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.     

Initial accuracy and reliability of current BDS-3 precise positioning,velocity estimation,and time transfer (PVT)

The primary system of Chinese global BeiDou satellite system (BDS-3) was completed to provide global services on December 27, 2018; this was a key milestone in the development process for BDS in terms of its provision of global services. Therefore, this study analyzed the current performance of BDS-3, including its precise positioning, velocity estimation, and time transfer (PVT). The datasets were derived from international GNSS monitoring and assessment system (iGMAS) tracking networks and the two international time laboratories in collaboration with the International Bureau of Weights and Measures (BIPM). With respect to the positioning, the focus is on the real-time kinematic (RTK) positioning and precise point positioning (PPP) modes with static and kinematic scenarios. The results show that the mean available satellite number is 4.8 for current BDS-3 system at short baseline XIA1–XIA3. The RTK accuracy for three components is generally within cm level; the 3D mean accuracy is 8.9 mm for BDS-3 solutions. For the PPP scenarios, the convergence time is about 4 h for TP01 and BRCH stations in two scenarios. After the convergence, the horizontal positioning accuracy is better than cm level and the vertical accuracy nearly reaches the 1 dm level. With respect to kinematic scenarios, the accuracy stays at the cm level for horizontal components and dm level for the vertical component at two stations. In terms of velocity estimation, the horizontal accuracy stays at a sub-mm level, and the vertical accuracy is better than 2 mm/s in the BDS-3 scenario, even in the Arctic. In terms of time and frequency transfer, the noise level of BDS-3 time links can reach 0.096 ns for long-distances link NT01–TP02 and 0.016 ns for short-distance links TP01–TP02. Frequency stability reaches 5E–14 accuracy when the averaging time is within 10,000 s for NT01–TP02 and 1E–15 for TP01–TP02.     

Carrier phase prediction method for GNSS precise positioning in challenging environment

Since the signals of global navigation satellite system (GNSS) are blocked frequently in challenging environments, the discontinuous carrier phases seriously affect the application of GNSS precise positioning. To improve the carrier phase continuity, this paper proposes a carrier phase prediction method based on carrier open-loop tracking. In the open-loop tracking mode, the carrier numerically controlled oscillator (NCO) is controlled by the predicted Doppler, but not by the loop filter output. To improve the phase prediction effective time, accurate receiver clock drift estimation is studied in the prediction method. The phase prediction performance is tested on GNSS software receiver. In the phase prediction effective time tests, open-loop processes were set for the tested channel. The test results show that, when some satellite signals are blocked in 15?s, the probability of carrier phase error less than quarter cycles is more than 94%. In the real time kinematic (RTK) positioning tests, some satellite signals are blocked in 10–15?s repeatedly. The test results show that, the carrier phase continuity is basically not affected by the signal interruption, and the RTK can almost keep continuous centimeter-level positioning accuracy without re-fixing the integer ambiguity.     

Evaluation and analysis on positioning performance of BDS/QZSS satellite navigation systems in Asian-Pacific region

By using the observation data and products of precise obit and clock offset from Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) and GNSS Research Centre, Curtin University in this paper, the positioning performance of BDS/QZSS satellite navigation system has been analyzed and evaluated in aspects of the quantity of visible satellites, DOP value, multipath effect, signal-to-noise ratio, static PPP and kinematic PPP. The analysis results show that compared to BDS single system when the cutoff angle are 30°and 40°, the DOP value of BDS/QZSS combined system has decreased above 20%, and the quantity of visible satellites increased about 16–30% respectively, because of the improved spatial geometric configuration. The magnitude of satellite multipath effect of BDS system shows the trend of MEO?>?IGSO?>?GEO, which is consistent with that of QZSS satellite system, as the constellation structure of the two systems is similar. The variation tendencies of signal-to-noise ratio with respect to elevation angle of the two systems are almost the same at all frequencies, showing that at the same elevation angle the signal-to-noise ratio of MEO satellites is higher than that of IGSO satellites, as the higher obit is the lower transmitting power is obtained. For having a specially designed obit, the variation of signal-to-noise ratio of BDS system is more stable. However, the magnitude of signal-to-noise ratio of QZSS system appears the trend of frequency 3?>?frequency 2?>?frequency 1. The static PPP performance of the BDS/QZSS combination system has been improved more significantly than the BDS single system in E, N and U directions. When the cutoff angle are at 7°, 15° and 30°, the PPP accuracy is increased about 25–34% in U direction, 10–13% and 23–34% in E and N directions respectively. When the elevation angle is large (40°), compared to BDS single system at lower elevation angles (7° and 15°) the PPP accuracy of the BDS/QZSS combination system is improved above 30% in U direction. In kinematic PPP performance, compared to BDS single system, the accuracy, availability and reliability of the BDS/QZSS combination system has been improved too, especially at large elevation angles (30° and 40°), the kinematic PPP accuracy in E and U directions has been improved about 10–50%, and above 50% in U direction. It can be concluded that the combination with QZSS system can improve the positioning accuracy, reliability and stability of BDS system. In the future, with the improvement of the satellite construction of Japan’s QZSS system and the global networking of China’s BDS satellites, the QZSS satellites will contribute greatly to improve the positioning accuracy, reliability, availability and stability of GNSS systems in areas such as cities, mountains, densely-packed buildings and severely covered areas in Asian-Pacific region.     

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.     

基于MLAMBDA的BDS/GPS单频RTK性能分析

GNSS RTK技术以其高精度、高效率、实时性的优点，被广泛应用于航空航天等领域.目前双频RTK技术已非常成熟并且应用较广.相比于双频，单频GNSS RTK在数据质量控制、定位误差处理等方面存在难点.因此单频RTK服务精度可能会受到限制，其定位性能有待研究.本文基于扩展卡尔曼滤波模型，通过MLAMBDA模糊度搜索方法和Ratio检验法，结合实测数据，对比分析BDS，GPS，BDS/GPS三种模式下的单频RTK定位性能.实验证明在静态场景下，三种模式的单频RTK定位精度都在厘米级，可满足高精度定位需求；动态场景下三种模式的模糊度固定率都在70%以上，可满足日常定位需求.在静态及动态应用场景下，北斗的模糊度固定率最高，模糊度解算所用时间短，能实现快速RTK定位.      

Satellite availability and positioning performance of uncombined precise point positioning using BeiDou-2 and BeiDou-3 multi-frequency signals

To realize the smooth transition from regional BeiDou Navigation Satellite System (BDS-2) to the global one (BDS-3), the integration of BDS-2 and BDS-3 is important for providing continuous, stable and reliable positioning, navigation and timing (PNT) services for global users. This work used 154 globally distributed multi-GNSS (Global Navigation Satellite System) experiment stations spanning 30 days to analyze the satellite availability and positioning performance of uncombined precise point positioning (UC-PPP) under current BDS-2 and BDS-3 constellations. We focused on three issues: the influence of BDS-3 receiver tracking abilities, the positioning performance among different areas, and the benefit of multi-frequency observations. The results show that the elliptical zone caused by poor BDS-2 satellite visibility is disappeared when the evenly distributed BDS-3 medium earth orbit satellites are introduced. When BDS-3 are integrated with BDS-2, the area with the Position Dilution of Precision (PDOP) less than 2 can be expanded to 75° S-75° N and 30° E-150° W. The positioning performance of BDS-3 and BDS-2/BDS-3 UC-PPP are seriously affected by the receiver tracking abilities of BDS-3 signals. When the maximum pseudo-random noise sequences (PRNs) of BDS-3 satellites tracked by stations are within 30 or 37, the positioning accuracy of static UC-PPP can be improved by 22.94% or 8.27% due to the integration of BDS-2 and BDS-3. Besides, the most improvement of BDS-2 and BDS-3 integration is achieved in Asia-Pacific regions, especially for the kinematic UC-PPP or the poor receiver tracking abilities of BDS-3. Similar to the multi-frequency BDS-2 UC-PPP, the benefit of multi-frequency signals for BDS-3 or BDS-2/BDS-3 UC-PPP is also non-vital. The three-dimensional positioning accuracy of BDS-2/BDS-3 multi-frequency UC-PPP in static mode and kinematic mode are 2.24 cm and 5.39 cm, while the corresponding convergence time are 49.62 min and 73.80 min, respectively. Compared with BDS-2, both the positioning accuracy and the convergence time of BDS-2/BDS-3 joint UC-PPP are improved by approximately over 50%, which indicates that BDS-3 has a great potential to provide high-quality PNT services as other global navigation satellite systems.     

BDS/GPS组合导航接收机自主完好性监测算法

为使接收机自主完好性监测（RAIM）技术应用于民航垂直引导进近（APV）飞行阶段成为可能,研究了BDS/GPS组合导航RAIM算法。提出了一种基于BDS/GPS定位解最优加权平均解的算法,结合最优加权平均解与BDS/GPS定位解的关系建立检验统计量,根据最大允许的虚警率计算检验门限,实现对故障所在卫星导航系统的检测,并采用加权最小二乘残差法对故障进行检测与识别。研究结果对多星座组合卫星导航系统应用于民航APV飞行阶段的导航具有一定的参考意义。      

基于混沌粒子群优化的北斗/GPS组合导航选星算法

全球卫星导航系统（GNSS）接收机在接收信号的过程中会受到诸如建筑物遮挡、信号干扰等因素的影响,无法得到全部可见星。为减轻多星座组合接收机的处理负担,研究利用部分可见卫星进行定位的快速选星算法,提出了一种基于混沌粒子群优化（CPSO）的北斗/GPS组合导航选星算法。首先,对当前历元时刻可见卫星进行连续编码,按照选星数目分组,每个分组视为一个粒子。然后,通过混沌映射初始化粒子种群,选取几何精度因子（GDOP）作为评价粒子优劣的适应度函数;粒子通过粒子群优化算法的速度-位移模型更新自身位置,逐渐趋近空间卫星几何分布较好的卫星组合全局最优解。最后,采集北斗/GPS实际数据对选星算法进行仿真验证和性能比较,结果表明,所提算法在选星颗数多于5颗时,单次选星耗时为遍历法选星的37.5%,选星结果的几何精度因子计算误差在0~0.6之间。该算法可适用于北斗/GPS组合导航定位不同选星颗数的情况。      

Inertial aided BDS triple-frequency integer ambiguity rounding method

The integer ambiguity resolution (AR) of carrier phase is significant for Global Navigation Satellite System (GNSS) precise positioning. However, in kinematic case, single-epoch AR methods based on alone GNSS are usually not reliable due to the instable pseudorange accuracy. Moreover, the computation of classical AR method Least Squares Ambiguity Decorrelation Adjustment (LAMBDA) is large. Thus, the inertial measurement unit (IMU) is introduced, a new inertial-aided AR method that directly rounds the float ambiguity of BeiDou triple-frequency combined observations, which is characterized by long wavelength, low carrier-phase noise and ionospheric delay, is proposed. The mathematical model of the new method is derived first. Then the impacts of the carrier-phase noise, ionospheric delay and inertial navigation system (INS) position error on the AR success ratio of combined observation are analyzed through probabilistic approach. Based on above investigation, the combinations (0, ?1, 1), (1, 4, ?5) and (4, ?2, ?3) are selected to resolve the original ambiguity. A vehicular integrated navigation test is performed to demonstrate the proposed method. The results show that the average AR success ratios of the three selected combinations, whose float ambiguity errors are 0.041, 0.146, 0.279 cycle respectively, are above 97.25% without regard to low-elevation C05. With respect to positioning accuracy based on our AR method when compared with IE software, the east, north, up error RMS of position are 0.042, 0.024, 0.069 m, respectively. In terms of the AR recover after the BeiDou signals outage, as long as 62 s BeiDou signal complete outage, all the ambiguities of all satellites could be re-fixed immediately. Besides, during the 90 s signals partial outage, the AR is not influenced by the position error, since the float ambiguity errors are all below half-cycle. The research of this contribution demonstrates the effectiveness of the proposed new method, which indicates it is applicable to kinematic positioning, even in BDS degraded and denied environments.     

BDS-2/BDS-3 uncalibrated phase delay estimation considering the intra-system bias

Intra-system biases (ISBs) between BDS-2 and BDS-3 are of critical importance when combining observations from the BDS-2 and BDS-3 systems, which is meaningful to fully take advantage of the BDS positioning capability. Meanwhile, ISBs should also be considered in the estimation of BDS uncalibrated phase delays (UPDs). In this research, we present a BDS-2/BDS-3 joint-processing scheme, as well as a method for estimating BDS UPDs. The characteristics of ISBs and the quality of BDS UPDs are analyzed based on 30-day data from 130 multi-GNSS experimental (MGEX) stations. Our results indicate that the ISBs are related to the type and version of the receiver. The ISBs can be regarded as constant across the course of a given day, and the mean standard deviation (STD) values of ISBs over one month for different types of receivers are generally within 0.2 m. Moreover, to assess the quality of UPD products, the residuals of the estimated UPDs and the utilization rates of the observation data are computed. The results show that the quality of BDS UPDs can be improved by correcting the satellite-induced pseudo-range variations, and by estimating the wide-lane (WL) UPD difference between BDS-2 and BDS-3. The average RMS values of the estimated residuals of WL UPD and narrow-lane (NL) UPD are 0.07 and 0.09 cycles, respectively; moreover, the utilization rate of the observation data of WL UPD and NL UPD can reach above 90 %. The performance of BDS precise point positioning (PPP) and PPP ambiguity resolution (PPP-AR) is analyzed in terms of positioning accuracy and convergence performance in both the static and kinematic modes. Compared with PPP ambiguity-float solutions, the positioning accuracy of PPP-AR is significantly improved, especially in the east direction. The impact of ISBs on PPP and PPP-AR is also analyzed, and the results indicate that ISBs can improve the convergence speed of float PPP, but can be disregarded in PPP-AR.     

Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (real-time kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used 7 days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 min of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 min to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology.     

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.     

Towards high accuracy GNSS real-time positioning with smartphones

The possibility to access undifferenced and uncombined Global Navigation Satellite System (GNSS) measurements on smart devices with an Android operating system allows us to manage pseudorange and carrier-phase measurements to increase the accuracy of real-time positioning. The goal is to perform real-time kinematic network positioning with smartphones, evaluating the positioning accuracy regarding an external mass-market device. The positioning of Samsung Galaxy S8+ and Huawei P10 plus smartphones was performed using a dedicated tool developed by the authors, considering a continuous operating reference station (CORS) network with a mean inter-station distance of about 50?km. The same positioning technique was also applied to an external GNSS low-cost single-frequency receiver (u-blox EVK-M8T) to compare performance between the receiver and antenna embedded in the previous smartphones and this low-cost receiver coupled with a mass-market antenna (Garmin GA38). Attention was also focused on the phase ambiguity resolution, that it is still a challenging aspect for mass-market devices: even if the two smartphones provide slightly different results, the accuracy obtainable today is greater than 60?cm with a precision of few centimetres in real-time, if a CORS network is available. For real-time applications using portable devices, decimetre-level accuracy is sufficient for many applications, such as rapid mapping and search and rescue activities: these results will open new frontiers in terms of real-time positioning with portable low-cost devices.     

Tightly combined GPS/Galileo RTK for short and long baselines: Model and performance analysis

To ensure the compatibility and interoperability with modernized GPS, Galileo satellites are capable of broadcasting navigation signals on carrier phase frequencies that overlap with GPS, i.e., GPS/Galileo L1-E1/L5-E5a. Moreover, the GPS/Galileo L2-E5b signals have different frequencies with wavelength differences smaller than 4.2?mm. Such overlapping and narrowly spaced signals between GPS and Galileo bring the opportunity to use the tightly combined double-differenced (DD) model for precise real-time kinematic (RTK) positioning, resulting in improved performance of ambiguity resolution and positioning with respect to the classical standard or loosely combined DD model. In this paper, we focus on the model and performance assessment of tightly combined GPS/Galileo L1-E1/L2-E5b/L5-E5a RTK for short and long baselines. We first investigate the tightly combined GPS/Galileo DD observational model for both short and long baselines with simultaneously considering the GPS/Galileo overlapping and non-overlapping frequencies. Particularly, we introduce a reparameterization approach to solve the rank deficiency that caused by the correlation between the DISB parameters and the DD ionospheric parameters for both overlapping and non-overlapping frequencies. Then we present performance assessment for the tightly combined GPS/Galileo RTK model with real-time estimation of the differential inter-system bias (DISB) parameters for short and long baselines in terms of ratio value, ambiguity dilution of precision (ADOP), ambiguity conditional number, decorrelation number, search count, empirical success rate, time-to-first-fix (TTFF), and positioning accuracy. Results from both static and kinematic experiments demonstrated that compared to the loosely combined model, the tightly combined model can deliver improved performance of ambiguity resolution and precise positioning with different satellite visibility. For the car-driven short baseline experiment with 10° elevation cut-off angle, the tightly combined model can not only significantly increase the ratio value by approximately 27.5% (from 16.0 to 20.4), but also reduce the ambiguity ADOP, the conditional number, and the search count in LAMBDA by approximately 22.2% (from 0.027 to 0.021 cycles), 14.9% (from 199.2 to 169.6), and 25.4% (from 150.1 to 112.0), respectively. Comparable decorrelation number, empirical success rate, and positioning accuracy are also obtained. For the car-driven long baseline experiment, it is also observed that the ambiguity resolution performance in terms of the ratio value, the decorrelation number, the condition number, and the search count are significantly improved by approximately 18.5% (from 2.7 to 3.2), 22.0% (from 0.186 to 0.227), 55.9% (from 937.6 to 413.7), and 10.3% (from 43.8 to 39.3), respectively. Moreover, comparable ADOP, empirical success rate, and positioning accuracy are obtained as well. Additionally, the TTFF can be reduced (from 54.1 to 51.8 epochs with 10° elevation cut-off angle) as well from the results of static experiments.     

Ambiguity resolution in precise point positioning with hourly data for global single receiver

Integer ambiguity resolution (IAR) can improve precise point positioning (PPP) performance significantly. IAR for PPP became a highlight topic in global positioning system (GPS) community in recent years. More and more researchers focus on this issue. Progress has been made in the latest years. In this paper, we aim at investigating and demonstrating the performance of a global zero-differenced (ZD) PPP IAR service for GPS users by providing routine ZD uncalibrated fractional offsets (UFOs) for wide-lane and narrow-lane. Data sets from all IGS stations collected on DOY 1, 100, 200 and 300 of 2010 are used to validate and demonstrate this global service. Static experiment results show that an accuracy better than 1 cm in horizontal and 1–2 cm in vertical could be achieved in ambiguity-fixed PPP solution with only hourly data. Compared with PPP float solution, an average improvement reaches 58.2% in east, 28.3% in north and 23.8% in vertical for all tested stations. Results of kinematic experiments show that the RMS of kinematic PPP solutions can be improved from 21.6, 16.6 and 37.7 mm to 12.2, 13.3 and 34.3 mm for the fixed solutions in the east, north and vertical components, respectively. Both static and kinematic experiments show that wide-lane and narrow-lane UFO products of all satellites can be generated and provided in a routine way accompanying satellite orbit and clock products for the PPP user anywhere around the world, to obtain accurate and reliable ambiguity-fixed PPP solutions.     

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.     

Particle filter-based real-time phase line bias estimation for GNSS-based attitude determination with common-clock receivers

Global navigation satellite system (GNSS)-based attitude determination has been widely adopted in a wide variety of terrestrial, sea, air, and space applications. Recently, the emergence of commercial multi-GNSS common-clock receivers has brought new opportunities for high-precision GNSS-based attitude determination with single-differenced (SD) model. However, the key requirement of using this approach is the accurate estimation of the troublesome line bias (LB) in real-time. In this contribution, we propose a particle filter-based real-time phase LB estimation approach that apply to SD model with single-system single-frequency observations from common-clock receiver. We first analyzed the relationship between the integer ambiguity ratio value and the phase LB. It is proved that the accuracy of a given phase LB value can be qualified by the related ambiguity resolution ratio value, and the normalized ratio value can therefore be used to represent the likelihood function of observations. Then, we presented the particle filter-based real-time phase LB estimation procedure, and assessed its performance using GPS L1/BDS B1I observations from two datasets collected with different types of common-clock receivers in terms of the accuracy and convergence time of phase LB estimation, the computation load, and the positioning and attitude determination accuracy with respect to the double-differenced (DD) model. Experimental results demonstrated that the phase LB could be accurately estimated with short convergence time (generally within 15 epochs). Moreover, compared with the classical DD approach, the particle filter-based SD approach delivers comparable positioning root-mean-square (RMS) errors in the North and East components but significantly smaller RMS errors in the Up component. Accordingly, the achievable yaw accuracy is comparable whereas the pitch accuracy is remarkably improved. The improvements of positioning accuracy in the Up component and pitch accuracy are approximately 35.7 % to 63.7 %, and 33.3 % to 63.1 %, respectively. Additionally, the single-epoch computation time with our particle filter-based SD approach is generally 0.08 s, which is obviously larger than the DD approach but could still meet the requirements of real-time applications below 10 Hz sampling.     

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.     

RTK model and positioning performance analysis using Galileo four-frequency observations

This paper proposes a real-time kinematic (RTK) model that uses one common reference satellite for the Galileo system with four frequency observations. In the proposed model, the double-differenced (DD) pseudorange and carrier phase biases among the different frequencies are estimated as unknown parameters to recover the integer features of the DD ambiguities among the different frequencies for ambiguity resolution and precise positioning. Analysis results show that the E5a, E5b, and E5 frequencies have virtually the same performance in terms of the positioning accuracy, observation residuals, and ratio values of ambiguity resolution. However, the E1 frequency performs worse than the E5a, E5b, and E5 frequencies. The RTK results for the combination of multiple frequencies are much better than those for a single-frequency observation, the coordinates’ standard deviation is improved about 20–30%, and the ambiguity fix time is improved about 10%.