Evaluation of COMPASS ionospheric model in GNSS positioning

As important products of GNSS navigation message, ionospheric delay model parameters are broadcasted for single-frequency users to improve their positioning accuracy. GPS provides daily Klobuchar ionospheric model parameters based on geomagnetic reference frame, while the regional satellite navigation system of China’s COMPASS broadcasts an eight-parameter ionospheric model, COMPASS Ionospheric Model(CIM), which was generated by processing data from continuous monitoring stations, with updating the parameters every 2 h. To evaluate its performance, CIM predictions are compared to ionospheric delay measurements, along with GPS positioning accuracy comparisons. Real observed data analysis indicates that CIM provides higher correction precision in middle-latitude regions, but relatively lower correction precision for low-latitude regions where the ionosphere has much higher variability. CIM errors for some users show a common bias for in-coming COMPASS signals from different satellites, and hence ionospheric model errors are somehow translated into the receivers’ clock error estimation. In addition, the CIM from the China regional monitoring network are further evaluated for global ionospheric corrections. Results show that in the Northern Hemisphere areas including Asia, Europe and North America, the three-dimensional positioning accuracy using the CIM for ionospheric delay corrections is improved by 7.8%–35.3% when compared to GPS single-frequency positioning ionospheric delay corrections using the Klobuchar model. However, the positioning accuracy in the Southern Hemisphere is degraded due apparently to the lack of monitoring stations there.     

基于三频数据的北斗卫星导航系统DCB参数精度评估方法

差分码偏差（Differential Code Biases,DCB）参数作为导航电文中重要的一项,是影响用户PNT服务的主要误差源之一。北斗卫星导航系统（后文简称“北斗系统”）发射三个频点的导航信号,在导航电文中需要发播卫星的2个TGD（Timing Group Delay）参数。文章首先介绍了北斗系统卫星DCB参数最小二乘解算与形式误差评估;其次根据北斗系统三频特点,提出了不同频点组合计算垂直方向电离层电子总含量（VTEC）互差的DCB精度定量评估方法,并与IGS(International GNSS Service)提供的GPS卫星DCB精度进行比较;最后,详细分析了DCB参数精度对用户等效距离误差（UERE）计算和定位计算的影响,分别采用卫星出场标定DCB参数和经过解算DCB参数进行评估。实测数据分析结果表明,北斗系统卫星DCB参数解算形式误差与IGS解算GPS卫星DCB参数形式误差相当,但受卫星类型和解算测站的几何分布限制,北斗系统卫星DCB参数解算不确定度相比IGS略差,估计精度优于0.5ns,不同频率组合计算VTEC互差绝对值均值优于0.6TECU。相比采用卫星出场标定值,采用系统解算DCB参数后,双频用户三维位置误差改善13.80%～47.42%。     

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.     

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.      

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.     

2006年12月13日太阳射电暴对GPS观测的影响

日地空间环境不仅影响航天器运行和安全, 也是导航、定位和通信等无线 电应用系统主要的误差源. 其中来自太阳L波段的射电暴被认为是全球导航卫星 系统(GNSS)稳定和性能的潜在威胁因素, 当L波段射电爆发达到一定阈值时, 将给用户带来不同程度的射电噪声干扰, 严重时会引起接收机失锁和定位服务 中断. 本文对2006年12月13日太阳射电暴对GPS造成的影响进行了研究, 利用太阳射电 观测数据、L波段闪烁观测数据和向阳面不同区域的GPS观测网数据, 分析 GPS观测对射电暴的响应. 结果表明, 此次事件对GPS观测产生了明显的影响, 射 电暴期间GPS发生幅度闪烁事件和明显失锁现象, 多个台站上空的多颗GPS 卫星 信号完全中断长达6min左右, 且多个台站上空锁定的卫星数目小于4颗, 使 得GPS定位完全失效. 相对而言, 射电暴期间日下点附近的GPS台站受到的影响 比远离日下点的大.      

高动态GPS卫星信号模拟器导航电文生成

为了测试全球定位系统GPS(Global Positioning System)接收机的性能,应用GPS信号模拟器来模拟各种条件下真实的GPS信号.GPS卫星信号发生器由硬件、计算机和软件组成.软件主要由卫星导航参数计算模块、目标运动轨迹计算模块、误差计算模块等模块组成.导航电文产生功能模块是高动态GPS卫星信号模拟器要解决的一项关键技术.给出了3个卫星星钟改正参数的物理意义和星历产生模型,根据这些参数并结合相应的时间参数来形成卫星导航电文.通过程序仿真并与导航电文进行验证,证明推导出的星历产生模型基本符合GPS星的星座排列规律.     

基于RT-LAB的组合导航仿真平台设计

设计了一种基于RT-LAB的SINS/GPS/CNS（Strapdown Inertial Navigation System/Global Positioning System/Celestial Navigation System）组合导航系统仿真平台方案,建立具有故障检测、隔离和系统重构能力的基于联邦卡尔曼滤波器的姿态、位置、速度组合导航系统方案和结构.将SINS与GPS的位置之差和速度之差作为SINS/GPS子滤波器的观测量,通过CNS给出的载体惯性姿态信息获得SINS的姿态误差角测量信息.仿真结果表明,该系统方案具有较强的容错性能、较高的导航精度和很强的实时性能,为组合导航技术的研究提供了有益的参考.     

一种惯性信息辅助下的GPS快捕方法

全球定位系统(GPS,Global Positioning System)信号的捕获时间直接影响高动态环境下GPS接收机的使用性能.在分析传统的外部信息辅助GPS捕获方法的基础上,提出了一种在惯性信息辅助下进行快速捕获的方法,该方法由粗捕获和精捕获构成.详细分析了该方法的实现方法和性能,进行了MATLAB/Simulink系统级仿真及蒙特卡罗仿真试验.仿真结果表明:在保证码相位捕获精度和提高频率分辨率的前提下,运用该方法可以显著缩短GPS接收机搜索捕获的时间,提高接收机的动态性能,相对无外部信息辅助的情况总捕获时间缩短至2%~3%.     

Multi-GNSS contributions to differential code biases determination and regional ionospheric modeling in China

Due to the limited number and uneven distribution globally of Beidou Satellite System (BDS) stations, the contributions of BDS to global ionosphere modeling is still not significant. In order to give a more realistic evaluation of the ability for BDS in ionosphere monitoring and multi-GNSS contributions to the performance of Differential Code Biases (DCBs) determination and ionosphere modeling, we select 22 stations from Crustal Movement Observation Network of China (CMONOC) to assess the result of regional ionospheric model and DCBs estimates over China where the visible satellites and monitoring stations for BDS are comparable to those of GPS/GLONASS. Note that all the 22 stations can track the dual- and triple-frequency GPS, GLONASS, and BDS observations. In this study, seven solutions, i.e., GPS-only (G), GLONASS-only (R), BDS-only (C), GPS + BDS (GC), GPS + GLONASS (GR), GLONASS + BDS (RC), GPS + GLONASS + BDS (GRC), are used to test the regional ionosphere modeling over the experimental area. Moreover, the performances of them using single-frequency precise point positioning (SF-PPP) method are presented. The experimental results indicate that BDS has the same ionospheric monitoring capability as GPS and GLONASS. Meanwhile, multi-GNSS observations can significantly improve the accuracy of the regional ionospheric models compared with that of GPS-only or GLONASS-only or BDS-only, especially over the edge of the tested region which the accuracy of the model is improved by reducing the RMS of the maximum differences from 5–15 to 2–3 TECu. For satellite DCBs estimates of different systems, the accuracy of them can be improved significantly after combining different system observations, which is improved by reducing the STD of GPS satellite DCB from 0.243 to 0.213, 0.172, and 0.165 ns after adding R, C, and RC observations respectively, with an increment of about 12.3%, 29.4%, and 32.2%. The STD of GLONASS satellite DCB improved from 0.353 to 0.304, 0.271, and 0.243 ns after adding G, C, and GC observations, respectively. The STD of BDS satellite DCB reduced from 0.265 to 0.237, 0.237 and 0.229 ns with the addition of G, R and GR systems respectively, and increased by 10.6%, 10.4%, and 13.6%. From the experimental positioning result, it can be seen that the regional ionospheric models with multi-GNSS observations are better than that with a single satellite system model.     

Rapid local ionosphere modeling based on Precise Point Positioning over Iran: A case study under 2014 solar maximum

Presently, the ionosphere effect is the main source of the error in the Global Positioning System (GPS) observations. This effect can largely be removed by using the two-frequency measurements, while to obtain the reasonable results in the single-frequency applications, an accurate ionosphere model is required. Since the global ionosphere models do not meet our needs everywhere, the local ionosphere models are developed. In this paper, a rapid local ionosphere model over Iran is presented. For this purpose, the GPS observations obtained from 40 GPS stations of the Iranian Permanent GPS Network (IPGN) and 16 other GPS stations around Iran have been used. The observations have been selected under 2014 solar maximum, from the days 058, 107, 188 and 271 of the year 2014 with different geomagnetic activities. Moreover, ionospheric observables based on the precise point positioning (PPP) have been applied to model the ionosphere. To represent our ionosphere model, the B-spline basis functions have been employed and the variance component estimation (VCE) method has been used to regularize the problem.To show the efficiency our PPP-derived local ionosphere model with respect to the International GNSS Service (IGS) global models, these models are applied on the single point positioning using single-frequency observations and their results are compared with the precise coordinates obtained from the double-differenced solution using dual-frequency observations. The results show that the 95th percentile of horizontal and vertical positioning errors of the single-frequency point positioning are about 3.1 and 13.6?m, respectively, when any ionosphere model are not applied. These values significantly improve when the ionosphere models are applied in the solutions. Applying CODE’s Rapid Global ionosphere map (CORG), improvements of 59% and 81% in horizontal and vertical components are observed. These values for the IGS Global ionosphere map (IGSG) are 70% and 82%, respectively. The best results are obtained from our local ionosphere model, where 84% and 87% improvements in horizontal and vertical components are observed. These results confirm the efficiency of our local ionosphere model over Iran with respect to the global models. As a by-product, the Differential Code Biases (DCBs) of the receivers are also estimated. In this line, we found that the intra-day variations of the receiver DCBs could be significant. Therefore, these variations must be taken into account for the precise ionosphere modeling.     

Evaluation of a regional real-time precise positioning system based on GPS/BeiDou observations in Australia

The performance of real-time (RT) precise positioning can be improved by utilizing observations from multiple Global Navigation Satellite Systems (GNSS) instead of one particular system. Since the end of 2012, BeiDou, independently established by China, began to provide operational services for users in the Asia-Pacific regions. In this study, a regional RT precise positioning system is developed to evaluate the performance of GPS/BeiDou observations in Australia in providing high precision positioning services for users. Fixing three hourly updated satellite orbits, RT correction messages are generated and broadcasted by processing RT observation/navigation data streams from the national network of GNSS Continuously Operating Reference Stations in Australia (AUSCORS) at the server side. At the user side, RT PPP is realized by processing RT data streams and the RT correction messages received. RT clock offsets, for which the accuracy reached 0.07 and 0.28?ns for GPS and BeiDou, respectively, can be determined. Based on these corrections, an accuracy of 12.2, 30.0 and 45.6?cm in the North, East and Up directions was achieved for the BeiDou-only solution after 30 min while the GPS-only solution reached 5.1, 15.3 and 15.5?cm for the same components at the same time. A further improvement of 43.7, 36.9 and 45.0 percent in the three directions, respectively, was achieved for the combined GPS/BeiDou solution. After the initialization process, the North, East and Up positioning accuracies were 5.2, 8.1 and 17.8?cm, respectively, for the BeiDou-only solution, while 1.5, 3.0, and 4.7?cm for the GPS-only solution. However, we only noticed a 20.9% improvement in the East direction was obtained for the GPS/BeiDou solution, while no improvements in the other directions were detected. It is expected that such improvements may become bigger with the increasing accuracy of the BeiDou-only solution.     

A MARS-based method for estimating regional 2-D ionospheric VTEC and receiver differential code bias

The geometry-free linear combination of dual-frequency GNSS reference station ground observations are currently used to build the Vertical Total Electron Content (VTEC) model of the ionosphere. As it is known, besides ionospheric delays, there are differential code bias (DCB) of satellite (SDCB) and receiver (RDCB) in the geometry-free observation equation. The SDCB can be obtained using the International GNSS Service (IGS) analysis centers, but the RDCB for regional and local network receivers are not provided. Therefore, estimating the RDCB and VTEC model accurately and simultaneously is a critical factor investigated by researchers. This study uses Multivariate Adaptive Regression Splines (MARS) to estimate the VTEC approximate model and then substitutes this model in the observation equation to form the normal equation. The least squares method is used to solve the RDCB and VTEC model together. The research findings show that this method has good modeling effectiveness and the estimated RDCB has good reliability. The estimated VTEC model applied to GPS single-frequency precise point positioning has better positioning accuracy in comparison to the IGS global ionosphere map (GIM).     

Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

The global positioning system (GPS) has become an essential tool for the high precision navigation and positioning. The quality of GPS positioning results mainly depends on the model’s formulations regarding GPS observations, including both a functional model, which describes the mathematical relationships between the GPS measurements and unknown parameters, and a stochastic model, which reflects the physical properties of the measurements. Over the past two decades, the functional models for GPS measurements have been investigated in considerable detail. However, the stochastic models of GPS observation data are simplified, assuming that all the GPS measurements have the same variance and are statistically independent. Such assumptions are unrealistic. Although a few studies of GPS stochastic models were performed, they are restricted to short baselines and short time session lengths. In this paper, the stochastic modeling for GPS long-baseline and zenith tropospheric delay (ZTD) estimates with a 24-h session is investigated using the residual-based and standard stochastic models. Results show that using the different stochastic modelling methods, the total differences can reach as much as 3–6 mm in the baseline component, especially in the height component, and 10 mm in the ZTD estimation. Any misspecification in the stochastic models will result in unreliable GPS baseline and ZTD estimations. Using the residual-based stochastic model, not only the precision of GPS baseline and ZTD estimation is obviously improved, but also the baseline and ZTD estimations are closer to the reference value.     

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.     

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.     

基于增强型单频GPS的高精度星间相对定位样条方法

为了实现高精度的分布式SAR星间相对定位,提出了一种基于增强型单频GPS的相对定位样条方法,即在单频GPS测量信息的基础上,增加星间距离观测信息,并结合相对位置参数的连续特性,建立了相对定位的样条模型,最后利用最小二乘法进行参数估计.仿真结果表明,新方法不仅能大大提高相对定位精度,而且还能有效地减少固定整周模糊度所需的历元.最后的理论分析证明了仿真的正确性.      

基于空间统计方法的电离层折射修正技术

针对中国上空电离层所具有的特殊性和GPS观测站在中国西部分布相对稀疏的特点, 尝试探索中国卫星增强系统电离层时延信息修正技术, 为卫星导航定位以及遥感、遥测等空间应用工程的电波修正提供数据. 利用中国地壳形变监测网提供的双频GPS数据, 以空间统计方法为主要工具, 给出了普通Kriging电离层估计算法, 构建了平静期和磁暴期电离层理论变异模型, 详细分析了电离层折射修正的精度. 结果表明, 将空间统计方法应用于卫星增强系统中的电离层时延改正问题, 有利于提高增强系统的电离层折射修正精度, 特别是在观测样点相对较少的情况下, 有利于系统完整性的实现.      

中国全球卫星导航信号基本框架设计

中国的全球卫星导航信号设计必须遵循许多约束条件,具备国际可协调性,导航信号的服务类型、载波中心频率、调制方式和伪随机码序列均需参加与GPS、Galileo进行的频率协调。依据参加与GPS频率协调的参考假设文件,描述了中国的全球卫星导航信号结构、基本参数、公开导航信号的伪随机扩频码序列和二次编码序列,计算表明伪随机扩频序列的性能与GPS信号伪随机扩频序列性能相当。     

Cycle slip detection using multi-frequency GPS carrier phase observations: A simulation study

The detection and repair of the cycle slip or gross error is a key step for high precision global positioning system (GPS) carrier phase navigation and positioning due to interruption or unlocking of GPS signal. A number of methods have been developed to detect and repair cycle slips in the last two decades through cycle slip linear combinations of available GPS observations, but such approaches are subject to the changing GPS sampling and complex algorithms. Furthermore, the small cycle slip and gross error cannot be completely repaired or detected if the sampling is quite longer under some special observation conditions, such as Real Time Kinematic (RTK) positioning. With the development of the GPS modernization or Galileo system with three frequencies signals, it may be able to better detect and repair the cycle slip and gross error in the future. In this paper, the cycle slip and gross error of GPS carrier phase data are detected and repaired by using a new combination of the simulated multi-frequency GPS carrier phase data in different conditions. Results show that various real-time cycle slips are completely repaired with a gross error of up to 0.2 cycles.