioning accuracy in the absence of external ionosphere products, but its convergence speed is slower.     

Evaluation on real-time dynamic performance of BDS in PPP,RTK, and INS tightly aided modes

Since China’s BeiDou satellite navigation system (BDS) began to provide regional navigation service for Asia-Pacific region after 2012, more new generation BDS satellites have been launched to further expand BDS’s coverage to be global. In this contribution, precise positioning models based on BDS and the corresponding mathematical algorithms are presented in detail. Then, an evaluation on BDS’s real-time dynamic positioning and navigation performance is presented in Precise Point Positioning (PPP), Real-time Kinematic (RTK), Inertial Navigation System (INS) tightly aided PPP and RTK modes by processing a set of land-borne vehicle experiment data. Results indicate that BDS positioning Root Mean Square (RMS) in north, east, and vertical components are 2.0, 2.7, and 7.6?cm in RTK mode and 7.8, 14.7, and 24.8?cm in PPP mode, which are close to GPS positioning accuracy. Meanwhile, with the help of INS, about 38.8%, 67.5%, and 66.5% improvements can be obtained by using PPP/INS tight-integration mode. Such enhancements in RTK/INS tight-integration mode are 14.1%, 34.0%, and 41.9%. Moreover, the accuracy of velocimetry and attitude determination can be improved to be better than 1?cm/s and 0.1°, respectively. Besides, the continuity and reliability of BDS in both PPP and RTK modes can also be ameliorated significantly by INS during satellite signal missing periods.     

Instantaneous BeiDou–GPS attitude determination: A performance analysis

The advent of modernized and new global navigation satellite systems (GNSS) has enhanced the availability of satellite based positioning, navigation, and timing (PNT) solutions. Specifically, it increases redundancy and yields operational back-up or independence in case of failure or unavailability of one system. Among existing GNSS, the Chinese BeiDou system (BDS) is being developed and will consist of geostationary (GEO) satellites, inclined geosynchronous orbit (IGSO) satellites, and medium-Earth-orbit (MEO) satellites. In this contribution, a BeiDou–GPS robustness analysis is carried out for instantaneous, unaided attitude determination.     

北斗卫星导航系统实时定轨与钟差处理策略

目前鲜有对北斗卫星导航系统（BeiDouNavigationSatelliteSystem,BDS）实时精密定轨与钟差确定的研究,文章提出了BDS实时轨道与实时钟差处理策略,包括了观测与动力学模型、实时轨道与实时钟差处理流程与评估方法。尤其对于实时钟差,为了提高计算效率,联合使用两个独立并行的线程估计非差绝对钟差和历元间相对钟差。利用多模全球卫星导航系统试验(MGEX)与全球连续检测评估系统（iGMAS）实测数据进行了北斗实时轨道与钟差解算,BDS实时轨道径向平均精度对于GEO卫星优于20cm,对于IGSO与MEO一般优于10cm;钟差精度对于GEO卫星为0.5~4.5ns,对于IGSO／MEO为0.2~2.0ns。基于目前的轨道与钟差结果,实时精密单点定位（PrecisePointPositioning,PPP）结果可以达到分米量级。     

A novel predictive algorithm for double difference observations of obstructed BeiDou geostationary earth orbit (GEO) satellites

Transmission link disturbances and device failure cause global navigation satellite system (GNSS) receivers to miss observations, leading to poor accuracy in real-time kinematic (RTK) positioning. Previously described solutions for this problem are influenced by the length of the prediction period, or are unable to account for changes in receiver state because they use information from previous epochs to make predictions. We propose an algorithm for predicting double difference (DD) observations of obstructed BeiDou navigation system (BDS) GEO satellites. Our approach adopts the first-degree polynomial function for predicting missing observations. We introduce a Douglas-Peucker algorithm to judge the state of the rover receiver to reduce the impact of predictive biases. Static and kinematic experiments were carried out on BDS observations to evaluate the proposed algorithm. The results of our navigation experiment demonstrate that RTK positioning accuracy is improved from meter to decimeter level with fixed ambiguity (horizontal?<?2?cm, vertical?<?18?cm). Horizontal accuracy is improved by over 50%, and the vertical accuracies of the results of the static and kinematic experiments are increased by 47% and 27% respectively, compared with the results produced by the classical approach. Though as the baseline becomes longer, the accuracy is weakened, our predictive algorithm is an improvement over existing approaches to overcome the issue of missing data.     

Orbit determination of BeiDou navigation satellite system maneuvered satellites based on instantaneous velocity pulses parameters

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver.     

Analysis on navigation accuracy of high orbit spacecraft based on BDS GEO and IGSO satellites

To make up for the insufficiency of earth-based TT&C systems, the use of GNSS technology for high-orbit spacecraft navigation and orbit determination has become a new technology. It is of great value to applying Geosynchronous Earth Orbit (GEO) and Inclined GeoStationary Orbit (IGSO) navigation satellites for supporting the navigation of high-orbit spacecraft since there are three different types of navigation satellites in BeiDou Navigation Satellite System (BDS): Medium Earth Orbit (MEO), GEO and IGSO. This paper conducts simulation experiments based on Two-Line Orbital Element (TLE) data to analyze and demonstrate the role of these satellites in the navigation of high-orbit spacecraft. Firstly, the spacecraft in GEO was used as the target satellite to conduct navigation experiments. Experiments show that for the spacecraft on the GEO orbit, after adding GEO and IGSO respectively on the basis of receiving MEO navigation satellite signals, the accuracies were improved by 7.22 % and 6.06 % respectively. When adding both GEO and IGSO navigation satellites at the same time, the accuracy can reach 16 m. In the second place, navigation and positioning experiments were carried out on three high elliptical orbit (HEO) satellites with different semimajor axis (32037.2 km, 42385.9 km, 67509.6 km). The experiments show that the number of visible satellites has been improved significantly after adding GEO and IGSO navigation satellites at the same time. The visible satellites in these three orbits were improved by 32.84 %, 41.12 % and 37.68 %, respectively compared with only observing MEO satellites.The RMS values of the navigation positioning errors of these three orbits are 25.59 m, 87.58 m and 712.48 m, respectively.     

Performance assessment of RTPPP positioning with SSR corrections and PPP-AR positioning with FCB for multi-GNSS from MADOCA products

The state-space representation (SSR) product of satellite orbit and clock is one of the most essential corrections for real-time precise point positioning (RTPPP). When it comes to PPP ambiguity resolution (PPP-AR), the fractional cycle bias (FCB) matters. The Japan Aerospace Exploration Agency (JAXA) has developed a multi-GNSS (i.e., global navigation satellite system) advanced demonstration tool for orbit and clock analysis (MADOCA), providing free and precise orbit and clock products. Because of the shortage of relevant studies on performance evaluation, this paper focuses on the performance assessment of RTPPP and PPP-AR by real-time and offline MADOCA products. To begin with, the real-time MADOCA products are evaluated by comparing orbit and clock with JAXA final products, which gives an objective impression of the correction. Second, PPP tests in static and simulated kinematic mode are conducted to further verify the quality of real-time MADOCA products. Finally, the offline MADOCA products are assessed by PPP and PPP-AR comparisons. The results are as follows: (1) Orbit comparisons produced an average error of about 0.04–0.13 m for the global positioning system (GPS), 0.14–0.16 m for the global navigation satellite system (GLONASS), and 0.07–0.08 m for the quasi-zenith satellite system (QZSS). The G15 satellite had the most accurate orbit, with a difference of 0.04 m between the JAXA orbit products and MADOCA’s counterpart, while the R07 satellite had the least accurate orbit with a difference of 0.16 m. Clock products had an accuracy of 0.4–1.3 ns for GPS, 1.4–1.6 ns for GLONASS, and 0.7–0.8 ns for QZSS in general. The G15 satellite had the most accurate clock with a difference of only 0.40 ns between the JAXA clock products and MADOCA products, and the R07 satellite had the least accurate clock with a difference of 1.55 ns. The orbit and clock products for GLONASS performed worse than those of GPS and QZSS. (2) After convergence, the positioning accuracy was 3.0–8.1 cm for static PPP and 8.1–13.7 cm for kinematic PPP when using multi-GNSS observations and precise orbit and clock products. The PFRR station performed the good performance both in static and kinematic mode with an accuracy of 2.99 cm and 8.08 cm, respectively, whereas the CPNM station produced the worst static performance with an error of 8.09 cm, and the ANMG station produced the worst kinematic performance with a counterpart of 13.69 cm. (3) The PPP-AR solution was superior to the PPP solution, given that, with respect to PPP, post-processing PPP-AR improved the positioning accuracy and convergence time by 13–32 % (3–89 %) in GPS-only mode by 2–15 % (5–60 %) in GPS/QZSS mode. Thus, we conclude that the current MADOCA products can provide SSR corrections and FCB products with positioning accuracy at the decimeter or even centimeter level, which could meet the demands of the RTPPP and PPP-AR solutions.     

Comparison of convergence time and positioning accuracy among BDS,GPS and BDS/GPS precise point positioning with ambiguity resolution

Precise point positioning (PPP) usually takes about 30?min to obtain centimetre-level accuracy, which greatly limits its application. To address the drawbacks of convergence speed and positioning accuracy, we develop a PPP model with integrated GPS and BDS observations. Based on the method, stations with global coverage are selected to estimate the fractional cycle bias (FCB) of GPS and BDS. The short-term and long-term time series of wide-lane (WL) FCB, and the single day change of narrow-lane (NL) FCB are analysed. It is found that the range of GPS and BDS non-GEO (IGSO and MEO) WL FCB is stable at up to a 30-day-time frame. At times frame of up to 60?days, the stability is reduced a lot. Whether for short-term or long-term, the changes in the BDS GEO WL FCB are large. Moreover, BDS FCB sometimes undergoes a sudden jump. Besides, 17 and 10 stations were used respectively to investigate the convergence speed and positioning errors with six strategies: BDS ambiguity-float PPP (Bfloat), GPS ambiguity-float PPP (Gfloat), BDS/GPS ambiguity-float PPP (BGfloat), BDS ambiguity-fixed PPP (Bfix), GPS ambiguity-fixed (Gfix), and BDS/GPS ambiguity-fixed (BGfix). The average convergence speed of the ambiguity-fixed solution is greatly improved compared with the ambiguity-float solution. In terms of the average convergence time, the Bfloat is the longest and the BGfix is the shortest among these six strategies. Whether for ambiguity-float PPP or ambiguity-fixed PPP, the convergence reduction time in three directions for the combined system is the largest compared with the single BDS. The average RMS value of the Bfix in three directions (easting (E), northing (N), and up (U)) are 2.0?cm, 1.5?cm, and 5.9?cm respectively, while those of the Gfix are 0.8?cm, 0.5?cm, and 1.7?cm. Compared with single system, the BDS/GPS combined ambiguity-fixed system (BGfix) has the fastest convergence speed and the highest accuracy, with average RMS as 0.7?cm, 0.5?cm, and 1.9?cm for the E, N, U components, respectively.     

Enhanced multipath mitigation method based on multi-resolution CNR model and adaptive statistical test strategy for real-time kinematic PPP

This study proposes an enhanced multipath mitigation method based on multi-resolution carrier-to-noise-ratio (CNR) model and adaptive statistical test strategy for real-time kinematic precise point positioning (PPP) applications. The multi-resolution CNR model is established with GPS observation data collected from DOY 152 to 181 of 2019 by 230 globally distributed IGS stations, which used to analyze the relevant factors affecting CNR. Statistical results indicate that the CNR is not only related to the satellite elevation, but also closely related to the receiver types and specific satellite. The maximum difference between different receivers can reach 20 dB for the same satellite at the same elevation. In addition, the performance of the CNR is also obviously different between each satellite, and the maximum difference between different satellites is about 10 dB for the same receiver at the same elevation. Hence, in terms of the method which is based on CNR information for multipath detection and mitigation, the independence of receiver types, satellite and frequency must be considered. With the above analysis, this study developed a multi-resolution CNR model based on different receiver types, different satellites and different elevation firstly. Then, combined with the adaptive statistical test strategy which is based on the difference of CNR between inter-frequency and the difference of CNR between adjacent epochs, the multipath can be detected effectively. For the epoch which affected by multipath, the down-weighted strategy based on CNR is adopted to mitigate the influence of multipath on positioning. Real-time kinematic PPP data are collected to assess the proposed method, and the results demonstrate that the proposed method can detect the multipath effectively, and the detection rate can reach 90.28%. Moreover, after adopting the mitigation strategy, the RMS bias of the east, north and up components are improved about 19.95%, 17.89% and 23.07% compared to the original results, respectively. It is worth noting that this proposed method is also suitable for other GNSS, such as GLONASS and BDS, but the corresponding CNR model must be established simultaneously.     

Estimation of QZSS differential code biases using QZSS/GPS combined observations from MGEX

As an important error source in Global Navigation Satellite System (GNSS) positioning and ionospheric modeling, the differential code biases (DCB) need to be estimated accurately, e.g., the regional Quasi-Zenith satellite system (QZSS). In this paper, the DCB of QZSS is estimated by adopting the global ionospheric modeling method based on QZSS/GPS combined observations from Multi-GNSS experiment (MGEX). The performance of QZSS satellite and receiver DCB is analyzed with observations from day of year (DOY) 275–364, 2018. Good agreement between our estimated QZSS satellite DCB and the products from DLR and CAS is obtained. The bias and root mean square (RMS) of DCB are mostly within ±0.3 ns. The day-to-day fluctuation of the DCB time series is less than 0.5 ns with about 96% of the cases for all satellites. However, the receiver DCB is a little less stable than satellite DCB, and their standard deviations (STDs) are within 1.9 ns. The result shows that the stability of the receiver DCBs is not significantly related to the types of receiver or antenna.     

基于帝国竞争优化的双目标综合决策选星算法

全球卫星导航系统（GNSS）的应用前景已经得到世界各国的普遍承认，其应用领域也趋于多样化，在此背景下，卫星接收机也要求其具有更快的解算速度和可靠的精度。针对目前多数接收机的选星算法都是固定选星数目从而限制算法机动性的问题，提出基于帝国竞争优化算法（ICA）的双目标综合决策选星算法。为了更好获取几何构型较好的卫星星座，引入可见卫星的卫星仰角和方向角先验信息，进行先验性约束，通过构建几何精度因子（GDOP）以及选星数目2个目标，进行综合决策的快速选星，提高了选星的灵活度，并且在满足用户精度的要求下减轻了多星座卫星接收机的计算负担。通过仿真实验和实测数据对双目标综合决策选星算法验证的结果表明:所提算法在高度截止角5°下引入先验性约束条件后平均选星数目在仿真数据和实测数据中缩减率分别为51.8%和45.4%，平均GDOP值较无约束下分别减少0.209 2和0.248 4。同时，所提算法单次选星平均耗时分别为0.168 4 s和0.303 1 s，与遍历法的选星耗时4 s相比，提高了95.79%和92.42%。      

Analysis of GNSS clock prediction performance with different interrupt intervals and application to real-time kinematic precise point positioning

Continuous and timely real-time satellite orbit and clock products are mandatory for real-time precise point positioning (RT-PPP). Real-time high-precision satellite orbit and clock products should be predicted within a short time in case of communication delay or connection breakdown in practical applications. For prediction, historical data describing the characteristics of the real-time orbit and clock can be used as the basis for performing the prediction. When historical data are scarce, it is difficult for many existing models to perform precise predictions. In this paper, a linear regression model is used to predict clock products. Seven-day GeoForschungsZentrum (GFZ) final clock products sampled at 30 s are used to analyze the characteristics of GNSS clocks. It is shown that the linear regression model can be used as the prediction model for the satellite clock products. In addition, the accuracy of the clock prediction for different satellites are analyzed using historical data with different periods (such as 2 and 10 epochs). Experimental results show that the accuracy of the clock with the linear regression prediction model using historical data with 10 epochs is 1.0 ns within 900 s. This is higher accuracy than that achieved using historical data of 2 epochs. Finally, the performance analysis for real-time kinematic precise point positioning (PPP) is provided using GFZ final clock prediction results and state space representation (SSR) clock prediction results when communication delay or connection breakdown occur. Experimental results show that the positioning accuracy without prediction is better than that with prediction in general, whether using the final clock product or the SSR clock product. For the final clock product, the positioning accuracy in the north (N), east (E), and up (U) directions is better than 10.0 cm with all visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 15.0 cm to 7.0 cm. For the SSR clock product, the positioning accuracy of N, E, and U directions is better than 12.0 cm with visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 12.0 cm to 9.0 cm.     

Switching and performance variations of on-orbit BDS satellite clocks

The information of the satellite clock switching and performance variations on-orbit of Chinese BeiDou-2 Navigation System (BDS) is not available for the public. In order to detect the BDS satellite clock switching and performances variation, we analyzed the precise clock offset products with a total duration of 5?years every BDS satellite equipped four atomic clocks from four different manufactures from January 2013 to October 2017. Three important contributions are concluded as follows. (1) It is found that the average time of on-orbit operation for BDS satellite clocks is about 1–2?years. There have been 22 times of clock switching for BDS satellites, of which the C05 and C08 satellites have been switched to the fourth (last) atomic clock. (2) There are frequent phase adjustments for BDS on-orbit satellite clocks, and the frequency series is relatively stable. Furthermore, there are semi-annual sinusoid cycles in the frequency drift series of C06 and C09 satellites. (3) The performances of MEO satellite clocks perform better than the IGSO and GEO satellite clocks. The average ten-thousand frequency stability of BDS satellite clocks is about 1E-13, which is worse than that of GPS and Galileo but better than that of GLONASS.     

LEO enhanced Global Navigation Satellite System (LeGNSS) for real-time precise positioning services

Global Navigation Satellite System (GNSS) has been widely used in many geosciences areas with its Positioning, Navigation and Timing (PNT) service. However, GNSS still has its own bottleneck, such as the long initialization period of Precise Point Positioning (PPP) without dense reference network. Recently, the concept of PNTRC (Positioning, Navigation, Timing, Remote sensing and Communication) has been put forward, where Low Earth Orbit (LEO) satellite constellations are recruited to fulfill diverse missions. In navigation aspect, a number of selected LEO satellites can be equipped with a transmitter to transmit similar navigation signals to ground users, so that they can serve as GNSS satellites but with much faster geometric change to enhance GNSS capability, which is named as LEO constellation enhanced GNSS (LeGNSS). As a result, the initialization time of PPP is expected to be shortened to the level of a few minutes or even seconds depending on the number of the LEO satellites involved. In this article, we simulate all the relevant data from June 8th to 14th, 2014 and investigate the feasibility of LeGNSS with the concentration on the key issues in the whole data processing for providing real-time PPP service based on a system configuration with fourteen satellites of BeiDou Navigation Satellite System (BDS), twenty-four satellites of the Global Positioning System (GPS), and sixty-six satellites of the Iridium satellite constellations. At the server-end, Precise Orbit Determination (POD) and Precise Clock Estimation (PCE) with various operational modes are investigated using simulated observations. It is found out that GNSS POD with partial LEO satellites is the most practical mode of LeGNSS operation. At the user-end, the Geometry Dilution Of Precision (GDOP) and Signal-In-Space Ranging Error (SISRE) are calculated and assessed for different positioning schemes in order to demonstrate the performance of LeGNSS. Centimeter level SISRE can be achieved for LeGNSS.     

Performance improvement of real-time PPP ambiguity resolution using a regional integer clock

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.     

An empirical solar radiation pressure model for satellites moving in the orbit-normal mode

We present a family of empirical solar radiation pressure (SRP) models suited for satellites orbiting the Earth in the orbit normal (ON) mode. The proposed ECOM-TB model describes the SRP accelerations in the so-called terminator coordinate system. The choice of the coordinate system and the SRP parametrization is based on theoretical assumptions and on simulation results with a QZS-1-like box-wing model, where the SRP accelerations acting on the solar panels and on the box are assessed separately. The new SRP model takes into account that in ON-mode the incident angle of the solar radiation on the solar panels is not constant like in the yaw-steering (YS) attitude mode. It depends on the elevation angle of the Sun above the satellite’s orbital plane. The resulting SRP vector acts, therefore, not only in the Sun-satellite direction, but has also a component normal to it. Both components are changing as a function of the incident angle. ECOM-TB has been used for precise orbit determination (POD) for QZS-1 and BeiDou2 (BDS2) satellites in medium (MEO) and inclined geosynchronous Earth orbits (IGSO) based on IGS MGEX data from 2014 and 2015. The resulting orbits have been validated with SLR, long-arc orbit fits, orbit misclosures, and by the satellite clock corrections based on the orbits. The validation results confirm that—compared to ECOM2—ECOM-TB significantly (factor 3–4) improves the POD of QZS-1 in ON-mode for orbits with different arc lengths (one, three, and five days). Moderate orbit improvements are achieved for BDS2 MEO satellites—especially if ECOM-TB is supported by pseudo-stochastic pulses (the model is then called ECOM-TBP). For BDS2 IGSOs, ECOM-TB with its 9 SRP parameters appears to be over-parameterized. For use with BDS2 IGSO spacecraft we therefore developed a minimized model version called ECOM-TBMP, which is based on the same axis decomposition as ECOM-TB, but has only 2 SRP parameters and is supported by pseudo-stochastic parameters, as well. This model shows a similar performance as ECOM-TB with short arcs, but an improved performance with (3-day) long-arcs. The new SRP models have been activated in CODE’s IGS MGEX solution in Summer 2018. Like the other ECOM models the ECOM-TB derivatives might be used together with an a priori model.     

Time synchronization of new-generation BDS satellites using inter-satellite link measurements

Autonomous satellite navigation is based on the ability of a Global Navigation Satellite System (GNSS), such as Beidou, to estimate orbits and clock parameters onboard satellites using Inter-Satellite Link (ISL) measurements instead of tracking data from a ground monitoring network. This paper focuses on the time synchronization of new-generation Beidou Navigation Satellite System (BDS) satellites equipped with an ISL payload. Two modes of Ka-band ISL measurements, Time Division Multiple Access (TDMA) mode and the continuous link mode, were used onboard these BDS satellites. Using a mathematical formulation for each measurement mode along with a derivation of the satellite clock offsets, geometric ranges from the dual one-way measurements were introduced. Then, pseudoranges and clock offsets were evaluated for the new-generation BDS satellites. The evaluation shows that the ranging accuracies of TDMA ISL and the continuous link are approximately 4?cm and 1?cm (root mean square, RMS), respectively. Both lead to ISL clock offset residuals of less than 0.3?ns (RMS). For further validation, time synchronization between these satellites to a ground control station keeping the systematic time in BDT was conducted using L-band Two-way Satellite Time Frequency Transfer (TWSTFT). System errors in the ISL measurements were calibrated by comparing the derived clock offsets with the TWSTFT. The standard deviations of the estimated ISL system errors are less than 0.3?ns, and the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. For the regional BDS network, the addition of ISL measurements for medium orbit (MEO) BDS satellites increased the clock tracking coverage by more than 40% for each orbital revolution. As a result, the clock predicting error for the satellite M1S was improved from 3.59 to 0.86?ns (RMS), and the predicting error of the satellite M2S was improved from 1.94 to 0.57?ns (RMS), which is a significant improvement by a factor of 3–4.     

Geosynchronous satellites expanding a future GNSS satellite constellation: A precise orbit determination study

The integration of geosynchronous orbit (GSO) satellites in Global Navigation Satellite Systems (GNSS) is mostly discussed to enable a regional enhancement for tracking. But how do GSO satellites affect the orbit determination of the rest of the constellation? How accurately can these orbits be determined in a future GNSS tracking scenario with optical links? In this simulation study we analyze the benefit of GSO satellites as an expansion of a MEO (Medium Earth Orbit) satellite constellation – we selected the Galileo satellite constellation – for MEO Precise Orbit Determination (POD). We address not only the impact on POD of MEO satellites but also the possibility to precisely determine the GSO satellites – geostationary orbits (GEO) and inclined geosynchronous orbits (IGSO) – in such an expanded MEO constellation. In addition to GNSS microwave observations, we analyze the influence of different optical links between the participating entities: Optical two-way Inter-Satellite Links (OISL) and ground-space oriented Optical Two-Way Links (OTWL). These optical measurements together with the GNSS microwave observations give a remarkable benefit for the POD capability. In the case of GNSS and OTWL, we simulate the measurements with regard to a network of 16 ground stations. We pay great attention to the simulation of systematic effects of all measurement techniques. We discuss the influence on the systematic errors as well as the formal orbit uncertainties. A MEO constellation expanded with GSO satellites as well as the use of optical links together with GNSS observations not only improves the MEO satellite orbits but also the GSOs to a great extent.     

Precise orbit determination and precision comparison for FY3C and FY3D with receiver antenna GPS and BDS PCV using spaceborne BDS and GPS observation data

The FY3C and FY3D satellites were equipped with global navigation satellite occultation detector (GNOS) receivers that received both GPS and BDS-2 signals. For further improving precise orbit determination (POD) precisions, we estimated receiver GPS and BDS signal phase center variations (PCV) models with 2° and 5° resolutions and set the different weights for GPS and BDS-2 observations in the combined POD. The BDS-based POD precision using BDS-2 satellite antenna phase center offset (PCO) values from the China Satellite Navigation Office (CSNO) are not as accurate as those obtained from the International GNSS Service (IGS) Multi-GNSS experiments project (MGEX). The estimated receiver GPS and BDS PCV models with 2° and 5° resolutions were estimated from the GPS phase residuals of GPS-based POD and BDS phase residuals of combined POD, respectively. In most cases, the POD precisions using the estimated PCVs with 2° resolution are superior to those with 5° resolution. The precisions of the BDS-based POD and combined POD were both improved by introducing the receiver BDS PCV models. The weighting for GPS and BDS-2 observations can further improve the precision of the combined POD. The tested results of selected weights are better than those with equal weight in the combined POD. The experiment results show that orbital precisions of FY3C are worse than those of FY3D.