An efficient solution of real-time data processing for multi-GNSS network

Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix–matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively.     

基于部分固定策略的多系统长距离基准站间模糊度快速解算

基准站间整周模糊度的快速准确固定是实现网络RTK高精度快速定位的前提。对于GPS/GLONASS/BDS组合系统长基线,模糊度维数大幅度增加,加之观测噪声、大气残余误差等因素的影响,很难快速准确地固定所有模糊度,尤其是低高度角卫星模糊度。提出了一种基于部分固定策略的GPS/GLONASS/BDS组合网络长基线部分模糊度快速解算方法,以截止高度角、模糊度固定成功率以及Ratio值为主要参数,优选模糊度固定子集,以实现长距离基准站间模糊度快速固定。通过实测GPS/GLONASS/BDS三系统长基线数据的实验验证,部分模糊度固定方法可有效避免低高度角卫星对模糊度固定的影响,从而显著提高模糊度固定时的成功率及Ratio值,缩短长距离基准站间模糊度准确固定所需的时间。     

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.     

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。     

Ambiguity resolution in precise point positioning with hourly data

Precise point positioning (PPP) has become a powerful tool for the scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station in PPP has been considered difficult, due to the receiver- and satellite-dependent uncalibrated hardware delays (UHD). However, recent studies show that if these UHD can be determined accurately in advance within a network of stations, then ambiguity resolution at a single station becomes possible. In this study, the method proposed by Ge et al. J Geod 82(7):389–399, 2007 is adopted with a refinement in which only one single-difference narrow-lane UHD between a pair of satellites is determined within each full pass over a regional network. This study uses the EUREF (European Reference Frame) Permanent Network (EPN) to determine the UHD from Day 245 to 251 in 2007. Then 12 International GNSS Service stations inside the EPN and 15 outside the EPN are used to conduct ambiguity resolution in hourly PPP. It is found that the mean positioning accuracy in all hourly solutions for the stations inside the EPN is improved from (3.8, 1.5, 2.8) centimeters to (0.5, 0.5, 1.4) centimeters for the East, North and Up components, respectively. For the stations outside the EPN, some of which are over 2,000 km away from the nearest EPN stations, the mean positioning accuracy in the East, North and Up directions still achieves (0.6, 0.6, 2.0) centimeters, respectively, when the EPN-based UHD are applied to these stations. These results demonstrate that ambiguity resolution at a single station can significantly improve the positioning accuracy in hourly PPP. Particularly, UHD can be even applied to a station which is up to thousands of kilometers from the UHD-determination network, potentially showing a great advantage over current network-based GPS augmentation systems. Therefore, it is feasible and beneficial for the operators of GPS regional networks and providers of PPP-based online services to provide these UHD estimates as an additional product.     

An enhanced strategy for GNSS data processing of massive networks

Although the computational burden of global navigation satellite systems (GNSS) data processing is nowadays already a big challenge, especially for huge networks, integrated processing of denser networks with data of multi-GNSS and multi-frequency is desired in the expectation of more accurate and reliable products. Based on the concept of carrier range, in this study, the precise point positioning with integer ambiguity resolution is engaged to obtain the integer ambiguities for converting carrier phases to carrier ranges. With such carrier ranges and pseudo-ranges, rigorous integrated processing is realized computational efficiently for the orbit and clock estimation using massive networks. The strategy is validated in terms of computational efficiency and product quality using data of the IGS network with about 460 stations. The experimental validation shows that the computation time of the new strategy increases gradually with the number of stations. It takes about 14 min for precise orbit and clock determination with 460 stations, while the current strategy needs about 82 min. The overlapping orbit RMS is reduced from 27.6 mm with 100 stations to 24.8 mm using the proposed strategy, and the RMS could be further reduced to 23.2 mm by including all 460 stations. Therefore, the new strategy could be applied to massive networks of multi-GNSS and multi-frequency receivers and possibly to achieve GNSS data products of higher quality.     

大型GNSS观测网的并行计算

CGCS2000精化及其全球拓展需要采用最新的模型,处理长期积累的大型GNSS观测网数据,大型GNSS网联合、快速和协同解算是空间基准精化、维持与服务的重要技术方向.在大数据技术背景下,以并行计算、云计算为代表的高性能计算技术逐渐成为大规模数据处理的首选方法.针对海量、多源、异构GNSS数据在解算处理与平差分析等方面面...     

长距离GPS/BDS双系统网络RTK方法

基于区域参考站网的网络实时动态定位(real-time kinematic,RTK)方法是实现全球定位系统(global positioning system,GPS)、北斗卫星导航系统(BeiDou satellite navigation system,BDS)高精度定位的主要手段.研究了一种长距离GPS/BDS双...     

GPS／GLONASS组合定位中模糊度的处理

在对GPS／GLONASS组合定位的周跳探测和修复方法进行深入研究的基础上，论述了适合于两种数据联合解算的GPS／GLONASS模糊度迭代处理方法及相应的基于FARA方法的整周模糊度固定方法。在现有BERNESE Ver4.0GSP数据处理软件的基础上，增加及改进了其中的若干模块，从而研制出组合定位系统高精度数据处理软件，并进行了试验计算。结果表明，所开发的组合定位系统数据处理软件内、外符合精度均达到mm级，证明了这种高精度相对定位理论、方法、软件的正确性和可行性。     

Precise GPS Positioning by Applying Ionospheric Corrections from an Active Control Network

In this article, initial results are presented of a method to improve fast carrier phase ambiguity resolution over longer baselines (with lengths up to about 200 km). The ionospheric delays in the global positioning system (GPS) data of these long baselines mainly hamper successful integer ambiguity resolution, a prerequisite to obtain precise positions within very short observation time spans. A way to correct the data for significant ionospheric effects is to have a GPS user operate within an active or permanently operating network use ionospheric estimates from this network. A simple way to do so is to interpolate these ionospheric estimates based on the expected spatial behaviour of the ionospheric delays. In this article such a technique is demonstrated for the Dutch Active Control Network (AGRS.NL). One hour of data is used from 4 of the 5 reference stations to obtain very precise ionospheric corrections after fixing of the integer ambiguities within this network. This is no problem because of the relatively long observation time span and known positions of the stations of the AGRS.NL. Next these interpolated corrections are used to correct the GPS data from the fifth station for its ionospheric effects. Initial conclusions about the performance of this technique are drawn in terms of improvement of integer ambiguity resolution for this baseline. ? 1999 John Wiley & Sons, Inc.     

Assessment of correct fixing rate for precise point positioning ambiguity resolution on a global scale

Ambiguity resolution (AR) for a single receiver has been a popular topic in Global Positioning System (GPS) recently. Ambiguity-resolution methods for precise point positioning (PPP) have been well documented in recent years, demonstrating that it can improve the accuracy of PPP. However, users are often concerned about the reliability of ambiguity-fixed PPP solution in practical applications. If ambiguities are fixed to wrong integers, large errors would be introduced into position estimates. In this paper, we aim to assess the correct fixing rate (CFR), i.e., number of ambiguities correctly fixing to the total number of ambiguities correctly and incorrectly fixing, for PPP user ambiguity resolution on a global scale. A practical procedure is presented to evaluate the CFR of PPP user ambiguity resolution. GPS data of the first 3 days in each month of 2010 from about 390 IGS stations are used for experiments. Firstly, we use GPS data collected from about 320 IGS stations to estimate global single-differenced (SD) wide-lane and narrow-lane satellite uncalibrated phase delays (UPDs). The quality of UPDs is evaluated. We found that wide-lane UPD estimates have a rather small standard deviation (Std) between 0.003 and 0.004 cycles while most of Std of narrow-lane estimates are from 0.01 to 0.02 cycles. Secondly, many experiments have been conducted to investigate the CFR of integer ambiguity resolution we can achieve under different conditions, including reference station density, observation session length and the ionospheric activity. The results show that the CFR of PPP can exceed 98.0 % with only 1 h of observations for most user stations. No obvious correlation between the CFR and the reference station density is found. Therefore, nearly homogeneous CFR can be achieved in PPP AR for global users. At user end, higher CFR could be achieved with longer observations. The average CFR for 30-min, 1-h, 2-h and 4-h observation is 92.3, 98.2, 99.5 and 99.7 %, respectively. In order to get acceptable CFR, 1 h is a recommended minimum observation time. Furthermore, the CFR of PPP can be affected by diurnal variation and geomagnetic latitude variation in the ionosphere. During one day at the hours when rapid ionospheric variations occur or in low geomagnetic latitude regions where equatorial electron density irregularities are produced relatively frequently, a significant degradation of the CFR is demonstrated.     

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.     

A strategy for GPS data processing in a precise local network during high solar activity

This paper presents the analyses connected with reduction of errors from ionospheric refraction using GPS data from local satellite networks. This is particularly essential during rising solar activity. The Bernese GPS Software v. 4.2 was used, as an analytical tool. The test data included measurements from a geodynamic network SUDETES situated in the Sudety Mountains across the border between the Czech Republic and Poland. A local ionospheric activity model developed from a regional model augmented with data from a local network has been tested at three levels. The criteria included comparison with a global model, the success rate of ambiguity determination using the quasi-ionosphere free and wide-lane/narrow-lane strategies, and in the position domain through analysis of residuals. The results show that the local model increases the success rate for ambiguity determination for the wide-lane/narrow-lane strategy and is available sooner than the global models. The output of the SUDETES network processing including the models of local ionospheric and tropospheric activity have been used to process data from a number of relatively small networks situated in the Sudety mountains.     

BDS/GPS单历元短基线动对动定位性能分析

针对在城市峡谷环境下观测卫星较少、观测质量差和周跳频繁,导致动对动定位过程中双差模糊度不连续的问题,提出了一种GPS/BDS组合系统的单历元模糊度解算方法。通过GPS/BDS组合定位提高了卫星的可用数量,利用单历元模糊度固定减弱了周跳频繁带来的影响。实验采用GPS/BDS组合的7组数据,分析了在不同高度角下动对动定位单历元解的模糊度固定率、解算失败率、粗差率和定位精度。结果表明,GPS/BDS组合动对动定位单历元模糊度解算方法,在高遮挡的城市峡谷环境仍然可以取得较好的定位结果。     

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.     

基于北斗三频约束的中长基线解算研究

利用北斗三频模糊度易固定的特点,提出一种具有北斗三频约束的BDS/GPS基础模糊度快速解算方法。针对中长基线,利用多历元平滑无电离层组合模糊度,从无电离层组合模糊度中分离出北斗基础模糊度;然后将北斗基础模糊度带入基线解算模型中,约束求解出GPS基础模糊度,最后将GPS与BDS基础模糊度回带观测方程,可实现基线的快速解算。经北斗实测数据验证表明,文中方法可快速固定GPS基础模糊度,较传统卡尔曼滤波求解模糊度方法,大大减少正确固定模糊度所需的原始观测历元数,实现基线的快速解算。     

PPP网解UPD模糊度固定的无基站差分大型CORS站整网快速精密解算

本文利用“国家基准一期工程”和上千全国部分省市CORS站的GNSS观测资料,基于PPP网解UPD模糊度固定技术实现了区域内无基站差分毫米级定位以及上千全国CORS站整网一次快速精密解算,这对于保障国家应急测绘快速响应、实现灾区基准快速建立以及快速获取和恢复国家统一坐标框架基准站坐标等具有重要的实用价值意义。首先,选取2015年8月1—31日198个国家GNSS连续运行基准站计算卫星端的宽巷、窄巷UPD,采用PPP网解UPD模糊度固定技术,对这些GNSS测站的载波相位进行模糊度固定:宽巷模糊度31 d固定率平均值在80%以上的测站共有193个;窄巷模糊度31 d固定率平均值在60%以上的测站共有165个。其次,对PPP整网一次快速解算定位结果进行统计分析,结果表明:31 d整网解算在NEU 3个方向的RMS分别为2.8、3.9、5.3 mm;标准差分别为2.1、3.2、6.7 mm。再者,使用中国区域内5个IGS观测站进行无基站差分精密定位,与SOPAC单天解ITRF2008框架下历元坐标的对比分析表明,31 d单日解外符合精度水平及高程方向均相差在毫米量级。最后,利用上述GNSS基准站解算出来的卫星端的宽、窄巷UPD(31 d),依次对2015年8月1—31日全国及部分省市1195个CORS站观测数据进行载波相位模糊度固定,得到无模糊度的精确相位观测值,从而使法方程中待估模糊度参数减少,克服了基准站网规模和测站个数的限制,实现了上千CORS站整网一次快速解算,对31 d月平均解与国际知名软件GAMIT/GLOBK的双差月解结果(2015年国家基础测绘任务成果)进行比较,结果显示,NEU 3个方向上差异在1 cm以内的测站分别为99.92%、99.33%、79.83%,其中U方向相差在1.5 cm为93.22%。综上所述,PPP网解UPD模糊度固定技术的方法,确保了区域内无基站精密定位、大网快速解算的精度和效率,能够满足灾区及国家坐标框架基准站坐标快速解算与恢复的迫切需求。     

基于BDS/GPS组合定位的部分模糊度固定效果分析

多系统组合有利于提高卫星导航定位的精度及可靠性,然而对于载波差分定位由于模糊度维数的陡增、观测噪声、大气残余误差等原因用传统的Lambda方法很难得到所有模糊度的固定解,采用部分模糊度方法固定最优的模糊度子集则相对容易。总结了现有的部分模糊度固定方法,分析了不同方法的特点,并用实测数据分析了BDS/GPS组合动态定位时部分模糊度固定的效果。实验结果表明,部分模糊度方法可以显著提高模糊度固定时的成功率及Ratio值,并且可以缩短RTK定位时的初始化时间,加快坐标的收敛速度,提高组合系统动态定位结果的精度。     

Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm

GPS Single-epoch Real-Time Kinematic positioning is immune to cycle slips and can be immediately re-initialized after loss-of-lock, providing high availability. This technique requires reliable ambiguity resolution: incorrect ambiguities can cause position errors of several meters, and failed ambiguity resolution reduces availability. However, a bias or inaccuracy in a single phase observation can prevent successful resolution of the whole set of ambiguities. Partial ambiguity resolution allows a subset of ambiguities to be resolved with greater probability of success than the full set. A new algorithm for resolving a subset of ambiguities with validation from previous epochs is described. If normal ambiguity resolution fails, all ambiguity subsets are generated and ordered with the best subsets first. Each subset is then resolved in turn. Fixed subsets are validated against values from previous epochs; this validation procedure greatly reduces the proportion of epochs with incorrect ambiguities. An additional algorithm is described that uses the fixed ambiguities as precise ranges to resolve the remaining unfixed ambiguities. In order to test these new algorithms, GPS data were collected from static and ship-based GPS receivers around Harwich harbor and processed from reference stations at distances up to 111 km. In the static tests the distance over which a 90% ambiguity resolution success rate for dual-frequency data was achieved was increased from 15 to 76 km. However, in some cases, the processing time was too long for this algorithm to be practical without a time-based cut-off. There is also a risk of incorrect ambiguities being propagated, particularly for single-frequency processing. In a ship-based test, the distance over which sufficient availability to support harbor navigation was achieved using single-epoch dual-frequency RTK was increased from 1 to 66 km.     

Instantaneous BDS + GPS undifferenced NRTK positioning with dynamic atmospheric constraints

As the Chinese BeiDou Navigation Satellite System (BDS) has become operational in the Asia-Pacific region, it is important to better understand and demonstrate the benefits of combining triple-frequency BDS with dual-frequency GPS observations for network-based real-time kinematic (NRTK) services. Undifferenced NRTK is a new NRTK service mode, it extends the concept of NRTK by not requiring reference station and specified reference satellite at the rover processing. In order to realize the undifferenced NRTK service, a strategy for real-time modeling the undifferenced (UD) augmentation information is given, in which the fixed double-differenced ambiguities are transformed into UD ones with the help of datum settings. Since this strategy is insensitive to existing ephemeris products, it is applicable to the services of current BDS regional reference networks. Furthermore, a processing scheme for ambiguity resolution (AR) with arbitrary-frequency observations is also presented in detail. An instantaneous and reliable BDS + GPS positioning service can be provided to the rovers in undifferenced NRTK processing mode. With the data collected at 31 stations from a continuously operating reference station network in Guangdong Province (GDCORS) of China, the efficiency of the proposed approaches using combined BDS and GPS observations is confirmed. For three rover stations during days 327–329, a total of 12,960 1-min tests were performed separately to demonstrate the performance of AR. Thanks to the dynamically refined priori information of residual tropospheric and ionospheric error, and the availability of more satellites and observations, the AR fixing rates of combined BDS and GPS systems improve by 13 to 65%, compared with those of the GPS-only system using the traditional WL-L1-IF scheme. The positioning accuracy has also significantly improved.