Galileo系统与GPS卫星定位系统相位组合观测值的模型研究

在介绍Galileo系统空间信号的基础上,以模糊度保持整数为前提,给出了Galileo系统的4个频率载波与GPS L2载波的组合相位观测值的定义,并对有关误差影响加以分析,最后根据一定的组合标准论述了具有相应特性的组合观测值,并给出一些典型的组合.      

适用于单频GPS用户的周跳探测方法

针对单频GPS(Global Position System)用户的载波相位周跳探测问题,在传统的载波相位和伪距组合方法的基础上提出了一种新的周跳探测方法.该方法将载波相位和码伪距的组合观测量在历元间做差形成差分序列,以此构造实时的周跳探测量,由于该探测量易受观测噪声的影响,因此使用仰角指数模型作为经验模型对于测距噪声进行估计,基于假设检验的方法,通过对该探测量是否超过相应的检测门限来判断是否存在周跳.在实测的GPS观测数据基础上,对这一方法进行了验证,结果表明:相对于传统的周跳探测方法,该方法可以更加及时、准确地发现较小的周跳,对于单频的GPS用户具有较好的适应性.      

基于载波相位三差的航天器GPS/INS组合定姿算法

研究了一种利用GPS载波相位三差观测信息的多天线GPS/INS组合定姿算法,其中包含一个基于惯性测量信息的GPS载波相位周跳检测算法。最后,通过仿真分析验证了该组合算法可以有效提高定姿精度,同时具有较好的稳定性。     

精密进近阶段的多系统GNSS组合RAIM可用性算法及分析

给出了多系统全球卫星导航系统（GNSS）组合接收机自主完好性监测（ReceiverAutonomousIntegrityMonitoring,RAIM）可用性计算方法,在此基础上利用GPS、GLONASS实测数据与BDS、Galileo全星座仿真数据,分析了BDS、GPS、GLONASS和Galileo不同组合在精密进近阶段的RAIM可用性。通过试验分析发现,BDS的5颗地球同步轨道卫星和3颗倾斜地球同步轨道卫星对亚洲、非洲和欧洲大部分地区的RAIM可用性有很大的贡献。这些地区站星间几何观测结构得到改善,使得RAIM可用性相对于其他地区有很大幅度的提升。在亚太地区APV-I阶段单系统导航情况下,北斗导航系统RAIM可用性达到99.5%,高于其他三个导航系统。在精密进近阶段（APV-I、APV-II和CAT-I）,BDS与其他导航系统（GPS、GLONASS和Galileo）的组合导航可以满足全球大部分区域的RAIM可用性需求,大多可达到100%。     

卫星不足情况下低成本MEMS-INS/GPS伪松组合导航

为了解决GPS可观测卫星不足情况下低成本微电子机械-惯性导航系统/全球定位系统（MEMS-INS/GPS）组合导航精度维持问题,提出基于灰色模型和自适应卡尔曼滤波的MEMS-INS/GPS伪松组合导航方法。以MEMS-INS/GPS松组合导航模式为框架,建立了伪松组合导航系统的状态空间模型。基于MEMS-INS/GPS的历史观测数据,使用灰色模型对MEMSINS/GPS观测差值进行预测,称为系统伪观测量。当GPS可观测卫星充分时,使用噪声自适应估计卡尔曼滤波对MEMS-INS/GPS进行松组合导航;当GPS可观测卫星不足时,使用噪声自适应估计卡尔曼滤波依据系统伪观测量,将MEMS-INS/GPS进行伪松组合导航。以车载低成本MEMSINS/GPS组合导航系统为例进行仿真和实验验证,结果表明：当GPS可观测卫星不足时,传统的MEMS-INS/GPS松组合导航精度迅速下降并发散,而MEMS-INS/GPS伪松组合导航精度与GPS正常工作时的导航精度相差不大,维持了较高精度的导航状态。     

GPS/Galileo组合导航的模糊度搜索空间

为了组合导航的载波相位模糊度固定,将目前在GPS中常用的模糊度固定方法--最小二乘降相关平差（LAMBDA）法直接应用于GPS/Galileo组合模糊度固定,发现其搜索空间的确定方法并不能很好地适应GPS/Galileo组合中模糊度维数较高的情况。通过对常规LAMBDA搜索空间确定方法的分析比较,在传统方法的基础上提出了一种专门针对高维模糊度固定的搜索空间确定方法--修正法确定模糊度搜索空间。通过对修正法进行仿真试验,证明该方法能保证在GPS/Galileo组合定位模式下实际备选模糊度个数基本与预先设定的备选模糊度个数一致,进而能在不降低模糊度固定成功率的基础上有效提高LAMBDA模糊度固定的搜索效率,其性能优于传统的模糊度搜索空间确定方法。     

新的GPS单频单历元定姿算法

LAMBDA算法依赖于初始的模糊度浮点解,但仅用载波相位观测方程需要多个历元才能获得浮点解,将导致初始化时间过长.针对这一问题,对GPS(Global Positioning System)单历元的载波相位单差方程进行特殊变换,将未知的整周模糊度看成噪声,从而构造出新的观测方程,和原始的观测方程进行组合求解,克服了仅用载波相位双差观测方程因为亏秩而无法在单历元获得浮点解的缺点,解决了初始化时间的问题.通过深入研究浮点解和固定解之间的关系,提出一种将低精度浮点解映射到固定解的方法,降低了LAMBDA算法对高精度浮点解的依赖性,避免了用多个历元获取浮点解的高精度,从而实现了单频、单历元的整周模糊度估计.通过实际测试,该算法成功率高于97%,能够有效地用于实时动态姿态解算.      

多GNSS全球电离层建模特性及其精度检验

分别以GPS单系统和融合BDS,GPS,GLONASS三系统两种方案,采用载波相位平滑伪距观测值和球谐函数,构建了全球电离层延迟模型并进行了对比和分析.本文以GPS单系统和融合三系统两种方法反演了2014年1月每日电离层变化过程,解算得出了频间偏差的月综合产品,并对结果进行了对比和分析.事实上,三系统融合不仅增加了可观测的卫星数,而且改善了穿刺点的几何分布.分析结果表明,三系统融合反演全球电离层在精度上优于GPS单系统,均有5~10 TECU的提高.计算得到的频间偏差结果显示,GPS优于GIONASS,BDS稳定性则较次之.     

GPS全视法时间传递回顾与展望

目前,时间传递技术正处于GPS伪码技术到GNSS多种技术组合的过渡时期,介绍了高精度时间传递技术在近年来的发展情况:首先回顾了GPS伪码共视(CV)与全视法(AV)时间传递,并证明全视法比共视法更具优越性。CCTF 2006通过,从MJD 53979,即2006九月(Circular T225)开始,使用AV法进行TAI比对。CV法需要满足共视条件,这限制了载波相位(CP)方法的应用,载波相位观测量比码观测量的观测精度可以高出两个数量级。由于CP观测数据优良,CCTF 2006推荐也可以引用CP观测数据进行时间传递。PPP方法是一种充分研究的时间传递方法,它充分地利用了载波相位信息,可以认为是伪码AV法的自然延伸。最后,给出我们的最新研究成果,即将GPS PPP和TW时间链路结合的方法,该方法结合两种时间传递链路的优点并消除了它们的缺点。     

利用GNSS反射信号载波测量湖面高度变化

给出一种利用导航卫星反射信号的载波相位测量光滑湖面高度变化的方法.首先建立载波相位观测方程,通过在直射与反射信号的观测量之间求单差,再在历元间求双差的方法,消除了大量误差并得到了直射与反射信号的几何路径差;然后根据各颗卫星的观测值和高度角等信息计算出湖面高度变化,并把各卫星得到的湖面高度度变化值进行加权平均以提高测量系统的精度和可靠性.仿真验证了方法在-15dB信噪比下达到了毫米级的测量精度.     

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.     

Calibration errors in determining slant Total Electron Content (TEC) from multi-GNSS data

The global navigation satellite system (GNSS) is presently a powerful tool for sensing the Earth's ionosphere. For this purpose, the ionospheric measurements (IMs), which are by definition slant total electron content biased by satellite and receiver differential code biases (DCBs), need to be first extracted from GNSS data and then used as inputs for further ionospheric representations such as tomography. By using the customary phase-to-code leveling procedure, this research comparatively evaluates the calibration errors on experimental IMs obtained from three GNSS, namely the US Global Positioning System (GPS), the Chinese BeiDou Navigation Satellite System (BDS), and the European Galileo. On the basis of ten days of dual-frequency, triple-GNSS observations collected from eight co-located ground receivers that independently form short-baselines and zero-baselines, the IMs are determined for each receiver for all tracked satellites and then for each satellite differenced for each baseline to evaluate their calibration errors. As first derived from the short-baseline analysis, the effects of calibration errors on IMs range, in total electron content units, from 1.58 to 2.16, 0.70 to 1.87, and 1.13 to 1.56 for GPS, Galileo, and BDS, respectively. Additionally, for short-baseline experiment, it is shown that the code multipath effect accounts for their main budget. Sidereal periodicity is found in single-differenced (SD) IMs for GPS and BDS geostationary satellites, and the correlation of SD IMs over two consecutive days achieves the maximum value when the time tag is around 4?min. Moreover, as byproducts of zero-baseline analysis, daily between-receiver DCBs for GPS are subject to more significant intra-day variations than those for BDS and Galileo.     

Tightly combined GPS/Galileo RTK for short and long baselines: Model and performance analysis

To ensure the compatibility and interoperability with modernized GPS, Galileo satellites are capable of broadcasting navigation signals on carrier phase frequencies that overlap with GPS, i.e., GPS/Galileo L1-E1/L5-E5a. Moreover, the GPS/Galileo L2-E5b signals have different frequencies with wavelength differences smaller than 4.2?mm. Such overlapping and narrowly spaced signals between GPS and Galileo bring the opportunity to use the tightly combined double-differenced (DD) model for precise real-time kinematic (RTK) positioning, resulting in improved performance of ambiguity resolution and positioning with respect to the classical standard or loosely combined DD model. In this paper, we focus on the model and performance assessment of tightly combined GPS/Galileo L1-E1/L2-E5b/L5-E5a RTK for short and long baselines. We first investigate the tightly combined GPS/Galileo DD observational model for both short and long baselines with simultaneously considering the GPS/Galileo overlapping and non-overlapping frequencies. Particularly, we introduce a reparameterization approach to solve the rank deficiency that caused by the correlation between the DISB parameters and the DD ionospheric parameters for both overlapping and non-overlapping frequencies. Then we present performance assessment for the tightly combined GPS/Galileo RTK model with real-time estimation of the differential inter-system bias (DISB) parameters for short and long baselines in terms of ratio value, ambiguity dilution of precision (ADOP), ambiguity conditional number, decorrelation number, search count, empirical success rate, time-to-first-fix (TTFF), and positioning accuracy. Results from both static and kinematic experiments demonstrated that compared to the loosely combined model, the tightly combined model can deliver improved performance of ambiguity resolution and precise positioning with different satellite visibility. For the car-driven short baseline experiment with 10° elevation cut-off angle, the tightly combined model can not only significantly increase the ratio value by approximately 27.5% (from 16.0 to 20.4), but also reduce the ambiguity ADOP, the conditional number, and the search count in LAMBDA by approximately 22.2% (from 0.027 to 0.021 cycles), 14.9% (from 199.2 to 169.6), and 25.4% (from 150.1 to 112.0), respectively. Comparable decorrelation number, empirical success rate, and positioning accuracy are also obtained. For the car-driven long baseline experiment, it is also observed that the ambiguity resolution performance in terms of the ratio value, the decorrelation number, the condition number, and the search count are significantly improved by approximately 18.5% (from 2.7 to 3.2), 22.0% (from 0.186 to 0.227), 55.9% (from 937.6 to 413.7), and 10.3% (from 43.8 to 39.3), respectively. Moreover, comparable ADOP, empirical success rate, and positioning accuracy are obtained as well. Additionally, the TTFF can be reduced (from 54.1 to 51.8 epochs with 10° elevation cut-off angle) as well from the results of static experiments.     

Combining GPS and GLONASS for time and frequency transfer

Geodetic time and frequency transfer (TFT) consists in a comprehensive modeling of code and carrier phase observations from Global Navigation Satellite System (GNSS) in order to determine the synchronization errors between two remote clocks connected to GNSS receivers. Using either common view (CV), or Precise Point Positioning (PPP), current GNSS time transfer uses only GPS measurements. This study combines GPS and GLONASS observations in geodetic TFT in order to determine the added value of the GLONASS data in the results. Using the software Atomium, we demonstrate on one hand that using both constellations improves the solution for both CV and PPP results when analysing short data batches. In that case, there are not enough GPS code data to calibrate the solution, and additional GLONASS code data allows us to retrieve a correct absolute value for the solution. On the other hand, the CV results of frequency transfer are not significantly affected by adding GLONASS data, while in PPP the combination with GLONASS modifies the frequency transfer results, and in particular the daily frequency offset, with maximum differences of 150 ps between the TFT solutions obtained with GPS-only or GPS + GLONASS.     

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.     

Multivariate bootstrapped relative positioning of spacecraft using GPS L1/Galileo E1 signals

GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft, mainly due to the stronger model given by the a priori knowledge of the length and geometry of the baselines, can be performed precisely using only single frequency observations. When the Galileo signals will come available, the number of observations at the L1 frequency will increase as we will have a GPS and Galileo multi-constellation. Moreover the L1 observations of the Galileo system and modernized GPS are more precise than legacy GPS and this, combined with the increased number of observations, will result in a stronger model for single frequency relative positioning. In this contribution we will develop an even stronger model by combining the attitude determination problem with relative positioning. The attitude determination problem will be solved by the recently developed Multivariate Constrained (MC-) LAMBDA method. We will do this for each spacecraft and use the outcome for an ambiguity constrained solution on the baseline between the spacecraft. In this way the solution for the unconstrained baseline is bootstrapped from the MC-LAMBDA solutions of each spacecraft in what is called: multivariate bootstrapped relative positioning. The developed approach will be compared in simulations with relative positioning using a single antenna at each spacecraft (standard LAMBDA) and a vectorial bootstrapping approach. In the simulations we will analyze single epoch, single frequency success rates as the most challenging application. The difference in performance for the approaches for single epoch solutions, is a good indication of the strength of the underlying models. As the multivariate bootstrapping approach has a stronger model by applying information on the geometry of the constrained baselines, for applications with large observation noise and limited number of observations this will result in a better performance compared to the vectorial bootstrapping approach. Compared with standard LAMBDA, it can reach a 59% higher success rate for ambiguity resolution. The higher success rate on the unconstrained baseline between the platforms comes without extra computational load as the constrained baseline(s) problem has to be solved for attitude determination and this information can be applied for relative positioning.     

GNSS geodetic techniques for time and frequency transfer applications

We performed an initial analysis of the pseudorange data of the GIOVE-B satellite, one of the two experimental Galileo satellites currently in operation, for time transfer.¹ For this specific aim, software was developed to process the GIOVE-B raw pseudoranges and broadcast navigation messages collected by the Galileo Experimental Sensor Stations (GESS) tracking network, yielding station clock phase errors with respect to the Experimental Galileo System Time (EGST). The software also allows processing the Global Positioning System (GPS) P1 and P2 pseudorange data with broadcast navigation message collected at the same stations to obtain the station clock phase errors with respect to the GPS system time (GPST). Differencing these solutions between stations provides two independent means of GNSS time transfer. We compared these time transfer results with Precise Point Positioning (PPP) method applied to GPS data in combined carrier-phase and pseudorange mode as well as in pseudorange-only mode to show their relative merits. The PPP solutions in combined carrier-phase and pseudorange mode showed the least instability of the methods tested herein at all scales, at few parts in 10¹⁵ at 1 day for the stations processed, following a tau^−½ interval dependency. Conversely, the PPP solutions in pseudorange-only mode are an order of magnitude worst (few parts in 10¹⁴ at 1 day for the stations processed) following a tau⁻¹ power-law, but slightly better than the single-satellite raw GPS time transfer solutions obtained using the developed software, since the PPP least-squares solution effectively averages the pseudorange noise. The pseudorange noise levels estimated from PPP pseudorange residuals and from clock solution comparisons are largely consistent, providing a validation of our software operation. The raw GIOVE-B time transfer, as implemented in this work, proves to be slightly better than single-satellite raw GPS satellite time transfer, at least in the medium term. However, one of the processed stations shows a combined GPS P1 and P2 pseudorange noise level at 2 m, a factor 2 worst than usually seen for geodetic receivers, so the GPS time transfer results may not be at their best for the cases processed. Over the short term, the GPS single-satellite time transfer instability outperforms the GIOVE-B by an order of magnitude at 1 s interval, which would be due to the different characteristics of the tracking loop filters for GPS P1 and P2 on one hand and the GIOVE-B signals on the other. Even at this preliminary stage and using an experimental satellite system, results show that the GIOVE-B (and hence Galileo) signals offer interesting perspectives for high precision time transfer between metrological laboratories.     

星载GPS观测数据的模拟研究

重点分析了星载GPS观测值模拟的原理、数学模型等，并用模拟软件模拟了CHAMP卫星的星载GPS观测值情况．结果表明，根据本文提供模拟方法所模拟的CHAMP星载GPS观测值，与实测值相比，无论是在大小还是观测噪声水平上都很接近，因此能满足不同层次人员对星载GPS模拟观测值的需要．