Initial assessment of the COMPASS/BeiDou-3: new-generation navigation signals

The successful launch of five new-generation experimental satellites of the China’s BeiDou Navigation Satellite System, namely BeiDou I1-S, I2-S, M1-S, M2-S, and M3-S, marks a significant step in expanding BeiDou into a navigation system with global coverage. In addition to B1I (1561.098 MHz) and B3I (1269.520 MHz) signals, the new-generation BeiDou-3 experimental satellites are also capable of transmitting several new navigation signals in space, namely B1C at 1575.42 MHz, B2a at 1176.45 MHz, and B2b at 1207.14 MHz. For the first time, we present an initial characterization and performance assessment for these new-generation BeiDou-3 satellites and their signals. The L1/L2/L5 signals from GPS Block IIF satellites, E1/E5a/E5b signals from Galileo satellites, and B1I/B2I/B3I signals from BeiDou-2 satellites are also evaluated for comparison. The characteristics of the B1C, B1I, B2a, B2b, and B3I signals are evaluated in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, triple-frequency carrier-phase ionosphere-free and geometry-free combination, and double-differenced carrier-phase and code residuals. The results demonstrate that the observational quality of the new-generation BeiDou-3 signals is comparable to that of GPS L1/L2/L5 and Galileo E1/E5a/E5b signals. However, the analysis of code multipath shows that the elevation-dependent code biases, which have been previously identified to exist in the code observations of the BeiDou-2 satellites, seem to be not obvious for all the available signals of the new-generation BeiDou-3 satellites. This will significantly benefit precise applications that resolve wide-lane ambiguity based on Hatch–Melbourne–Wübbena linear combinations and other applications such as single-frequency precise point positioning (PPP) based on the ionosphere-free code–carrier combinations. Furthermore, with regard to the triple-frequency carrier-phase ionosphere-free and geometry-free combination, it is found that different from the BeiDou-2 and GPS Block IIF satellites, no apparent bias variations could be observed in all the new-generation BeiDou-3 experimental satellites, which shows a good consistency of the new-generation BeiDou-3 signals. The absence of such triple-frequency biases simplifies the potential processing of multi-frequency PPP using observations from the new-generation BeiDou-3 satellites. Finally, the precise relative positioning results indicate that the additional observations from the new-generation BeiDou-3 satellites can improve ambiguity resolution performance with respect to BeiDou-2 only positioning, which indicates that observations from the new-generation BeiDou-3 satellites can contribute to precise relative positioning.     

Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution

The Global Positioning System (GPS) and Galileo will transmit signals on similar frequencies, that is, the L1–E1 and L5–E5a frequencies. This will be beneficial for mixed GPS and Galileo applications in which the integer carrier phase ambiguities need to be resolved, in order to estimate the positioning unknowns with centimeter accuracy or better. In this contribution, we derive the mixed GPS + Galileo model that is based on “inter-system” double differencing, that is, differencing the Galileo phase and code observations relative to those corresponding to the reference or pivot satellite of GPS. As a consequence of this, additional between-receiver inter-system bias (ISB) parameters need to be solved as well for both phase and code data. We investigate the size and variability of these between-receiver ISBs, estimated from L1 and L5 observations of GPS, as well as E1 and E5a observations of the two experimental Galileo In-Orbit Validation Element (GIOVE) satellites. The data were collected using high-grade multi-GNSS receivers of different manufacturers for several zero- and short-baseline setups in Australia and the USA. From this analysis, it follows that differential ISBs are only significant for receivers of different types and manufacturers; for baselines formed by identical receiver types, no differential ISBs have shown up; thus, implying that the GPS and GIOVE data are then fully interoperable. Fortunately, in case of different receiver types, our analysis also indicates that the phase and code ISBs may be calibrated, since their estimates, based on several datasets separated in time, are shown to be very stable. When the single-frequency (E1) GIOVE phase and code data of different receiver types are a priori corrected for the differential ISBs, the short-baseline instantaneous ambiguity success rate increases significantly and becomes comparable to the success rate of mixed GPS + GIOVE ambiguity resolution based on identical receiver types.     

伽利略卫星导航系统信号质量及定位性能分析

伽利略系统(Galileo)是全球四大卫星导航系统之一,目前已初步具备全球定位能力。研究Galileo的信号质量和双／三频定位性能不仅对Galileo系统应用具有重要价值,对多全球卫星导航系统（GNSS）融合定位也有重要促进作用。在使用基准站网(MGEX)地面跟踪站的基础上,分析了伽利略信号的载噪比、多路径、以及双／三频精密单点定位(PPP)的定位精度。结果表明,Galileo与GPS相比,载噪比E5> E5a≈E5b≈L5>E1≈L1>L2,多路径误差E5      

GPS/Galileo long baseline computation: method and performance analyses

Modernized GPS and Galileo will provide triple-frequency signals for civil use, generating a high interest to examine the improvement of positioning performance using the triple-frequency signals from both constellations over baselines up to hundreds or thousands of kilometers. This study adopts a generalized GPS/Galileo long-range approach to process the mutually compatible GPS and Galileo triple-frequency measurements for high-precision long baseline determination. The generalized approach has the flexibility to deal with GPS and Galileo constellations separately or jointly, and also the capability to handle dual or triple-frequency measurements. We compared the generalized long-range approach with the Bernese v5.0 software on two test baselines located in East Asia and obtained highly compatible computational results. Further, in order to assess possible improvement of GPS/Galileo long baseline determination compared with the current dual-frequency (L1/L2) GPS, we simulated GPS and Galileo measurements of the test baselines. It is shown that the current level of accuracy of daily baseline solutions can be improved by using the additional Galileo constellation. Both the additional constellation and the triple-frequency measurements can improve ambiguity resolution performance, but single-constellation triple-frequency ambiguity resolution is more resistant to the influences of code noise and multipath than dual-constellation dual-frequency ambiguity resolution. Therefore, in environments where large code noise or multipath is present, the use of triple-frequency measurements is the main factor for improving ambiguity resolution performance.     

Ambiguity resolution for triple-frequency geometry-free and ionosphere-free combination tested with real data

The recent GPS Block IIF satellites SVN62 and SVN63 and the Galileo satellites GIOVE-A, GIOVE-B, PFM and FM2 already send signals on more than two frequencies, and more GNSS satellites will provide tracking data on at least three frequencies in the near future. In this paper, a simplified general method for ambiguity resolution minimizing the noise level for the triple-frequency geometry-free (GF) and ionosphere-free (IF) linear combinations is presented, where differently scaled code noise on the three frequencies was introduced. For the third of three required linear combinations, the most demanding one in triple-frequency ambiguity resolution, we developed a general method using the ambiguity-corrected phase observations without any constraints to search for the optimal GF and IF linear combination. We analytically demonstrate that the noise level of this third linear combination only depends on the three frequencies. The investigation concerning this frequency-dependent noise factor was performed for GPS, Galileo and Compass frequency triplets. We verified the theoretical derivations with real triple-frequency GPS and Galileo data from the Multi-GNSS Experiment (M–GEX) of the International GNSS Service (IGS). The data of about 30 M–GEX stations around the world over 11 days from 29 April 2012 to 9 May 2012 were used for the test. For the third linear combinaton using Galileo E1, E5b and E5a, which is expected to have the worst performance among all the GNSS frequency triplets in our investigation, the formal errors of the estimated ambiguities are in most cases below 0.2 cycles after 400 observation epochs. If more GPS satellites sending signals on three frequencies or more stations tracking Galileo E6 signal are available in the future, an improvement by a factor of two to three can be expected.     

Precise ionosphere-free single-frequency GNSS positioning

Ionospheric delays can be efficiently eliminated from single-frequency data using a combination of carrier phases and code ranges. Unfortunately, GPS and GLONASS ranges are relatively noisy which can limit the use of the positioning method. Nevertheless, position standard deviations are in the range of 6–8 cm (horizontal) and 7–9 cm (3d) obtained from diurnal data batches from selected IGS reference stations can be further reduced to 2–3 cm (3d) for weekly smoothed averages. GPS data sets collected in Ghana (Africa) reveal a typical level of 10 cm of deviation that must be anticipated under average conditions. Looking at the future of GNSS, the European Galileo system will, in contrast to GPS, provide the broadband signal E5 that is by far less affected by multipath thus providing rather precise range measurements. Simulated processing runs featuring both high ionospheric and tropospheric delay variations show a 3d position precision of 4 cm even for a data batch as short as just 1 h, whereas GPS L1/Galileo E1 performance is close to 13 cm for the same data set.     

GNSS非差非组合数据处理与PPP-RTK高精度定位

本文首先回顾了GNSS差分和组合数据处理的起源、特点和应用,并阐述了其在多频多模背景下的局限。然后,引出了非差非组合数据处理的诸多优势,介绍了构建满秩非差非组合函数模型的消秩亏方法。基于该方法,本文系统构建了系列非差非组合PPP-RTK模型,包括伪距加相位和仅用相位两大类。两类模型均考虑不同的大气约束而衍生出电离层加权、浮点和固定3种变体,且所有模型均顾及码分多址和频分多址两类系统。最后,本文测试分析了非差非组合PPP-RTK在无人船、无人机和农机应用中的动态定位性能。试验结果表明,3个场景下的模糊度首次固定时间均在10 s以内,模糊度固定成功率在96%以上,水平定位精度优于2 cm,高程定位精度优于5 cm。在Galileo+GPS+BDS三系统农机定位中,仅用相位PPP-RTK与伪距加相位PPP-RTK定位性能相当。与Galileo+GPS双系统定位相比,三系统PPP-RTK将模糊度首次固定时间从几百秒缩短至几秒,模糊度固定成功率从85%左右提升至99%以上,定位精度提升了30%左右。     

BDS-3和Galileo组合的RTK定位性能分析

北斗三号卫星导航系统（BeiDou-3 navigation satellite system, BDS-3）已全面建成并向全球用户提供可靠的定位、导航和授时（positioning, navigation and timing, PNT）服务。为了实现与其他全球卫星导航系统（global navigation satellite system, GNSS）的兼容性和互操作性,BDS-3在BDS-2的基础上调制了B1C和B2a两个新信号,与伽利略系统（Galileo）的E1和E5a实现了频率的复用。系统间偏差（inter-system bias, ISB）对于实现不同GNSS之间的融合处理至关重要,为此提出了基于单差模型的ISB估计与应用算法,并对BDS-3与Galileo重叠频率之间的ISB进行了分析。基于可跟踪BDS-3新信号的几类接收机,揭示了BDS-3和Galileo之间的ISB的特性,在此基础上分析了BDS-3和Galileo组合的实时动态（real-time kinematic, RTK）定位性能。结果表明,基于相同类型的接收机B1C-E1和B2a-E5a之间是不存在ISB...     

BDS/GNSS融合精密单点定位性能分析

随着北斗卫星导航系统(BDS)的全球组网成功,基于BDS的应用研究正在如火如荼的进行中,尤其是包括BDS在内的多频多模融合定位正成为研究的重点.利用MGEX(Multi-GNSS Experiment)多个测站的BDS、GPS、GLONASS、Galileo观测数据,基于RTKLIB开源代码,在Visual Studi...     

GPS,Galileo, QZSS and IRNSS differential ISBs: estimation and application

Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISBs) corresponding to signals of different constellations but transmitted at identical frequencies can be calibrated, such that only one common pivot satellite is sufficient for inter-system ambiguity resolution at that particular frequency. Recently, many new GNSS satellites have been launched. At the beginning of 2016, there were 12 Galileo IOV/FOC satellites and 12 GPS Block IIF satellites in orbit, while the Indian Regional Navigation Satellite System (IRNSS) had five satellites launched of which four are operational. More launches are scheduled for the coming years. As a continuation of the earlier studies, we analyze the magnitude and stability of the DISBs corresponding to these new satellites. For IRNSS this article presents for the first time DISBs with respect to the L5/E5a signals of GPS, Galileo and QZSS for a mixed-receiver baseline. It is furthermore demonstrated that single-frequency (L5/E5a) ambiguity resolution is tremendously improved when the multi-GNSS observations are all differenced with respect to a common pivot satellite, compared to classical differencing for which a pivot satellite is selected for each constellation.     

Galileo status: orbits,clocks, and positioning

The European Global Navigation Satellite System Galileo is close to declaration of initial services. The current constellation comprises a total of 12 active satellites, four of them belonging to the first generation of In-Orbit Validation satellites, while the other eight are Full Operational Capability (FOC) satellites. Although the first pair of FOC satellites suffered from a launch anomaly resulting in an elliptical orbit, these satellites can be used for scientific applications without relevant limitations. The quality of broadcast orbits and clocks has significantly improved since the beginning of routine transmissions and has reached a signal-in-space range error of 30 cm. Precise orbit products generated by the scientific community achieve an accuracy of about 5 cm if appropriate models for the solar radiation pressure are applied. The latter is also important for an assessment of the clock stability as orbit errors are mapped to the apparent clock. Dual-frequency single point positioning with broadcast orbits and clocks of nine Galileo satellites that have so far been declared healthy already enables an accuracy at a few meters. Galileo-only precise point positioning approaches a precision of 2 cm in static mode using daily solutions.     

Short and zero baseline analysis of GPS L1 C/A, L5Q, GIOVE E1B, and E5aQ signals

Stochastic properties of GNSS range measurements can accurately be estimated using a geometry-free short and zero baseline analysis method. This method is now applied to dual-frequency measurements from a new field campaign. Results are presented for the new GPS L5Q and GIOVE E5aQ wideband signals, in addition to the GPS L1 C/A and GIOVE E1B signals. As expected, the results clearly show the high precision of the new signals, but they also show, rather unexpectedly, significant, slowly changing variations in the pseudorange code measurements that are probably a result of strong multipath interference on the data. Carrier phase measurement noise is assessed on both frequencies, and finally successful mixed GPS-GIOVE double difference ambiguity resolution is demonstrated.     

Estimation of satellite position,clock and phase bias corrections

Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.     

基于钟差解耦的GNSS精密单点定位模糊度固定模型及效果分析

精密单点定位模糊度固定可以显著提升定位精度,钟差解耦模型作为一种重要的模糊度固定模型,却鲜有文献对其进行研究。本文首先给出了基于钟差解耦模型的用于模糊度固定的产品估计策略,分析了传统的消电离层模型和钟差解耦模型钟差重构形式的差异,导出了提取卫星码偏差的钟差估计模型。然后,深入研究了钟差解耦模型在钟差估计收敛速度等方面的优势。不同于其他模型将宽巷模糊度偏差视为天内常数,钟差解耦模型逐历元估计该偏差项,基于此展开对宽巷模糊度偏差天内时变特性的研究。最后,评价了解耦钟差的精度,并利用解耦钟差产品进行精密单点定位模糊度固定试验。结果表明,相比于提取卫星码偏差的卫星钟差估计模型,钟差解耦模型在钟差估计中的收敛速度更快,钟差产品更加稳定;宽巷模糊度偏差在天内较为稳定;解耦钟差产品具有较高的精度,相比于传统消电离层组合模型,基于该产品的精密单点定位模糊度固定可显著提升定位精度。     

Efficiency of carrier-phase integer ambiguity resolution for precise GPS positioning in noisy environments

Precise GPS positioning relies on tracking the carrier-phase. The fractional part of carrier-phase can be measured directly using a standard phase-locked loop, but the integer part is ambiguous and the ambiguity must be resolved based on sequential carrier-phase measurements to ensure the required positioning precision. In the presence of large phase-measurement noise, as can be expected in a jamming environment for example, the amount of data required to resolve the integer ambiguity can be large, which requires a long time for any generic integer parameter estimation algorithm to converge. A key question of interest in significant applications of GPS where fast and accurate positioning is desired is then how the convergence time depends on the noise amplitude. Here we address this question by investigating integer least-sqaures estimation algorithms. Our theoretical derivation and numerical experiments indicate that the convergence time increases linearly with the noise variance, suggesting a less stringent requirement for the convergence time than intuitively expected, even in a jamming environment where the phase noise amplitude is large. This finding can be useful for practical design of GPS-based systems in a jamming environment, for which the ambiguity resolution time for precise positioning may be critical.     

Assessment of GPS + Galileo and multi-frequency Galileo single-epoch precise positioning with network corrections

Several processing strategies that use dual-frequency GPS-only solution, multi-frequency Galileo-only solution, and finally tightly combined dual-frequency GPS + Galileo solution were tested and analyzed for their applicability to single-epoch long-range precise positioning. In particular, a multi-system GPS + Galileo solution was compared to GPS double-frequency solution as well as to Galileo double-, triple-, and quadruple-frequency solutions. Also, the performance of the strategies was analyzed under clear-sky and obstructed satellite visibility in both single-baseline and multi-baseline modes. The results indicate that tightly combined GPS + Galileo instantaneous positioning has a clear advantage over single-system solutions and provides an accurate and reliable solution. It was also confirmed that application of multi-frequency observations in case of Galileo system has an advantage over a dual-frequency solution.     

BeiDou B2/Galileo E5b短基线紧组合相对定位模型及性能评估

随着GPS和GLONASS系统的现代化以及Galileo和BeiDou卫星导航系统的建设,GNSS正朝多频多系统的方向发展。本文对BeiDou B2/Galileo E5b短基线紧组合相对定位的模型与算法进行了研究,详细推导了BeiDou B2/Galileo E5b短基线紧组合相对定位的模型与算法,并对其定位性能进行了分析。重点分析了BeiDou B2与Galileo E5b频点的接收机间差分系统间偏差的长期稳定性,结果表明:基线两端的接收机类型(包括固件版本)相同时,差分系统间偏差接近于0;基线两端的接收机类型不同时,差分系统间偏差较大,但具有长期稳定性,因此能够事先标定并作为改正数用于后续的定位中。最后基于BeiDou B2/Galileo E5b单频单历元相对定位试验对系统间紧组合模型的定位效果进行了比较验证。结果表明,相对于传统的松组合模型,使用改正系统间偏差的紧组合模型能够显著提高模糊度固定的成功率,尤其是在遮挡比较严重、单系统可观测到的卫星数较少的情况下,模糊度固定成功率可以提高10%~25%。     

TJS-2 geostationary satellite orbit determination using onboard GPS measurements

This study analyzes the quality of onboard data of tracking signals from GPS satellites on the far side of the earth and determines the orbit of the geostationary satellite using code and carrier phase observations with 30-h and 3-day orbit arc length. According to the analysis results, the onboard receiver can track 6–8 GPS satellites, and the minimum and maximum carrier to noise spectral densities were 24 and 45 dB-Hz, respectively. For a GPS receiver on a high-altitude platform above the navigation constellations, the blocking of the earth and a weak signal strength usually cause a piece-wise GPS signal tracking and an increase in the number of ambiguity parameters. Individual GPS satellites may be continuously tracked for as little as several minutes and as long as 3 h. Moreover, considering the negative sign of elevation angles reflects the fact that GPS satellites are tracked below the receiver in the study. GPS satellites appear mainly in the elevation angle range of ??53° to ??83°, and dilution of precision values could reach ten or one hundred and more. Also, it is observed that when a signal suffers from atmospheric refraction, other GPS signals tracked simultaneously by the receiver experience strong systematic errors in the code observations. Based on single-frequency code and carrier phase measurements, the mean 3D root mean square (RMS) value of the overlap comparisons between 30-h orbit determination arcs is 2.14 m. However, we found that there were also some biases in the carrier phase residuals, which contributed to poor orbit accuracy. To eliminate the effects of the biases, we established a correction sequence for each GPS satellite. After corrections, the mean 3D RMS was reduced to 0.99 m, representing a 53% improvement.     

Precise relative positioning using real tracking data from COMPASS GEO and IGSO satellites

China completed a basic COMPASS navigation network with three Geostationary and three Inclined Geosynchronous satellites in orbit in April 2011. The network has been able to provide preliminary positioning and navigation functions. We first present a quality analysis using 1-week COMPASS measurements collected in Wuhan. Satellite visibility and validity of measurements, carrier-to-noise density ratio and code noise are analyzed. The analysis of multipath combinations shows that the noise level of COMPASS code measurements is higher than that of GPS collected using the same receiver. Second, the results of positioning are presented and analyzed. For the standalone COMPASS solutions, an accuracy of 20 m can be achieved. An accuracy of 3.0 m for the vertical, 1.5 m for the North and about 0.6–0.8 m for the East component is obtained using dual-frequency code only measurements for a short baseline. More importantly, code and phase measurements of the short baseline are processed together to obtain precise relative positioning. Kinematic solutions are then compared with the ground truth. The precision of COMPASS only solutions is better than 2 cm for the North component and 4 cm for the vertical. The standard deviation of the East component is smaller than 1 cm, which is even better than that of the East component of GPS solutions. The accuracy of GPS/COMPASS combination solutions is at least 20 % better than that of GPS alone. Furthermore, the geometry-based residuals of double differenced phase and code measurements are analyzed. The analysis shows that the noise level of un-differenced phase measurements is about 2–4 mm on both B1 and B2 frequencies. For the code measurements, the noise level is less than 0.45 m for B1 CA and about 0.35 m for B2 P code. Many of the COMPASS results presented are very promising and have been obtained for the first time.     

BDS-2/BDS-3/GPS/Galileo双频精密单点定位精度分析与评价

由于北斗卫星导航系统(BDS)已完成正式组网,有必要对BDS的定位性能进行精度评估与分析. 本文主要通过在MGEX (Multi-GNSS Experiment)选取8个测站5天的观测数据,以北斗二号/北斗三号(BDS-2/BDS-3)为主分析BDS-2/BDS-3、BDS-2/BDS-3/Galileo、BDS-2/BDS-3/GPS、BDS-2/BDS-3/GPS/Galileo四种不同组合卫星系统静态精密单点定位(PPP)性能,试验结果表明:BDS-2/BDS-3静态PPP在东(E)、北(N)、天顶(U)方向上的定位精度和收敛速度分别优于2.49 cm、2.27 cm、4.04 cm和34.6 min、19.3 min、28.1 min;BDS-2/BDS-3/Galileo静态PPP在E、N、U方向上的定位精度和收敛速度分别优于1.81 cm、1.65 cm、2.94 cm和20.4 min、13.0 min、18.6 min;BDS-2/BDS-3/GPS静态PPP在E、N、U方向上的定位精度和收敛速度分别优于1.67 cm、1.62 cm、2.82 cm和18.3 min、10.2 min、16.1 min;BDS-2/BDS-3/GPS/Galileo静态PPP在E、N、U方向上的定位精度和收敛速度分别优于1.46 cm、1.40 cm、2.45 cm和14.5 min、9.3 min、14.5 min.