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.     

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

The use of ionospheric tomography and elevation masks to reduce the overall error in single-frequency GPS timing applications

Signals from Global Positioning System (GPS) satellites at the horizon or at low elevations are often excluded from a GPS solution because they experience considerable ionospheric delays and multipath effects. Their exclusion can degrade the overall satellite geometry for the calculations, resulting in greater errors; an effect known as the Dilution of Precision (DOP). In contrast, signals from high elevation satellites experience less ionospheric delays and multipath effects. The aim is to find a balance in the choice of elevation mask, to reduce the propagation delays and multipath whilst maintaining good satellite geometry, and to use tomography to correct for the ionosphere and thus improve single-frequency GPS timing accuracy. GPS data, collected from a global network of dual-frequency GPS receivers, have been used to produce four GPS timing solutions, each with a different ionospheric compensation technique. One solution uses a 4D tomographic algorithm, Multi-Instrument Data Analysis System (MIDAS), to compensate for the ionospheric delay. Maps of ionospheric electron density are produced and used to correct the single-frequency pseudorange observations. This method is compared to a dual-frequency solution and two other single-frequency solutions: one does not include any ionospheric compensation and the other uses the broadcast Klobuchar model. Data from the solar maximum year 2002 and October 2003 have been investigated to display results when the ionospheric delays are large and variable. The study focuses on Europe and results are produced for the chosen test site, VILL (Villafranca, Spain). The effects of excluding all of the GPS satellites below various elevation masks, ranging from 5° to 40°, on timing solutions for fixed (static) and mobile (moving) situations are presented. The greatest timing accuracies when using the fixed GPS receiver technique are obtained by using a 40° mask, rather than a 5° mask. The mobile GPS timing solutions are most accurate when satellites at lower elevations continue to be included: using a mask between 10° and 20°. MIDAS offers the most accurate and least variable single-frequency timing solution and accuracies to within 10 ns are achieved for fixed GPS receiver situations. Future improvements are anticipated by combining both GPS and Galileo data towards computing a timing solution.     

基于帝国竞争优化的双目标综合决策选星算法

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

多路径效应对GPS多普勒测速的影响

针对全球定位系统（GPS）多普勒观测值在城市环境中受多路径效应影响，从而导致测速误差大的问题，从多普勒频移产生的原理入手，通过运动学理论分析，构建了接收机、反射点与卫星整体运动与多普勒频移误差关系模型。模型分析结果表明:多普勒频移误差与卫星观测向量、反射点切线法向量、接收机运动速度及反射点运动速度有关。最后通过5种不同场景的GPS数据验证了所提模型的正确性。在多路径情况下，当接收机或反射点运动时，可能会导致巨大的测速误差，使得结果不具备可靠性。      

伪距波动原因中的星体多径因素排除

针对卫星可视弧段内伪距测量异常波动现象，从信号质量监测角度研究了卫星可视弧段内导航信号测距偏差变化问题，确认伪距波动是否由星体多径引起.利用大口径天线跟踪北斗卫星，采用两套采集设备实现了卫星可视弧段内的B1频点信号多次高载噪比采集，根据基于参考波形的测距偏差估计方法分别处理多组采集数据，获得了不同仰角上的测距偏差.在一个仰角下的采集数据，当滤波器带宽远远大于信号带宽时，采样率与下变频器均不同的两套采集设备获得的测距偏差相同，且测距偏差均与相关间距及滤波器带宽有关，但当滤波器带宽超过15MHz后，测距偏差的差异可以忽略.比较不同仰角下的测距偏差，在卫星可视弧段内测距偏差变化很小，因此认为星体多径引起卫星可视弧段内信号质量的变化不是伪距测量异常波动的原因.      

一种地基GNSS接收机差分码偏差估算方法

GNSS不同频点间的码伪距作差会引入信号的差分码偏差(DCB),包括GNSS卫星及地面接收机的DCB.本文提出一种地基GNSS接收机差分码偏差参数估算方法,首先由电离层文件参数作线性插值,计算出电离层延迟误差.之后对IGS站观测文件进行加权最小二乘法估计,得到GPS卫星和地面GNSS接收机的L1C频点和L2P频点间码偏...     

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.     

AIUB-CHAMP02S: The influence of GNSS model changes on gravity field recovery using spaceborne GPS

The gravity field model AIUB-CHAMP02S, which is based on six years of CHAMP GPS data, is presented here. The gravity field parameters were derived using a two step procedure: In a first step a kinematic trajectory of a low Earth orbiting (LEO) satellite is computed using the GPS data from the on-board receiver. In this step the orbits and clock corrections of the GPS satellites as well as the Earth rotation parameters (ERPs) are introduced as known. In the second step this kinematic orbit is represented by a gravitational force model and orbit parameters.     

GLONASS卫星可见性的一种预测方法

基于GLONASS接收机研制的实践,提出了一种GLONASS卫星可见性的预测方法.根据GLONASS卫星的某一已知状态和GLONASS卫星的运行规律,计算GLONASS卫星的地心地固空间直角坐标,然后转换为以地面观测点为参考的站心极坐标,求出卫星的高度角,得出卫星对于地面用户的可见性.这种算法计算简便,准确度高,在接收机的研制中具有实用价值.     

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.     

基于固定模糊度PPP的低轨卫星实时精密定轨

传统动力学定轨法受制于动力学模型精度，传统几何定轨法精度受限，只能达到亚米级，而基于精密单点定位（PPP）模式的几何定轨法一般采用浮点解，定轨精度及可靠性较基于双差模式的相对定位较差。为提高PPP模式低轨定轨的定位性能，利用中国区域内外的IGS测站计算出当前所有卫星的宽巷和窄巷相位小数偏差产品，对经过中国大陆区域上空的国产低轨卫星海洋二号（HY-2）和资源三号 (ZY-3) 卫星进行固定模糊度PPP的定轨解算，与事后精密轨道结果进行比较，分析其外符合精度。结果表明：仅利用约10min弧段的HY-2和ZY-3卫星数据，切向与径向的定轨精度可达2cm左右，法向为5cm左右，较浮点解定轨精度大幅提升。基于固定模糊度PPP的定轨方法能够满足厘米级的实时精密定轨。     

Early analysis of precise orbit and clock offset determination for the satellites of the global BeiDou-3 system

Eight new-generation BeiDou satellites (BeiDou-3) have been launched into Medium Earth Orbit (MEO), allowing for global coverage since March 2018, and they are equipped with new hydrogen atomic clocks and updated rubidium clocks. Firstly, we analyzed the signals for the carrier-to-noise-density ratio (C/N0) and pseudorange multipath (MP) by using international GNSS (Global Navigation Satellite System) Monitoring and Assessment System (iGMAS) station data, and found that B1C has a lower C/N0, and B2a has the same level of C/N0 as the B1I and B3I signals. For pseudorange multipath, compared with the BeiDou-2 satellites, the obvious systematic variation of MP scatters related to the elevation angle is greatly improved for the BeiDou-3 and BeiDou-3e satellites signals. For the signals of the BeiDou-3 satellites, the order of the Root Mean Square (RMS) values of multipath and noise is B3I?<?B1I?<?B2a?<?B1C. Then, the comparison of the precise orbit determination and clock offset determination for the BeiDou-2, BeiDou-3, and BeiDou-3 experimental (BeiDou-3e) satellites was done by using 10 stations from iGMAS. The 3D precision of the 24?h orbit overlap is 24.55, 25.61, and 23.35?cm for the BeiDou-3, BeiDou-3e, and BeiDou-2 satellites, respectively. BeiDou-3 satellite has a comparable precision to that of the BeiDou-2 satellite. For the precision of clock offset estimation, the Standard Deviation (STD) of the BeiDou-3 MEO satellite is 0.350?ns, which is an improvement of 0.042?ns over that of the BeiDou-2 MEO satellite. The stabilities of the BeiDou-3 and BeiDou-3e onboard clocks are better than those of BeiDou-2 by factors of 2.84 and 1.61 at an averaging time of 1000 and 10,000?s, respectively.     

A fast satellite selection algorithm with floating high cut-off elevation angle based on ADOP for instantaneous multi-GNSS single-frequency relative positioning

With the Global Navigation Satellite System (GNSS) developing, the single-frequency single-epoch multiple GNSSs (multi-GNSS) relative positioning has become feasible. Since a larger number of the observed satellites make the instantaneous (single-epoch) positioning time-consuming, a proper satellite selection is necessary. Among the present methods, the satellite selection with a fixed high cut-off elevation angle (CEA) is least time-consuming. However, there is no criterion how large a fixed high CEA should be to achieve a high success rate and less time consumption. Besides, a fixed high CEA makes the number of visible satellites largely variable, which affects the success rate. Hence, a satellite selection strategy based on ambiguity dilution of precision (ADOP) is proposed. Firstly, the theoretical proof that the ADOP increases the least when removing satellites are all low-elevation-angle satellites is given, which is important to achieve the fast positioning with a high success rate. Then, the threshold $\beta$ is calculated for a different number of satellites and a given ADOP. The satellites are selected based on their elevation angles from high to low until $\beta$ of the selected satellites becomes smaller than the corresponding threshold; this method is called the extended floating CEA multi-GNSS (EF-multi-GNSS). The comparison of the single-frequency single-epoch positioning performance of the EF-multi-GNSS with the satellite selections based on a fixed low CEA (L-multi-GNSS) and a fixed high CEA (H-multi-GNSS) via the relative positioning experiments shows that: (1) the EF-multi-GNSS with a minimal number of satellites can achieve the fast positioning and a high success rate close to 100%. It can greatly reduce the time consumption of the L-multi-GNSS, by about 64.0%, by selecting 12.6 satellites of 23.4 satellites; (2) the floating CEA of EF-multi-GNSS eliminates the consideration how large a fixed high CEA should be, and a CEA larger than the fixed high CEA of the H-multi-GNSS makes it more suitable for different conditions.     

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.     

An improved approach to model ionospheric delays for single-frequency Precise Point Positioning

PPP with low-cost, single-frequency receivers has been receiving increasing interest in recent years because of its large amount of possible users. One crucial issue in single-frequency PPP is the mitigation of ionospheric delays which cannot be removed by combining observations on different frequencies. For this purpose, several approaches have been developed, such as, the approach using ionospheric model corrections with proper weight, the GRAPHIC (Group and Phase Ionosphere Calibration) approach, and the method to model ionospheric delays over a station with a low polynomial or stochastic process. From our investigation on the stochastic characteristics of the ionospheric delay over a station, it cannot be precisely represented by either a deterministic model in the form of a low-order polynomial or a stochastic process for each satellite, because of its strong irregular spatial and temporal variations. Therefore, a novel approach is developed accordingly in which the deterministic representation is further refined by a stochastic process for each satellite with an empirical model for its power density. Furthermore, ionospheric delay corrections from a constructed model using GNSS data are also included as pseudo-observations for a better solution. A large data set collected from about 200 IGS stations over one month in 2010 is processed with the new approach and several commonly adopted approaches for validation. The results show its significant improvements in terms of positioning accuracy and convergence time with a negligible extra processing time, which is also demonstrated by data collected with a low-cost, handheld, single-frequency receiver.     

航天GPS接收机信号搜索捕获策略

航天GPS接收机的无辅助冷启动时间是一项重要指标,研究近地轨道应用的12通道C/A码导航型接收机减小冷启动时间的方法.分析GPS信号的多普勒频率和伪码相位搜索方法、捕获检测器及其参数选择、多普勒频率搜索步长和伪码搜索速率, 得到多普勒频率搜索步长为500?Hz,伪码搜索速率为475码元/s.研究轨道倾角、轨道高度、GPS天线仰角和轨道偏心率等因素对多普勒频率搜索范围的影响.阐述根据GPS卫星间夹角的统计信息选择合理的卫星分配方法.分析和仿真结果表明,根据GPS卫星间夹角的统计信息选择合理的卫星分配方法,可将冷启动时间减少25%~30%,影响多普勒频率搜索范围的因素按程度依次为:轨道倾角、轨道高度、GPS天线仰角和轨道偏心率,再考虑这些因素时可将冷启动时间减少25%~40%.     

观测资料和卫星钟差对PPP参数收敛影响分析

在GPS 单点定位中, 参数解算的收敛时间和收敛稳定性是重要的研究内容之一, 影响收敛时间和收敛稳定性的因素很多, 本文主要就观测资料的不同采样间隔、卫星钟差资料的不同采样间隔、不同的定位精度要求对精密单点定位中参数收敛时间的影响进行了深入的分析探讨, 以中国上海GPS综合应用网中的12个测站资料为例, 分析了采样间隔、定位精度要求与收敛时间的关系, 并对不同采样间隔的收敛时间进行了统计分析, 得出一些初步结论.      

航天器应急姿态捕获中GPS信号的应用

星载全球定位系统（GPS）卫星接收机在测量接收各GPS卫星信号时,可同时得到接收信号的信号强度测量辅助数据E。理论分析表明,接收信号的强度E与信号入射天线的法向夹角α强相关。如建立E与α稳定的先验模型,E就可以作为测量值,计算入射天线的角度α。在同一时刻,通过三个以上GPS卫星信号入射天线的角度α,可计算星载GPS卫星接收机接收天线的空间姿态。确定姿态的精度取决于E与α相关先验模型的稳定性。利用CHAMP卫星星载接收机在轨实测数据检验,估算的初始姿态精度为2°~3°。该方法可作为航天器故障状态下应急姿态捕获的一种辅助手段,也可为携带星载GPS而无高精度定姿要求的简易航天器提供一种新的无附加成本的定姿途径。