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.     

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.      

Demonstration of a high sensitivity GNSS software receiver for indoor positioning

Advances in signal processing techniques contributed to the significant improvements of GNSS receiver performance in dense multipath environments and created the opportunities for a new category of high-sensitivity GNSS (HS-GNSS) receivers that can provide GNSS location services in indoor environments. The difficulties in improving the availability, reliability, and accuracy of these indoor capable GNSS receivers exceed those of the receivers designed for the most hostile urban canyon environments. The authors of this paper identified the vector tracking schemes, signal propagation statistics, and parallel processing techniques that are critical to a robust HS-GNSS receiver for indoor environments and successfully incorporated them into a fully functional high-sensitivity software receiver. A flexible vector-based receiver architecture is introduced to combine these key indoor signal processing technologies into GSNRx-hs™ – the high sensitivity software navigation receiver developed at the University of Calgary. The resulting receiver can perform multi-mode vector tracking in indoor environment at various levels of location and timing uncertainties. In addition to the obvious improvements in time-to-first-fix (TTFF) and signal sensitivity, the field test results in indoor environments surrounded by wood, glass, and concrete showed that the new techniques effectively improved the performance of indoor GNSS positioning. With fine GNSS timing, the proposed receiver can consistently deliver indoor navigation solution with the horizontal accuracy of 2–15 m depending on the satellite geometry and the indoor environments. If only the coarse GNSS timing is available, the horizontal accuracy of the indoor navigation solution from the proposed receiver is around 30 m depending on the coarse timing accuracy, the satellite geometry, and the indoor environments. From the preliminary field test results, it has been observed that the signal processing sensitivity is the dominant factor on the availability of the indoor navigation solution, while the GNSS timing accuracy is the dominant factor on the accuracy of the indoor navigation solution.     

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.     

Mitigation of receiver biases in ionospheric observables from PPP with ambiguity resolution

PPP (Precise Point Positioning) is a GNSS (Global Navigation Satellite Systems) positioning method that requires SSR (State Space Representation) corrections in order to provide solutions with an accuracy of centimetric level. The so-called RT-PPP (Real-time PPP) is possible thanks to real-time precise SSR products, for orbits and clocks, provided by IGS (International GNSS Service) and its associate analysis centers such as CNES (Centre National d'Etudes Spatiales). CNES SSR products also enable RT-PPP with integer ambiguity resolution. In GNSS related literature, PPP with ambiguity resolution (PPP-AR) in real-time is often referred as PPP-RTK (PPP – Real Time Kinematic). PPP-WIZARD (PPP - With Integer and Zero-difference Ambiguity Resolution Demonstrator) is a software that is made available by CNES. This software is capable of performing PPP-RTK. It estimates slant ionospheric delays and other GNSS positioning parameters. Since ionospheric effects are spatially correlated by GNSS data from active networks, it is possible to model and provide ionospheric delays for any position in the network coverage area. The prior knowledge ionospheric delays can reduce positioning convergence for PPP-RTK users. Real-time ionospheric models could benefit from highly precise ionospheric delays estimated in PPP-AR. In this study, we demonstrate that ionospheric delays obtained throughout PPP-AR estimation are actu ally ionospheric observables. Ionospheric observables are biased by an order of few meters caused by the receiver hardware biases. These biases prohibit the use of PPP-WIZARD ionospheric delays to produce ionospheric models. Receiver biases correction is essential to provide ionospheric delays while using PPP-AR based ionospheric observables. In this contribution, a method was implemented to estimate and mitigate receiver hardware biases influence on slant ionospheric observables from PPP-AR. In order to assess the proposed approach, PPP-AR data from 12 GNSS stations were processed over a two-month period (March and April 2018). A comparison between IGS ionospheric products and PPP-AR based ionospheric observables corrected for receiver biases, resulted in a mean of differences of −39 cm and 51 cm standard deviation. The results are consistent with the accuracy of the IGS ionospheric products, 2–8 TECU, considering that 1 TECU is ~16 cm in L1. In another analysis, a comparison of ionospheric delays from 5 pairs of short baselines GNSS stations found an agreement of 0.001 m in mean differences with 22 cm standard deviation after receiver biases were corrected. Therefore, the proposed solution is promising and could produce high quality (1–2 TECU) slant ionospheric delays. This product can be used in a large variety of modeling approaches, since ionospheric delays after correction are unbiased. These results indicate that the proposed strategy is promising, and could benefit applications that require accuracy of 1–2 TECU (~16–32 cm in L1).     

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.     

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.     

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.     

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.     

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.     

Using only observation station data for PPP ambiguity resolution by UPD estimation

This article proposes a new method for uncalibrated phase delay (UPD) estimation to improve the accuracy of precise point positioning (PPP), which uses only observation station data. This means that the station used to generate the UPDs is the same station to which they are applied. First, dual-frequency observation equations based on a raw PPP model are developed. Then, the UPDs are calculated from integer linear combinations of float ambiguities. Third, with the UPD corrections, the least-squares ambiguity decorrelation adjustment (LAMBDA) method is utilized to obtain the integer ambiguities. Since only observation station data are used for UPD estimation, the partial ambiguity resolution (PAR) method is adopted to increase the possibility of finding a subset of integer ambiguities. The UPD estimation and ambiguity resolution are performed in each epoch. To obtain the correct integer ambiguity, the ratio test and success rate (bootstrapping) are used to evaluate the estimated integer ambiguity. Finally, by treating the integer ambiguities as constants, fixed solutions can be obtained. Quality control is also applied throughout the entire data processing procedure to obtain high quality float and fixed solutions. Data from 22 stations of the International Global Navigation Satellite System (GNSS) Service (IGS) in East Asia on day of year (DOY) 206, 2017, are used to verify the feasibility of this method. The experimental results show that compared with the float solution, the proposed method can significantly improve the accuracy in the east, north and up directions by 24%, 21% and 18% for static PPP and 36%, 18% and 34% for dynamic PPP, respectively. However, the accuracy of the proposed method is still lower than that of the fixed solutions obtained by the PRIDE-PPPAR software, in which the fractional cycle bias is computed based on reference network data. These findings sufficiently show that the proposed method can offer better solution accuracy than the float solution. However, the quality of the UPDs estimated only from observation station data is not as good as that of the estimates obtained based on reference network data.     

基于地面基站的定位系统构建和方案

针对大型、复杂、多功能建筑,其内部信号环境恶劣,卫星导航的信号衰减较大,较难稳定捕获跟踪,建筑内多径效应严重,短多径对定位精度的影响较大,直接使用卫星导航信号进行定位难度大的问题,提出了一种基于地面基站的大区域（建筑群）室内定位方案。根据频率与信号穿透性能和空间衰减之间的关系,选择甚高频频段作为信号载波,采用码伪距和载波伪距联合定位的方式,可同时兼顾覆盖性和定位性能。利用所提出的新型定位方式,搭建了一个基本测试系统,通过信号的产生、发射、无线传播,进行了信号的捕获、跟踪和伪距求差解算,初步验证了本文方法的可行性及覆盖能力。      

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.     

SHAKING: Adjusted spherical harmonics adding KrigING method for near real-time ionospheric modeling with multi-GNSS observations

Precise positioning based on Global Navigation Satellite System (GNSS) technique requires high accuracy ionospheric total electron content (TEC) correction models to account for the ionospheric path delay errors. We present an adjusted Spherical Harmonics Adding KrigING method (SHAKING) approach for regional ionospheric vertical TEC (VTEC) modeling in real time. In the proposed SHAKING method, the VTEC information over the sparse observation data area is extrapolated by the Adjusted Spherical Harmonic (ASH) function, and the boundary distortion in regional VTEC modeling is corrected by the stochastic VTEC estimated using Kriging interpolation. Using real-time GPS, GLONASS and BDS-2/3 data streams of the Crust Movement Observation Network of China (CMONOC), the SHAKING-based regional ionospheric VTEC maps are re-constructed over China and its boundary regions. Compared to GNSS VTECs derived from the independent stations, the quality of SHAKING solution improves by 13–31% and 6–33% with respect to the ASH-only solution during high and low geomagnetic periods, respectively. Compared to the inverse distance weighting (IDW) generated result, significant quality improved of SHAKING-based VTEC maps is also observed, especially over the edge areas with an improvement of 60–80%. Overall, the proposed SHAKING method exhibits notable advantage over the existing regional VTEC modeling techniques, which can be used for regional TEC modeling and associated high-precision positioning applications.     

Comprehensive outage compensation of real-time orbit and clock corrections with broadcast ephemeris for ambiguity-fixed precise point positioning

The main challenge in real-time precise point positioning (PPP) is that the data outages or large time lags in receiving precise orbit and clock corrections greatly degrade the continuity and real-time performance of PPP positioning. To solve this problem, instead of directly predicting orbit and clock corrections in previous researches, this paper presents an alternative approach of generating combined corrections including orbit error, satellite clock and receiver-related error with broadcast ephemeris. Using ambiguities and satellite fractional-cycle biases (FCBs) of previous epoch and the short-term predicted tropospheric delay through linear extrapolation model (LEM), combined corrections at current epoch are retrieved and weighted with multiple reference stations, and further broadcast to user for continuous enhanced positioning during outages of orbit and clock corrections. To validate the proposed method, two reference station network with different inter-station distance from National Geodetic Survey (NGS) network are used for experiments with six different time lags (i.e., 5 s, 10 s, 15 s, 30 s, 45 s and 60 s), and one set of data collected by unmanned aerial vehicle (UAV) is also used. The performance of LEM is investigated, and the troposphere prediction accuracy of low elevation (e.g., 10–20degrees) satellites has been improved by 44.1% to 79.0%. The average accuracy of combined corrections before and after LEM is used is improved by 12.5% to 77.3%. Without LEM, an accuracy of 2–3 cm can be maintained only in case of small time lags, while the accuracies with LEM are all better than 2 cm in case of different time lags. The performance of simulated kinematic PPP at user end is assessed in terms of positioning accuracy and epoch fix rate. In case of different time lags, after LEM is used, the average accuracy in horizontal direction is better than 3 cm, and the accuracy in up direction is better than 5 cm. At the same time, the epoch fix rate has also increased to varying degrees. The results of the UAV data show that in real kinematic environment, the proposed method can still maintain a positioning accuracy of several centimeters in case of 20 s time lag.     

基于多约束因子图优化的无人车定位与建图方法

针对目前在特定场景下应用的低速无人车定位系统极度依赖全球导航卫星系统（GNSS）,存在定位精度不高、漂移误差大、受环境影响严重等问题,提出一种低成本、高精度的无人车定位与建图方法。该方法基于三维激光定位与建图（SLAM）技术。首先,使用点云主成分分析（PCA）实现基于特征匹配的激光里程计;其次,将GNSS位置信息、点云分割聚类得到的地平面和点云聚类特征作为位姿约束分别加入图优化框架,消除激光里程计的累积误差;最后,得到最优位姿和大规模场景的点云地图,以实现无人车的自主定位导航。利用包含大型户外城市街道环境的KITTI数据集对所提出的SLAM算法进行了评估,结果表明:系统在3km运动距离情况下定位偏差可控制在1.5 m以下,在局部精度和全局一致性方面均优于其他里程计系统,为无人车的定位提供了新思路。      

An improved cyclic multi model-eXtreme gradient boosting (CMM-XGBoost) forecasting algorithm on the GNSS vertical time series

The study of GNSS vertical coordinate time series forecasting is helpful for monitoring the crustal plate movement, dam or bridge deformation monitoring, and global or regional coordinate system maintenance. The eXtreme Gradient Boosting (XGBoost) algorithm is a machine learning algorithm that can evaluate features, and it has a great potential and stability for long-span time series forecasting. This study proposes a multi-model combined forecasting method based on the XGBoost algorithm. The method constitutes a new time series as features through the fitting and forecasting results of the forecasting model. The XGBoost model is then used for forecasting. In addition, this method can obtain higher precision forecasting results through circulation. To verify the performance of the forecasting method, 1095 epochs of data in the Up coordinate of 16 GNSS stations are selected for the forecasting test. Compared with the CNN-LSTM model, the experimental results of our forecasting method show that the mean absolute error (MAE) values are reduced by 30.23 %～52.50 % and the root mean square error (RMSE) values are reduced by 31.92 %～54.33 %. The forecasting results have higher accuracy and are highly correlated to the original time series, which can better forecast the vertical movement of the GNSS stations. Therefore, the forecasting method can be applied to the up component of the GNSS coordinate time series.     

Performance assessment of real-time multi-GNSS integrated PPP with uncombined and ionospheric-free combined observables

For precise position services, the real-time precise point positioning (PPP) is a promising technology. The real-time PPP performance is expected to be improved by multi-system combination. The performance of real-time multi-system PPP needs to be periodically investigated, with the increasing number of available satellites and the continuously improved quality of real-time precise products of satellite clocks and orbits. In this study, a comprehensive performance assessment is conducted for the four-system integrated real-time PPP (FSIRT-PPP) with GPS, BDS, Galileo and GLONASS in both static and kinematic modes. The datasets from 118 stations spanning approximately a month are used for analysis, and the real-time stream CLK93 is employed. The superior performance of FSIRT-PPP is validated by comparing with the results of GPS/BDS, GPS/Galileo, GPS/GLONASS, GPS-only, BDS-only, Galileo-only and GLONASS-only cases. The FSIRT-PPP using ionospheric-free (IF) combined observables can achieve a convergence time of 10.9, 4.8 and 11.8 min and a positioning accuracy of 0.4, 0.5 and 0.7 cm in the static mode in the east, north and up directions, respectively, while the derived statistic is 15.4, 7.0 and 16.4 min, and 1.6, 1.2 and 3.4 cm in the kinematic mode in the three directions, respectively. Moreover, we also compare the position solutions of real-time PPP adopting IF combined and uncombined (UC) observables, and prove the mathematical equivalence between the two PPP models in the converged stage, provided that there are no external ionospheric corrections or constraints given to the estimated ionospheric delays in the UC model. The difference between the fully converged positioning accuracy of IF-based and UC-based real-time PPP is marginal, but the UC-based real-time PPP has longer convergence time due to the influence of the significant unmodeled time-varying errors in the real-time precise products as well as the different parameterization between them. For completeness, the real-time kinematic PPP results in harsh environments and the post-processed PPP results are also presented.     

Total electron content monitoring using triple frequency GNSS: Results with Giove-A/-B data

Triple frequency GNSS will be fully operational within the next decade, opening opportunities for new applications. Dual frequency GNSS already allow to study the ionosphere through the estimation of Total Electron Content (TEC). However, the precision is limited by the ambiguity resolution process. This paper studies a triple frequency TEC monitoring technique in which the use of Geometry-Free and Iono-Free linear combinations improves the ambiguity resolution process and therefore the precision of TEC. We have tested it on a set of triple frequency Giove-A/-B data from January and December 2008. The conclusions achieved are (1) TEC values are affected by an error of about 2–2.5 TECU produced through the ambiguity resolution process; (2) the error caused by the Geometric Free phase combination delays (hardware, multipath, noise, antenna phase center) on TEC is about 0.2 TECU; (3) the total error on TEC approximately reach 2–3 TECU.