差分GPS载波相位整周模糊度快速解算方法

本文提出了一种整周模糊度的快速求解方法,将差分GPS的测量值分配到主要测量值集合和次要测量值集合中,用主要集合中的相位测量值限定简约搜索空间,而次要集合中的相位测量值用来验证候选集合。利用已知的基线长度的约束条件,对搜索空间进行了简约,提高了求解整周模糊度的速度,同时,通过Cholesky分解提高搜索效率。     

0.99999999 confidence ambiguity resolution with GPS and Galileo

In this short contribution it is demonstrated how integer carrier phase cycle ambiguity resolution will perform in near future, when the US GPS gets modernized and the European Galileo becomes operational. The capability of ambiguity resolution is analyzed in the context of precise differential positioning over short, medium and long distances. Starting from dual-frequency operation with GPS at present, particularly augmenting the number of satellites turns out to have beneficial consequences on the capability of correctly resolving the ambiguities. With a 'double' constellation, on short baselines, the confidence of the integer ambiguity solution increases to a level of 0.99999999 or beyond. Electronic Publication     

Triple-frequency GPS precise point positioning with rapid ambiguity resolution

At present, reliable ambiguity resolution in real-time GPS precise point positioning (PPP) can only be achieved after an initial observation period of a few tens of minutes. In this study, we propose a method where the incoming triple-frequency GPS signals are exploited to enable rapid convergences to ambiguity-fixed solutions in real-time PPP. Specifically, extra-wide-lane ambiguity resolution can be first achieved almost instantaneously with the Melbourne-Wübbena combination observable on L2 and L5. Then the resultant unambiguous extra-wide-lane carrier-phase is combined with the wide-lane carrier-phase on L1 and L2 to form an ionosphere-free observable with a wavelength of about 3.4 m. Although the noise of this observable is around 100 times the raw carrier-phase noise, its wide-lane ambiguity can still be resolved very efficiently, and the resultant ambiguity-fixed observable can assist much better than pseudorange in speeding up succeeding narrow-lane ambiguity resolution. To validate this method, we use an advanced hardware simulator to generate triple-frequency signals and a high-grade receiver to collect 1-Hz data. When the carrier-phase precisions on L1, L2 and L5 are as poor as 1.5, 6.3 and 1.5 mm, respectively, wide-lane ambiguity resolution can still reach a correctness rate of over 99 % within 20 s. As a result, the correctness rate of narrow-lane ambiguity resolution achieves 99 % within 65 s, in contrast to only 64 % within 150 s in dual-frequency PPP. In addition, we also simulate a multipath-contaminated data set and introduce new ambiguities for all satellites every 120 s. We find that when multipath effects are strong, ambiguity-fixed solutions are achieved at 78 % of all epochs in triple-frequency PPP whilst almost no ambiguities are resolved in dual-frequency PPP. Therefore, we demonstrate that triple-frequency PPP has the potential to achieve ambiguity-fixed solutions within a few minutes, or even shorter if raw carrier-phase precisions are around 1 mm. In either case, we conclude that the efficiency of ambiguity resolution in triple-frequency PPP is much higher than that in dual-frequency PPP.     

一种BDS/GPS宽巷模糊度固定方法

针对目前双频伪距与相位观测值线性组合法(MW法)固定BDS/GPS宽巷模糊度所需平滑历元个数多的问题,提出一种附有北斗超宽巷约束的BDS/GPS几何相关的宽巷模糊度固定方法。利用伪距载波组合确定出北斗(0,-1,1)超宽巷模糊度并回代到观测方程,将超宽巷观测方程作为约束条件与BDS/GPS宽巷观测方程联立,以共有的位置参数将上述观测信息融合单历元固定BDS/GPS宽巷模糊度。基于实测数据结果表明,相对于常规的MW法,采用本文提出的有几何BDS/GPS宽巷模糊度固定方法,能够提高BDS/GPS宽巷模糊度的解算精度和时效性,适合中短基线且电离层不活跃情况下BDS/GPS宽巷模糊度的解算。     

基于北斗三频的BDS/GPS宽巷模糊度逐级单历元固定方法

利用北斗三频超宽巷模糊度波长较长易于固定的优势,提出一种基于北斗三频的BDS/GPS宽巷模糊度逐级单历元固定方法。首先利用载波和伪距组合固定BDS(0,-1,1)和(1,4,-5)两个超宽巷模糊度,根据固定后的超宽巷模糊度变换得到BDS宽巷模糊度(1,-1,0),然后将BDS宽巷模糊度作为约束条件与GPS宽巷观测方程联立得到GPS宽巷模糊度浮点解和其方差协方差阵,最后采用LAMBDA算法实现GPS宽巷模糊度的固定。实验结果表明,BDS超宽巷组合可实现100%固定,采用BDS约束GPS宽巷模糊度固定时ratio值均大于2,大于5的占97.8%以上,因此文中提出的方法可实现BDS/GPS双系统宽巷模糊度单历元固定,有效提升GNSS模糊度解算的时效性。     

一种GPS整周模糊度单历元解算方法

仅利用单历元的载波相位观测值进行整周模糊度解算,观测方程秩亏,给单历元模糊度解算带来很大困难.因此,本文提出一种单历元确定GPS整周模糊度的方法.利用单历元测码伪距观测值和双频载波相位观测值组成双差观测方程,根据方差矩阵对宽巷模糊度进行分组,采用基于LABMDA方法的逐步解算方法来确定双差相位观测值的宽巷模糊度.确定宽...     

Single GPS receiver time-relative positioning with loop misclosure corrections

Time-relative positioning makes use of observations taken at two different epochs and stations with a single global positioning system (GPS) receiver to determine the position of the unknown station with respect to the known station. The limitation of this method is the degradation over time of the positioning accuracy due to the temporal variation of GPS errors (ionospheric delay, satellite clock corrections, satellite ephemerides, and tropospheric delay). The impact of these errors is significantly reduced by adding to the one-way move from the known to the unknown station, a back move to the known station. A loop misclosure is computed from the coordinates obtained at the known station at the beginning and at the end of the loop, and is used to correct the coordinates of the unknown station. The field tests, presented in this paper, show that using the loop misclosure corrections, time-relative positioning accuracy can be improved by about 60% when using single frequency data, and by about 40% with dual frequency data. For a 4-min processing interval (an 8-min loop) and a 95% probability level, errors remain under 20 cm for the horizontal components and 36 cm for the vertical component with single frequency data; and under 11 cm for the horizontal components and 29 cm for the vertical component with dual frequency data.     

GLONASS ambiguity resolution of mixed receiver types without external calibration

GLONASS processing from mixed receiver types is typically subject to unmodeled inter-frequency phase biases which prevent carrier phase ambiguity parameters from converging to integers. Receiver-dependent values have been proposed to mitigate the contribution of these biases, but are still subject to a number of issues, such as firmware updates. Recent studies have demonstrated that the origin of inter-frequency biases is a misalignment between phase and code observations, and could be calibrated to first order by manufacturers. In this contribution, a calibration-free method for GLONASS ambiguity resolution is presented in which ambiguities naturally converge to integers. A mandatory condition is that two GLONASS satellites with adjacent frequency numbers are observed simultaneously, although this condition can be relaxed once a fixed solution has been obtained. This approach then permits the integration of different receiver types and firmware versions into seamless processing.     

Rapid GPS ambiguity resolution for short and long baselines

 A method of quick initial carrier cycle ambiguity resolution is described. The method applies to high-quality dual-band global positioning system observations. Code measurements on both frequencies must be available. The rapidity of the method is achieved through smoothing pseudoranges by phase observables and forming linear combinations between the phase observables. Two cases are investigated. Case 1: ionospheric bias is neglected (short distances); and case 2: the bias is taken into account (longer distances, more than, say, 10 km). The method was tested on six baselines, from 1 to 31 km long. In most cases, single-epoch ambiguity resolution was achieved. Received: 6 October 1999 / Accepted: 4 March 2002     

基于宽巷/窄巷法的星载GPS相位数据的模糊度解算和周跳探测

星载GPS技术是卫星精密定轨及其任务顺利执行的关键,而模糊度和周跳问题是星载GPS相位数据应用的难题。本文利用宽巷/窄巷法对星载GPS相位数据进行模糊度计算和周跳探测,给出了模糊度计算和周跳探测的计算公式和解算步骤。利用宽巷/窄巷法对CHAMP卫星实际星载GPS数据进行了处理,结果表明该方法是可行的,同时由于卫星的高速运动,星载GPS数据的模糊度解算和周跳探测难度也较大。     

Rapid PPP ambiguity resolution using GPS+GLONASS observations

Integer ambiguity resolution (IAR) in precise point positioning (PPP) using GPS observations has been well studied. The main challenge remaining is that the first ambiguity fixing takes about 30 min. This paper presents improvements made using GPS+GLONASS observations, especially improvements in the initial fixing time and correct fixing rate compared with GPS-only solutions. As a result of the frequency division multiple access strategy of GLONASS, there are two obstacles to GLONASS PPP-IAR: first and most importantly, there is distinct code inter-frequency bias (IFB) between satellites, and second, simultaneously observed satellites have different wavelengths. To overcome the problem resulting from GLONASS code IFB, we used a network of homogeneous receivers for GLONASS wide-lane fractional cycle bias (FCB) estimation and wide-lane ambiguity resolution. The integer satellite clock of the GPS and GLONASS was then estimated with the wide-lane FCB products. The effect of the different wavelengths on FCB estimation and PPP-IAR is discussed in detail. We used a 21-day data set of 67 stations, where data from 26 stations were processed to generate satellite wide-lane FCBs and integer clocks and the other 41 stations were selected as users to perform PPP-IAR. We found that GLONASS FCB estimates are qualitatively similar to GPS FCB estimates. Generally, 98.8% of a posteriori residuals of wide-lane ambiguities are within \(\pm 0.25\) cycles for GPS, and 96.6% for GLONASS. Meanwhile, 94.5 and 94.4% of narrow-lane residuals are within 0.1 cycles for GPS and GLONASS, respectively. For a critical value of 2.0, the correct fixing rate for kinematic PPP is only 75.2% for GPS alone and as large as 98.8% for GPS+GLONASS. The fixing percentage for GPS alone is only 11.70 and 46.80% within 5 and 10 min, respectively, and improves to 73.71 and 95.83% when adding GLONASS. Adding GLONASS thus improves the fixing percentage significantly for a short time span. We also used global ionosphere maps (GIMs) to assist the wide-lane carrier-phase combination to directly fix the wide-lane ambiguity. Employing this method, the effect of the code IFB is eliminated and numerical results show that GLONASS FCB estimation can be performed across heterogeneous receivers. However, because of the relatively low accuracy of GIMs, the fixing percentage of GIM-aided GPS+GLONASS PPP ambiguity resolution is very low. We expect better GIM accuracy to enable rapid GPS+GLONASS PPP-IAR with heterogeneous receivers.     

Improving carrier-phase ambiguity resolution in global GPS network solutions

Integer carrier-phase ambiguity resolution is one of the critical issues for precise GPS applications in geodesy and geodynamics. To resolve as many integer ambiguities as possible, the ‘most-easy-to-fix’ double-difference ambiguities have to be defined. For this purpose, several strategies are implemented in existing GPS software packages, such as choosing the ambiguities according to the baseline length or the variances of the estimated real-valued ambiguities. Although their efficiencies are demonstrated in practice, it is proven in this paper that they do not reflect all effects of varying data quality, because they are based on theoretical considerations of GPS data processing. Therefore, a new approach is presented, which selects the double-difference ambiguities according to their probability of being fixed to the nearest integer. The probability is computed from estimates and variances of wide-lane and narrow-lane ambiguities. Together with an optimized ambiguity fixing procedure, the new approach is implemented in the routine data processing for the International GPS Service (IGS) at GeoForschungsZentrum (GFZ) Potsdam. Within a sub-network of about 90 IGS stations, it is demonstrated that more than 97% of the independent ambiguities are fixed correctly compared to 75% by a commonly used method, and that the additionally fixed ambiguities improve the repeatability of the station coordinates by 10–26% in regions with sparse site distribution.     

基于部分模糊度解算的BDS/GPS组合RTK算法

GNSS多频率组合RTK定位逐步进入实际应用,存在模糊度维数增多、搜索空间增大,导致模糊度搜索运算量增大及模糊度固定效率低等问题。文中提出一种多星座部分模糊度解算算法,该算法综合考虑卫星高度角、模糊度固定成功率及Ratio值来筛选卫星进行模糊度解算。通过一组动态跑车实验分析表明:相比于全模糊度解算(FAR),部分模糊度解算(PAR)可以有效地提高BDS/GPS组合RTK的模糊度固定率,其模糊度固定率从79.9%(FAR)提高到99.1%(PAR),且PAR算法定位结果可靠性更高。     

Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS,BDS, GLONASS,Galileo

This paper focuses on the precise point positioning (PPP) ambiguity resolution (AR) using the observations acquired from four systems: GPS, BDS, GLONASS, and Galileo (GCRE). A GCRE four-system uncalibrated phase delay (UPD) estimation model and multi-GNSS undifferenced PPP AR method were developed in order to utilize the observations from all systems. For UPD estimation, the GCRE-combined PPP solutions of the globally distributed MGEX and IGS stations are performed to obtain four-system float ambiguities and then UPDs of GCRE satellites can be precisely estimated from these ambiguities. The quality of UPD products in terms of temporal stability and residual distributions is investigated for GPS, BDS, GLONASS, and Galileo satellites, respectively. The BDS satellite-induced code biases were corrected for GEO, IGSO, and MEO satellites before the UPD estimation. The UPD results of global and regional networks were also evaluated for Galileo and BDS, respectively. As a result of the frequency-division multiple-access strategy of GLONASS, the UPD estimation was performed using a network of homogeneous receivers including three commonly used GNSS receivers (TRIMBLE NETR9, JAVAD TRE_G3TH DELTA, and LEICA). Data recorded from 140 MGEX and IGS stations for a 30-day period in January in 2017 were used to validate the proposed GCRE UPD estimation and multi-GNSS dual-frequency PPP AR. Our results show that GCRE four-system PPP AR enables the fastest time to first fix (TTFF) solutions and the highest accuracy for all three coordinate components compared to the single and dual system. An average TTFF of 9.21 min with \(7{^{\circ }}\) cutoff elevation angle can be achieved for GCRE PPP AR, which is much shorter than that of GPS (18.07 min), GR (12.10 min), GE (15.36 min) and GC (13.21 min). With observations length of 10 min, the positioning accuracy of the GCRE fixed solution is 1.84, 1.11, and 1.53 cm, while the GPS-only result is 2.25, 1.29, and 9.73 cm for the east, north, and vertical components, respectively. When the cutoff elevation angle is increased to \(30{^{\circ }}\), the GPS-only PPP AR results are very unreliable, while 13.44 min of TTFF is still achievable for GCRE four-system solutions.     

Galileo/GPS组合观测值模糊度解算方法研究

Galileo和GPS的多个频率可形成有良好特性的组合观测值,利用这些组合观测值可以直接解算载波相位模糊度。本文选用不同波长的Galileo/GPS多频组合观测值,按不同组合方式分步固定整周模糊度,并计算出每步模糊度解算的成功率。本文研究表明,选用合理的观测值组合方式,Galileo/GPS组合观测值模糊度解算方法能以较高的成功率固定组合观测值模糊度及基本载波模糊度。     

Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods

This paper investigates single epoch ambiguity resolution performance using Galileo four frequency data. Two commonly used ambiguity resolution methods are used in the tests, including the Cascade Ambiguity Resolution (CAR) and the Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) methods. For CAR method, four optimal combinations are carefully selected according to their wavelength to noise ratios and success rate for ambiguity fixing. The test results show, in general, the LAMBDA method performs better than the CAR method. The speed of ambiguity resolution is closely related to the carrier phase measurement precision. With carrier phase measurement precision of 3 mm, single epoch ambiguity resolution can be achieved at every epoch with simulated 1-s interval 24-h Galileo data (total epochs 86,400). With the increase of carrier phase noise, ambiguity resolution performances become worse. When the noise level is increased to 12 mm, single epoch ambiguity resolution can only be achieved about 50% of epochs.     

长距离GPS/BDS参考站网多频载波相位整周模糊度解算方法

长距离网络RTK是实现GPS/BDS高精度实时定位的主要手段之一,其核心是长距离参考站网GPS/BDS整周模糊度的快速准确确定。本文提出了一种长距离GPS/BDS参考站网载波相位整周模糊度解算方法,首先利用GPS双频观测数据计算和确定宽巷整周模糊度,同时利用BDS的B2、B3频率观测值确定超宽巷整周模糊度。然后建立GPS载波相位整周模糊度和大气延迟误差的参数估计模型,附加双差宽巷整周模糊度的约束,解算双差载波相位整周模糊度,并建立参考站网大气延迟误差的空间相关模型。根据B2、B3频率的超宽巷整周模糊度建立包含大气误差参数的载波相位整周模糊度解算模型,利用大气延迟误差空间相关模型约束BDS双差载波相位整周模糊度的解算。克服了传统的使用无电离层组合值解算整周模糊度的不利影响。采用实测长距离CORS网GPS、BDS多频观测数据进行算法验证,试验结果证明该方法可实现长距离参考站网GPS/BDS载波相位整周模糊度的准确固定。