利用改正数信息的北斗三号实时精密单点定位及性能分析

北斗三号全球卫星导航系统已正式建成并开通服务。为了利用实时改正数信息系统地揭示北斗三号精密单点定位性能，并为用户提供理论依据和应用参考，首先解算了卫星实时精密轨道、钟差及其改正数，分析了其精度。然后基于实时改正数信息，利用监测站广播星历和观测数据，分别进行了双频静态、双频仿动态、单频静态和单频仿动态仿实时精密单点定位，以评估其性能。结果表明：北斗三号MEO卫星实时轨道和钟差精度均值分别约为12cm和0.2ns，满足实时精密单点定位需求。静态实时精密单点定位精度优于动态，双频优于单频，均可达到分米级。对于定位收敛时间，双频静态最短，约为40min；双频动态和单频静态均约为85min；单频动态最长，约为120min。     

基于单频GPS接收机的低轨卫星准实时定轨算法研究

研究在不依赖于GPS差分基准站的情况下,利用单频GPS接收机对低轨卫星进行定轨的算法。文章先对影响卫星定轨的各种误差进行简要的分析,根据分析的结果对传统载波相位平滑伪距观测方程进行适当修正,然后,再利用修正的方程对伪距观测进行平滑,最后利用单点定位法进行轨道解算。仿真结果表明,在只需给定少数几个历元数据的情况下,利用单频接收机可以达到米级的定轨精度。     

Comparative analysis of four different single-frequency PPP models on positioning performance and atmosphere delay retrieval

Single-frequency precise point positioning (SF-PPP) has attracted increasing attention due to its high precision and cost effectiveness. With various strategies to handle the dominant error, i.e., ionosphere delay, the ionosphere-float (IF), ionosphere-free-half (IFH), ionosphere-corrected (IC), and ionosphere-weighted (IW) SF-PPP models are certain to possess different characteristics and performance levels. This study is dedicated to assessing and comparing the four models from model characteristics, positioning performance, and atmosphere delay retrieval. The model comparison shows that IC and IW models are full-rank while IF and IFH models have a rank deficiency of size one that will result in biased estimations, which means the better solvability of IC and IW models. The experiments are carried out based on the 7-day Global Positioning System (GPS) observations collected at 57 global Multi-GNSS Experiment (MGEX) stations and Global Ionosphere Map (GIM) products. The results indicate that the IW model can accelerate SF-PPP convergence and achieve higher positioning accuracy compared to the other three SF-PPP models, especially in kinematic mode. With convergence criteria of 0.25 m in horizontal and 0.5 m in vertical, the east/north/up convergence times of IW model are 0.5/15.0/25.0 min and 0.5/16.0/36.5 min for static and kinematic modes, respectively. The IW model is able to achieve an instantaneous positioning accuracy of 0.28/0.35/0.75 m. In addition, a real kinematic test also demonstrates the best positioning solutions of IW model. Regarding troposphere delay retrieval, the IF, IFH, and IW models obtain a comparable daily accuracy of 3.0 cm on average, while the IC model achieves the worst accuracy of 8.0 cm. For precise ionosphere delay estimation, IW model only needs an average initialization time of 34.3 min, but a longer initialization time of 51.6 min is required for IF model. The daily precision of ionosphere delay estimation for IW model can reach up to 10.8 cm. At the present accuracy of GIM products, it is suggested that the IW model should be adopted for SF-PPP first due to its superior performance in positioning and atmosphere delay retrieval.     

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.      

时间序列分析在周跳探测与修复中的应用

周跳是GPS载波相位测量数据处理中必须解决的关键问题,为了获得高精度的导航定位结果,必须对其进行快速准确地探测与修复。分析了周跳产生的原因及其特点,结合时间序列分析理论,提出了一种新的周跳探测与修复方法。首先对载波相位测量数据进行四次差分处理;然后建立了载波相位测量数据的加权预测模型,并给出了权值计算方法;最后通过对比载波相位预测值与实际测量值的大小来探测与修复周跳。利用实际数据验证表明：新方法适用于单频接收机,可以对3周以上的周跳进行准确探测与修复。     

双频双星座地基增强系统精度和完好性算法

针对单频单星座地基增强系统（GBAS）无法满足飞机III类精密进近与着陆导航性能需求的问题，提出了将北斗导航卫星系统（BDS）与全球定位系统（GPS）进行融合，构建一种新型的基于GPS/BDS的双频双星座GBAS。首先，分析了GBAS的工作原理，并对Hatch滤波器的误差进行了分析，给出了一种适用于双频GBAS的无码载偏离载波相位平滑伪距算法；然后，对机载完好性算法进行了研究，给出了H0和H1假设下的机载保护级计算方法；最后，进行了系统验证实验，实验结果表明，单星座GBAS不能满足飞机III类精密进近与着陆导航的性能需求，GPS和BDS融合后可见卫星个数得到提升，优化了卫星几何分布，进而使得系统的可用性由80.6081%提升到大于99.9999%。     

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.     

GPS data processing of networks with mixed single- and dual-frequency receivers for deformation monitoring

In order to obtain crustal deformations of higher spatial resolution, existing GPS networks must be densified. This densification can be carried out using single-frequency receivers at moderate costs. However, ionospheric delay handling is required in the data processing. We adapt the Satellite-specific Epoch-differenced Ionospheric Delay model (SEID) for GPS networks with mixed single- and dual-frequency receivers. The SEID model is modified to utilize the observations from the three nearest dual-frequency reference stations in order to avoid contaminations from more remote stations. As data of only three stations are used, an efficient missing data constructing approach with polynomial fitting is implemented to minimize data losses. Data from large scale reference networks extended with single-frequency receivers can now be processed, based on the adapted SEID model. A new data processing scheme is developed in order to make use of existing GPS data processing software packages without any modifications. This processing scheme is evaluated using a sub-network of the German SAPOS network. The results verify that the new scheme provides an efficient way to densify existing GPS networks with single-frequency receivers.     

Precision analysis of troposphere sensing using GPS single-frequency signals

Various studies have been performed to investigate the accuracy of troposphere zenith wet delays (ZWDs) determined from GPS. Most of these studies use dual-frequency GPS data of large-scale networks with long baselines to determine the absolute ZWDs. For small-scale networks the estimability of the absolute ZWDs deteriorates due to high correlation between the solutions of the ZWDs and satellite-specific parameters as satellite clocks. However, as relative ZWDs (rZWDs) can always be estimated, irrespective of the size of the network, it is of interest to understand how the large-scale network rZWD-performance of dual-frequency GPS using an ionosphere-float model compares to the small-scale network rZWD-performance of single-frequency GPS using an ionosphere-weighted model. In this contribution such an analysis is performed using undifferenced and uncombined network parametrization modelling. In this context we demonstrate the ionosphere weighted constraints, which allows the determination of the rZWDs independent from signals on the second frequency. Based on an analysis of both simulated and real data, it is found that under quiet ionosphere conditions, the accuracy of the single-frequency determined rZWDs in the ionosphere-weighted network is comparable to that of the large-scale dual-frequency network without ionospheric constraints. Making use of the real data from two baselines of 15?days, it was found that the absolute differences of the rZWDs applying the two strategies are within 1?cm in over 90% and 95% of the time for ambiguity-float and -fixed cases, respectively.     

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.