Estimating inter-system biases for tightly combined Galileo/BDS/GPS RTK

The overlapping carrier frequencies L1/E1, L5/E5a and B2/E5b from GPS/Galileo/BDS allow inter-system double-differencing of observations, which shows a clear advantage over differencing of the observations of each constellation independently. However, the inter-system biases destroy the integer nature of the inter-system double-differencing ambiguities. Two methods of direct rounding and parameter estimation are used to determine the ISB value. By analyzing data collected from Curtin University from 2015 to 2018, the phase and code inter-system bias (ISB) are related to the receiver type, firmware version and the selected overlapping frequency. Upgrade of receiver firmware version results in changes of ISB values. For example, the upgrade of Javad firmware in Dec, 15, 2017 causes the difference of 0.5 cycles ISB between BDS GEO and non-GEO satellites. By comparing the three dynamic models which include white noise process, random walk process, and random constant in the parameter estimation method, the ISB determined by the random constant model is consistent with the value obtained by the direct rounding method. After the calibration of ISBs, the performances of tightly combined positioning are assessed. The success rate of ambiguity resolution and accuracy of positioning for the tight combination (TC) are significantly improved in comparison with that for the loose combination (LC) over short baselines. For L5/E5a, on which only few satellites can be observed, the maximum increase in success rates of ambiguity resolution can reach 31.7%, i.e., from 54.9% of LC to larger than 86.6% of TC, and the positioning accuracies can even be increased by 0.13 m, i.e., from 0.208 of LC to 0.074 m of TC in East direction for the mix-receiver TRIMBLE NETR9-SEPT POLARX4 in 2018.     

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.     

The update of BDS-2 TGD and its impact on positioning

Timing group delay (TGD) is an important parameter that affects the positioning performance of global navigation satellite systems (GNSS). The BeiDou navigation satellite system (BDS) broadcasts TGD corrections from B3I frequency to B1I and B2I frequencies, namely TGD₁ and TGD₂. On July 21, 2017, BDS updated TGD values with a maximum change of more than 4 ns. In this contribution, we explain the motivation for the BDS TGD update, which is due to the systematic bias between narrowly correlated and widely correlated pseudo-ranges in BDS monitoring receivers. To investigate the impact of the updated TGD, BDS signal-in-space range error (SISRE) and user positioning performance regarding single point positioning (SPP) and precise point positioning (PPP) are analyzed. Results show that after the update of TGD, the difference between the new TGD and multi-GNSS experiment (MGEX) differential code bias (DCB) decreases from 1.38 ns to 0.29 ns on TGD₁ and from 0.40 ns to 0.25 ns on TGD₂. With the contribution of more accurate TGD, the systematic bias of BDS radial SISRE no longer exists, and the overall BDS SISRE also reduces from 1.33 m to 0.87 m on B1I/B2I frequency, from 1.05 m to 0.89 m on B1I frequency, from 0.92 m to 0.91 m on B2I frequency, respectively, which proves the similar precision of BDS TGD and MGEX DCB. One week of statistical results from 28 globally distributed MGEX stations shows that the SPP performance improves on non-B3I frequencies after the TGD update, with a maximum improvement of more than 22% for the B1I/B2I or B1I/B3I combination. The new TGD mainly reduces SPP positioning bias in the East component. The updated TGD also slightly improves the PPP convergence performance for the B1I/B3I combination, but mostly contributes to a more accurate estimation of the receiver clock and ambiguities.     

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.     

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.     

Tight integration of BDS-3/BDS-2/GPS/Galileo observations considering the new overlapping DISBs and its application in obstructed environments

Tight integration can enhance the model strength and positioning performance by considering the characteristic of differential inter-system bias (DISB), especially in obstructed environments. However, limited work emphasizes the comprehensive analysis of five-frequency DISBs between BDS-3 and other systems considering the receiver type, receiver configuration, and antenna type. In addition, the overlapping DISBs between BDS-3 and BDS-2 are also in great demand for further investigation since they are often regarded as one system. In this study, one DISB-float model is introduced to estimate the DISBs, and one DISB-fixed model and one DISB-free model are formulated to enhance the model strength of tight integration. Four dedicated datasets were collected to estimate the DISBs, which are also comprehensively analyzed considering the receiver type, receiver configuration, and antenna type. The results show that the DISBs between BDS-3 and other systems are rather stable over a certain period and are related to the receiver type and receiver configuration, whereas are not related to the antenna type. More interestingly, the B1I code DISB between BDS-3 and BDS-2 exhibits significant magnitude with a mean value of ?1.44 m for the baseline composed of two different receivers. In this case, the B1I code DISB must be considered and the tight integration between BDS-3 and BDS-2 considering its calibration can improve the positioning performance. Besides, the tight integration of the DISB-fixed model can significantly improve the positioning accuracy between multiple GNSS. Compared to the loose integration, the improvement of 60.6 %, 56.6 %, and 61.2 % can be obtained in the E, N, and U directions, when only two satellites are available for each system. In real obstructed environments, the tight integration of the DISB-free model can also improve the positioning performance in terms of positioning availability and accuracy, as well as the ambiguity resolution performance.     

Performance assessment of real-time orbit determination for the Haiyang-2D using onboard BDS-3/GPS observations

The Global Navigation Satellite System (GNSS) receivers equipped on the Haiyang-2D (HY-2D) satellite is capable of tracking the signals of both the third generation of BeiDou satellite navigation System (BDS-3) and the Global Positioning System (GPS), which make it feasible to assess the performance of real-time orbit determination (RTOD) for the HY-2D using onboard GNSS observations. In this study, the achievable accuracy and convergence time of RTOD for the HY-2D using onboard BDS-3 and GPS observations are analyzed. Benefiting from the binary-offset-carrier (BOC) modulation, the BDS-3 C1X signal includes less noise than the GPS C1C signal, which has the same signal frequency and chipping rate. The root mean squares (RMS) of the noises of C1X and C1C code measurements are 0.579 m and 1.636 m, respectively. Thanks to a ten-times higher chipping rate, the code measurements of BDS-3 C5P, GPS C1W and C2W are less noisy. The RMS of code noises of BDS-3 C5P, GPS C1W, and C2W are 0.044 m, 0.386 m, and 0.272 m, respectively. For the HY-2D orbit, the three-dimensional (3D) and radial accuracies can reach 31.8 cm and 7.5 cm with only BDS-3 observations, around 50 % better than the corresponding accuracies with GPS. Better performance of the BDS-3 in RTOD for the HY-2D is attributed to the high quality of its broadcast ephemeris. When random parameters are used to absorb ephemeris errors, substantial improvement is seen in the accuracy of HY-2D orbit with either BDS-3 or GPS. The 3D RMS of HY-2D orbit errors with BDS-3 and GPS are enhanced to 23.1 cm and 33.6 cm, and the RMS of the radial components are improved to 6.1 cm and 13.3 cm, respectively. The convergence time is 41.6 and 75.5 min for the RTOD with BDS-3 and GPS, while it is reduced to 39.2 and 27.4 min after the broadcast ephemeris errors are absorbed by random parameters. Overall, the achievable accuracy of RTOD with BDS-3 reaches decimeter level, which is even better than that with GPS, making real-time navigation using onboard BDS-3 observations a feasible choice for future remote sensing missions.     

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.     

Preliminary analysis of the quality and positioning performance of BDS-3 global interoperable signal B1C&B2a

BeiDou-3 Navigation Satellite System (BDS-3) satellites are equipped with the new generation GNSS signals B1C and B2a, which support the interoperability with GPS and Galileo systems. In this study, the pseudo-range multipath error and carrier phase observation noise of the BDS-3 B1C and B2a signals were evaluated based on zero baseline measurements from the day of year (DOY) 113 to 116, 2020. Further, the precision and performance of the single point positioning (SPP) and precise point positioning (PPP) are assessed at 9 stations. This assessment manifests that the standard deviations (STDs) of the pseudo-range multipath error are about 0.09 ~ 0.22 m, while STDs of the carrier phase observation noise are about 0.075 mm. For the single-frequency SPP, its positioning precision is about 2.03 ~ 4.85 m and 3.29 ~ 10.73 m at the 99.99% confidence level in horizontal and vertical directions, respectively, while the dual-frequency SPP precision is about 1.92 ~ 8.02 m and 4.81 ~ 12.77 m in horizontal and vertical directions, respectively. For the daily static PPP, the convergence time is about 20 ~ 30 min, while the daily positioning precision can reach 1.38 ~ 4.42 cm and -1.31 ~ 4.34 cm in horizontal and vertical directions, respectively. In general, the quality and the SPP and PPP performance of the BDS-3 B1C&B2a signals are comparable to the GPS and Galileo.     

Effect of biases in integrity monitoring for RTK positioning

In road transport, continuous high-accuracy positioning is required in real time. To ensure the proper functioning and safety of vehicular applications, integrity monitoring (IM) is needed to protect from the positioning errors under a certain alert limit (AL) with a pre-defined probability of misleading information (MI). In this study, a detailed threat model is developed for real-time kinematic (RTK) positioning application of short baselines. The model distinguishes between ambiguity-float and -fixed scenarios, and considers the influences of phase and code multipath as well as between-receiver atmospheric residuals. With the float ambiguities temporally constrained, the bias contribution that propagates with time-updated ambiguities was studied analytically for the horizontal protection level (HPL) in IM. Based on real data from both static and kinematic experiments, HPL was computed along the direction of the semi-major axis of the horizontal error ellipse. In ambiguity-float and -fixed cases, the HPL was mostly several meters and decimetres, respectively. It was found that time-propagated biases play a dominant role in the ambiguity-float HPL, and among them, phase and code multipath had in general the largest contributions. For ambiguity-fixed case, the phase multipath was found to play a dominant role in the HPL. This shows the importance of considering the biases in the RTK IM for both the ambiguity-float and -fixed scenarios. Given a horizontal alert limit (HAL) of 5 m, the availabilities of ambiguity-float solutions were low, i.e., below 50% for the static roof tests and below 5% for the kinematic road tests. For the ambiguity-fixed scenario, with HAL at 0.5 m, integrity availability was nearly 100% for the static roof tests and above 85% for the kinematic road tests.     

GPS phase difference variation statistics: A comparison between phase scintillation index and proxy indices

Scintillated GPS phase observations are traditionally characterized by the phase scintillation index, derived from specialized GPS receivers usually tracking at 50 Hz. Geodetic quality GPS receivers, on the other hand, are normally tracking at frequencies up to 1 Hz. However, availability of continuously operating geodetic receivers both in time and geographical location are superior to scintillation receiver’s coverage in many parts of the world. This motivates scintillation studies using regional and global geodetic GPS networks. Previous studies have shown the usefulness of GPS estimated total electron content variations for detecting ionospheric irregularities. In this paper, collocated geodetic and scintillation receivers are employed to compare proxy indices derived from geodetic receivers with the phase scintillation index during quiet and moderately disturbed ionospheric conditions. Sensitivity of the phase scintillation indices at high latitude stations to geomagnetic activity is discussed. Global mapping of ionospheric disturbances using proxy indices from real-time 1 Hz GPS stations are also presented.     

Evaluation of rapid phase clock/bias products for PPP ambiguity resolution and its application to the M7.1 2019 Ridgecrest,California earthquake

Precise point positioning with ambiguity resolution (PPP-AR) is a useful tool for high-precision geodetic and geophysical applications, while phase bias products are the prerequisite to implement PPP-AR. Wuhan University has been providing the final (the best operationally post-processing solution based) phase clock/bias products with a latency of two weeks since March of 2019, while a dedicated open-source software package PRIDE PPP-AR is released to leverage these products for high-precision positioning. In order to satisfy some both time and precision critical applications, such as rapid earthquake response, Wuhan University also released rapid (with comparable quality but with much shorter delivery latency) phase clock/bias products with a latency of less than 24 h and updated PRIDE PPP-AR in July 2019. We first introduce the phase clock/bias generation and validation schemes and the maintenance of routine products provision. Then, with 14 days (July 2 to July 15 in 2019) of GPS data collected from 146 globally distributed IGS (International GNSS Service) stations, we evaluated the positioning performance of the rapid products with respect to their final counterparts. It is found that positioning precision of PPP-AR using rapid products is comparable to that using final products, especially in kinematic positioning mode. When rapid products are used, the RMS of PPP-AR in static mode with respect to IGS weekly solutions can reach 1.7 mm, 1.8 mm and 5.5 mm in the east, north and up components, respectively. Furthermore, the RMS of epoch-wise positions with respect to daily solutions for the east, north and up components are 0.51 cm, 0.57 cm and 1.51 cm for PPP-AR with rapid products in kinematic mode. It demonstrates that the rapid phase clock/bias products can sufficiently meet the precision requirement of most geodetic and geophysical applications yet with much shorter time delay. Finally, we study the July 6th M7.1 2019 Ridgecrest, California earthquake using the rapid phase clock/bias products and demonstrate their comparable performance against the final products.     

A study on TEC reduction during the tail phase of the 21st June 2020 annular solar eclipse

Ionospheric response during the annular solar eclipse of June 21, 2020, has been examined in terms of the Total Electron Content (TEC) obtained from six Global Positioning System (GPS) receivers positioned in the Chinese-Taiwanese region. We have shown TEC variation from satellites designated by PRNs (Pseudo-Random Noise code) 2, 6, and 19. PRN wise TEC trend was observed to depend upon satellite-pass trajectory to the receiver's location during the eclipse period. A time lag of ~15–30 min is also observed in maximum TEC decrement after the phase of maximum eclipse. Instead of the percentage of eclipse magnitude, a reduction in TEC is seen more for the station for which the orbital track of respective satellites was in closer view relative to receivers for more hours of eclipse window. Additionally, the eclipse day diurnal variations are compared with the pre-eclipse day TEC trend, and observed results show a clear decrease in TEC values at all chosen stations after the eclipse onset then reached the lowest value a few minutes afterward the maximum eclipse phase.     

An analysis on combined GPS/COMPASS data quality and its effect on single point positioning accuracy under different observing conditions

With the rapid development of the COMPASS system, it is currently capable of providing regional navigation services. In order to test its data quality and performance for single point positioning (SPP), experiments have been conducted under different observing conditions including open sky, under trees, nearby a glass wall, nearby a large area of water, under high-voltage lines and under a signal transmitting tower. To assess the COMPASS data quality, the code multipath, cycle slip occurrence rate and data availability were analyzed and compared to GPS data. The datasets obtained from the experiments have also been utilized to perform combined GPS/COMPASS SPP on an epoch-by-epoch basis using unsmoothed single-frequency code observations. The investigation on the regional navigation performance aims at low-accuracy applications and all tests are made in Changsha, China, using the “SOUTH S82-C” GPS/COMPASS receivers. The results show that adding COMPASS observations can significantly improve the positioning accuracy of single-frequency GPS-only SPP in environments with limited satellite visibility. Since the COMPASS system is still in an initial operational stage, all results are obtained based on a fairly limited amount of data.     

电离层不规则结构对GPS性能的影响

电离层不规则结构的存在可引起无线电信号的幅度和相位发生随机起伏, 这 种电离层闪烁现象会影响全球定位系统(Global Positioning System, GPS)的 性能, 降低定位精度, 严重时导致信号失锁. 电离层不规则结构对GPS性能的 影响涉及电离层物理、接收机设计和表征卫星几何分布的精度衰减因子(Dilution of Positioning, DOP)等多方面因素. 本文通过对表征电离层不规则结构参数 的分析, 根据GPS接收机跟踪环路和闪烁信号模型, 综合研究了电离层闪烁对 GPS接收机载波跟踪环和码跟踪环跟踪误差的影响; 结合实际观测, 评述 了电离层不规则结构对单频和双频GPS接收机定位性能的影响, 在此基础上 提出了有待深入研究的问题及具体建议.      

A real-time combined quality control method for GNSS precise positioning in harsh environments

Global Navigation Satellite System (GNSS) precise positioning can be significantly affected by severe multipath effects and outliers in harsh environments, and highly relies on quality control strategies. Previous studies mainly focus on the posterior residuals to check and exclude the outliers in GNSS observations, limited work emphasizes the combined quality control method considering both the prior and posterior knowledge simultaneously. This paper proposed a real-time combined quality control method to process the multipath effects and outliers in harsh environments simultaneously. Specifically, in the prior stage, a modified multipath processing strategy is proposed for both phase and code observations, then a modified detection, identification, and adaptation (DIA) method considering the maximum times of data snooping is studied in the posterior stage. Two dedicated experiments in real harsh environments were carried out to evaluate the performance of the proposed combined quality control method. For the static experiment, the proposed method exhibits smaller positioning errors, the best positioning accuracy, and the highest availability in this study. Specifically, the proposed method exhibits an improved percentage of 55.4 %, 56.3 %, and 59.7 % for positioning accuracy compared to those without the quality control method in the E, N, and U directions, respectively. Besides, the proposed method can further improve the performance of ambiguity resolution with an improved percentage of 32.2 %. For the kinematic experiment, the three-dimensional positioning accuracy of the proposed method is 0.577 m, which exhibits a 40.0 % improvement compared to those without the quality control method. Also, the proposed method exhibits better performance under relatively strong multipath effects. In this sense, the proposed real-time combined quality control method is highly appreciated in terms of positioning availability, accuracy, and ambiguity resolution for GNSS precise positioning, especially in harsh environments.     

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.     

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.     

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%.