A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services

Currently, the GNSS computing modes are of two classes: network-based data processing and user receiver-based processing. A GNSS reference receiver station essentially contributes raw measurement data in either the RINEX file format or as real-time data streams in the RTCM format. Very little computation is carried out by the reference station. The existing network-based processing modes, regardless of whether they are executed in real-time or post-processed modes, are centralised or sequential. This paper describes a distributed GNSS computing framework that incorporates three GNSS modes: reference station-based, user receiver-based and network-based data processing. Raw data streams from each GNSS reference receiver station are processed in a distributed manner, i.e., either at the station itself or at a hosting data server/processor, to generate station-based solutions, or reference receiver-specific parameters. These may include precise receiver clock, zenith tropospheric delay, differential code biases, ambiguity parameters, ionospheric delays, as well as line-of-sight information such as azimuth and elevation angles. Covariance information for estimated parameters may also be optionally provided. In such a mode the nearby precise point positioning (PPP) or real-time kinematic (RTK) users can directly use the corrections from all or some of the stations for real-time precise positioning via a data server. At the user receiver, PPP and RTK techniques are unified under the same observation models, and the distinction is how the user receiver software deals with corrections from the reference station solutions and the ambiguity estimation in the observation equations. Numerical tests demonstrate good convergence behaviour for differential code bias and ambiguity estimates derived individually with single reference stations. With station-based solutions from three reference stations within distances of 22–103 km the user receiver positioning results, with various schemes, show an accuracy improvement of the proposed station-augmented PPP and ambiguity-fixed PPP solutions with respect to the standard float PPP solutions without station augmentation and ambiguity resolutions. Overall, the proposed reference station-based GNSS computing mode can support PPP and RTK positioning services as a simpler alternative to the existing network-based RTK or regionally augmented PPP systems.     

基于多接收机模糊度关联的动态PPP快速重新收敛方法

针对由于遮挡等原因造成卫星信号中断后精密单点定位（precise point positioning,PPP）需要重新收敛的问题,提出了一种基于多接收机模糊度关联的动态PPP快速重新收敛方法。以远海地区精密定位为背景,充分利用了远海地区实践应用中经常在测量船的不同位置上架设多台接收机的基本特点,建立不同接收机的模糊度之间的关系,获取发生数据中断的接收机的先验模糊度,进而完成动态PPP的快速重新收敛。实验结果表明,附加基线长度约束的两个接收机单历元固定双差模糊度的成功率在99%以上;在单历元固定双差模糊度的情况下,无论数据中断多长时间,所提算法都可以单历元完成动态PPP的重新收敛,并且收敛后的定位精度同数据中断前的定位精度相同。     

GLONASS phase bias estimation and its PPP ambiguity resolution using homogeneous receivers

Integer ambiguity resolution (IAR) appreciably improves the position accuracy and shortens the convergence time of precise point positioning (PPP). However, while many studies are limited to GPS, there is a need to investigate the performance of GLONASS PPP ambiguity resolution. Unfortunately, because of the frequency-division multiple-access strategy of GLONASS, GLONASS PPP IAR faces two obstacles. First, simultaneously observed satellites operate at different wavelengths. Second and most importantly, distinct inter-frequency bias (IFB) exists between different satellites. For the former, we adopt an undifferenced method for uncalibrated phase delay (UPD) estimation and proposed an undifferenced PPP IAR strategy. We select a set of homogeneous receivers with identical receiver IFB to perform UPD estimation and PPP IAR. The code and carrier phase IFBs can be absorbed by satellite wide-lane and narrow-lane UPDs, respectively, which is in turn consistent with PPP IAR using the same type of receivers. In order to verify the method, we used 50 stations to generate satellite UPDs and another 12 stations selected as users to perform PPP IAR. We found that the GLONASS satellite UPDs are stable in time and space and can be estimated with high accuracy and reliability. After applying UPD correction, 91 % of wide-lane ambiguities and 99 % of narrow-lane ambiguities are within (?0.15, +0.15) cycles of the nearest integer. After ambiguity resolution, the 2-hour static PPP accuracy improves from (0.66, 1.42, 1.55) cm to (0.38, 0.39, 1.39) cm for the north, east, and up components, respectively.     

卫星钟差解算及其星间单差模糊度固定

整数相位模糊度解算可以显著提高GNSS精密单点定位（PPP）的精度。本文提出一种解算卫星钟差的方法,通过固定星间单差模糊度恢复出能够支持单台接收机进行整数模糊度解算的卫星钟差,即所谓的“整数”钟差。为了实现星间单差模糊度固定,分别通过卫星端宽巷FCB解算和模糊度基准的选择与固定恢复出宽巷和窄巷模糊度的整数性质。为了证明本文方法的可行性,采用IGS测站的GPS数据进行卫星钟差解算试验。结果表明,在解算钟差时,星间单差模糊度固定的平均成功率为73%。得到的卫星钟差与IGS最终钟差产品相比,平均的RMS和STD分别为0.170和0.012 ns。448个IGS测站的星间单差宽巷和窄巷模糊度小数部分的分布表明本文得到的卫星钟差和FCB产品具备支持PPP用户进行模糊度固定的能力。基于以上产品开展了模拟动态PPP定位试验,结果表明模糊度固定之后,N、E、U和3D的定位精度（RMS）分别达到0.009、0.010、0.023和0.027 m,与不固定模糊度或采用IGS钟差的结果相比,分别提高了30.8%、61.5%、23.3%和37.2%。     

GNSS非组合PPP部分模糊度固定方法与结果分析

在精密单点定位(precise point positioning,PPP)技术中,模糊度固定错误将导致严重的定位偏差,为保证PPP模糊度实现更可靠的固定,需对模糊度子集的选取方式进行优化。提出了一种将质量控制与施密特正交化相结合的PPP部分模糊度固定方法。在全球导航卫星系统（global navigation satellite system,GNSS）多系统融合条件下, 选取多模GNSS实验数据,在非差非组合PPP模型中对比分析施密特正交化方法与高度角选星方法,并进行模糊度固定及定位性能验证。结果表明,施密特正交化方法相比高度角选星方法,各天与各站平均历元固定率在静态模式下分别提高了7.74%与11.46%,在仿动态模式下分别提高了7.90%与7.78%;各天与各站的首次固定时间在静态模式下分别提高了22.30%与25.42%,在仿动态模式下分别提高了20.44%与19.65%。在PPP模糊度固定和定位精度方面,多系统融合相比单BDS(BeiDou navigation satellite system)提升效果明显,在95%分位数条件下,水平和高程方向收敛时间分别平均减少20.00 min和19.00 min,水平和高程方向定位精度分别平均改善了1.50 cm和1.12 cm。在非差非组合PPP模型中,采用施密特正交化PPP部分模糊度固定方法可以显著提升模糊度固定性能,改善定位精度。     

Regional reference network augmented precise point positioning for instantaneous ambiguity resolution

Integer ambiguity fixing can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP), but it still takes approximate 15 min of time to achieve reliable integer ambiguity solutions. In this contribution, we present a new strategy to augment PPP estimation with a regional reference network, so that instantaneous ambiguity fixing is achievable for users within the network coverage. In the proposed method, precise zero-differenced atmospheric delays are derived from the PPP fixed solution of the reference stations, which are disseminated to, and interpolated at user stations to correct for L1, L2 phase observations or their combinations. With the corrected observations, instantaneous ambiguity resolution can be carried out within the user PPP software, thus achieving the position solutions equivalent to the network real-time kinematic positioning (NRTK). The strategy is validated experimentally. The derived atmospheric delays and the interpolated corrections are investigated. The ambiguity fixing performance and the resulted position accuracy are assessed. The validation confirms that the new strategy can provide comparable service with NRTK. Therefore, with this new processing strategy, it is possible to integrate PPP and NRTK into a seamless positioning service, which can provide an accuracy of about 10 cm anywhere, and upgrade to a few centimeters within a regional network.     

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.     

PPP/PPP-RTK新进展与北斗/GNSS PPP定位性能比较

首先简要回顾了精密单点定位（PPP）技术在最近几年的发展现状,重点总结了高采样率钟差实时快速估计、多系统组合PPP模糊度固定、多频GNSS PPP模型及其模糊度固定、PPP快速初始化、PPP-RTK等若干热点方向的最新研究进展。在此基础上,利用目前四大卫星导航系统（GPS、GLONASS、Galileo、北斗）最新的实际观测数据,全面比较分析了各系统及多系统组合PPP定位性能,重点给出了北斗二号+北斗三号PPP浮点解和固定解的定位精度、收敛时间和首次固定时间。结果表明：我国北斗导航卫星系统已经可以实现与其他导航卫星系统基本相当的PPP定位性能。北斗二号+北斗三号组合PPP的收敛时间/首次固定时间20~30 min;静态解的东、北、天方向定位精度在毫米到厘米级;动态解水平方向约5 cm,高程方向约7 cm;多系统组合可显著提高PPP定位精度、收敛时间和首次固定时间：固定解定位精度比浮点解在东、北、天方向分别提升了14.8%、12.0%和12.8%;相比单GPS,多系统组合PPP浮点解的收敛时间和固定解首次固定时间分别缩短了36.5%和40.4%。     

Removing attitude-related variations in the line-of-sight for kinematic GPS positioning

We are presenting a method for removing attitude-related variations (ATTRVs) in dynamic 1 Hz GPS positioning. The ATTRVs are separated into vertical and horizontal components. These result from the translational and rotational motions of the vehicle, which is a marine research vessel in our case. We have developed new observation equations that use corrected pseudoranges and carrier phases to account for ATTRVs. In the present contribution, we are only focusing on the vertical signals. These modeled ATTRVs are included as corrections in the line-of-sight (LoS) to each GPS satellite in the RINEX data sets using a new software called RNXATTCOR. Precise IGS sp3-orbits are used as inputs together with precise lever arm coordinates of the onboard GPS antennas, observations from the marine inertial navigation system and a priori 3D position of the vessel. The corrected RINEX data sets are then processed using kinematic processing or sequential processing in Precise Point Positioning (PPP) mode. The reduction of the standard deviation from a running mean in the final processed GPS time series is about 95%. The current method is being proposed for marine geodesy science applications such as along-track calibration/validation of altimetry products, and also for applications related to offshore kinematic high precision GPS positioning such as drilling, offshore platforms stability, marine pipeline positioning, earthquake monitoring and tsunami detection.     

非差增强信息与差分虚拟观测数据的等价变换理论

针对目前非差精密单点定位增强信息无法直接用于RTK(real time kinematic)相对定位的问题,研究了基于附加坐标约束的参考站非差精密单点模糊度固定解提取非差改正信息的方法,并建立了非差增强信息与虚拟参考站观测信息等价变换模型,重点论述了空间状态域信息(state space representation,SSR)在等价变换中的区别应用。根据RTK模糊度部分固定技术,利用实测数据设计实验证明了算法的正确性与可用性。结果表明,虚拟零基线可获得与网络RTK同等精度的定位效果,从而实现了区域增强系统在非差与差分模式上的高度统一。     

BDS/GPS精密单点定位收敛时间与定位精度的比较

采用武汉大学卫星导航定位技术研究中心发布的北斗精密卫星轨道和钟差,在TriP 2.0软件的基础上实现了BDS PPP定位算法,并利用大量实测数据进行了BDS/GPS静态PPP和动态PPP浮点解试验。结果表明,BDS静态PPP的收敛时间约为80min,动态PPP的收敛时间为100min;对于3h的观测数据,静态PPP收敛后定位精度优于5cm,动态PPP收敛后水平方向优于8cm,高程方向约12cm;与GPS PPP类似,东分量上定位精度较北分量稍差。当前由于BDS的全球跟踪站有限,精密轨道和钟差精度不如GPS,因此BDS PPP的收敛时间较GPS长,但收敛后可实现厘米至分米级的绝对定位。     

区域参考站网支撑的PPP和RTK一体化服务及其性能

GNSS区域参考站网可为大范围PPP和RTK终端用户提供快速精密定位服务,然而不同技术体制下的误差影响因素及服务模式不同,服务端数据处理方法及终端定位性能也会有所差异。本文在实现参考站非差模糊度固定的基础上,给出了基于区域参考站网的PPP及RTK一体化服务方法,并对两种技术体制的终端定位效果进行了全面评估。采用西北某省站间距约100 km的CORS站网数据进行试验分析,结果表明,采用区域参考站网解算的整数钟/UPD产品进行PPP固定解动态定位时精度较高,水平方向RMS可达0.5 cm,区域大气改正数可以显著提升定位终端的初始化速度,对于PPP和RTK,60.0%和87.7%的时段单历元即可得到固定解。需要注意的是,基于VRS模式的RTK定位等价于大气强约束,在大气建模精度较差时定位精度会显著下降,而采用虚拟大气约束的PPP-RTK定位精度几乎不受影响。     

联合GEO/IGSO/MEO的北斗PPP模糊度固定方法与试验分析

由于北斗地球静止轨道（geostationary earth orbiting,GEO）卫星轨道精度较低且其观测值受多路径误差和伪距偏差影响严重,目前各分析中心尚未针对北斗GEO卫星提供长期稳定的相位小数偏差（uncalibrated phase delay,UPD）产品,北斗精密单点定位（precise point positioning,PPP）模糊度固定技术研究主要针对倾斜轨道（inclined geosynchronous orbiting,IGSO）和中地球轨道（medium earth orbiting,MEO）卫星。本文采用Wanninger和Beer的高度角模型消除了IGSO/MEO观测值伪距偏差,并通过小波变换提取低频分量修正伪距观测值的方法削弱了GEO卫星多路径和伪距偏差的影响。由于窄巷UPD估值受未模型化误差影响较大,本文改进了窄巷UPD估计的策略,该策略利用上一历元成功估计的窄巷UPD对当前历元的浮点模糊度进行改正,剔除了残差较大的浮点模糊度,修正固定错误的整周模糊度,从而提高了窄巷UPD的精度和稳定性。利用估计得到的UPD产品,本文实现了联合GEO、IGSO和MEO卫星的北斗非差PPP模糊度固定,并对其定位性能进行分析。结果表明：联合GEO、IGSO和MEO卫星的PPP固定解的首次固定时间和收敛时间均可以缩短到30 min以内;6 h后的E、N、U方向的定位误差由（1.35、0.35、2.75）cm减少到（1.07、0.26、2.24）cm,分别减少了20%、27%和18%。     

Assessment of long-range kinematic GPS positioning errors by comparison with airborne laser altimetry and satellite altimetry

Long-range airborne laser altimetry and laser scanning (LIDAR) or airborne gravity surveys in, for example, polar or oceanic areas require airborne kinematic GPS baselines of many hundreds of kilometers in length. In such instances, with the complications of ionospheric biases, it can be a real challenge for traditional differential kinematic GPS software to obtain reasonable solutions. In this paper, we will describe attempts to validate an implementation of the precise point positioning (PPP) technique on an aircraft without the use of a local GPS reference station. We will compare PPP solutions with other conventional GPS solutions, as well as with independent data by comparison of airborne laser data with “ground truth” heights. The comparisons involve two flights: A July 5, 2003, airborne laser flight line across the North Atlantic from Iceland to Scotland, and a May 24, 2004, flight in an area of the Arctic Ocean north of Greenland, near-coincident in time and space with the ICESat satellite laser altimeter. Both of these flights were more than 800 km long. Comparisons between different GPS methods and four different software packages do not suggest a clear preference for any one, with the heights generally showing decimeter-level agreement. For the comparison with the independent ICESat- and LIDAR-derived “ground truth” of ocean or sea-ice heights, the statistics of comparison show a typical fit of around 10 cm RMS in the North Atlantic, and 30 cm in the sea-ice region north of Greenland. Part of the latter 30 cm error is likely due to errors in the airborne LIDAR measurement and calibration, as well as errors in the “ground truth” ocean surfaces due to drifting sea-ice. Nevertheless, the potential of the PPP method for generating 10 cm level kinematic height positioning over long baselines is illustrated.     

GPS非差相位精密单点定位技术探讨

探讨了精密单点定位的基本原理，处理方法，所涉及的误差改正及数据处理中的一些关键技术；采用直接内插IGS卫星精密星历的方法代替利用IGS跟踪站进行轨道精化方法计算卫星轨道参数，对现有精密单点定位计算方法进行了简化，使之更具有实用性。最后利用自主研发的精密非差单点定位软件计算和分析了实测数据。计算结果表明，经过大约15min的初始化后，非差相位单历元的定位结果精确度在X，Y，Z方向上均优于20cm。     

GPS非差相位精密单点定位方法与实现

探讨了精密单点定位的基本原理、处理方法、所涉及的误差改正及数据处理中的一些关键技术;采用直接内插IGS卫星精密星历的方法代替利用IGS跟踪站进行轨道精化方法计算卫星轨道参数,对现有精密单点定位计算方法进行了简化,使之更具有实用性。最后利用自主研发的精密非差单点定位软件计算和分析了实测数据。计算结果表明,经过大约15 min的初始化后,非差相位单历元的定位结果精确度在X,Y,Z方向上均优于20 cm。     

Impact of sampling rate of IGS satellite clock on precise point positioning

Both static and kinematic testings are investigated by using IGS 5min, 30s and 5s-interval precise satellite clock products in precise point positioning (PPP) solution. Test results show that the sampling rate of IGS satellite clock has very little effect on the static PPP solution. All the three types of sampling intervals of precise satellite clock can satisfy mm-cm level of positioning accuracy; higher sampling rate has no significant improvement for PPP solution. However, sampling rate of satellite clock has a significant impact on the PPP solution in kinematic PPP. The higher the interval of satellite clock, the better the accuracy achieved. The accuracy of kinematic PPP achieved by using 30s-interval precise satellite clock is improved by nearly 30–50 percent with respect to the solution by using 5min-interval precise satellite clock, but using 5s and 30s-interval satellite clock can almost produce the same accuracy of kinematic solution. Moreover, the use of precise satellite clock products from different analysis centers may also produce more or less effect on the PPP solution.     

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.     

单参考星下全星座单差FCB估计与应用

单差FCB应用于模糊度固定解PPP中,能够提高定位精度并加快收敛速度。但由于地球遮挡,单颗卫星无法与全部卫星形成共视,因此单颗参考星下无法获得所有卫星的单差FCB。若播发多个参考星下的单差FCB作为补充,则会增加数据传输负担。为兼顾可用性与数据量,本文依据差分传递原理将不同参考星的单差FCB转换至同一参考星下,采用基于GPHASE初值的抗差估计对转换后的FCB进行合并,以获得单参考星下全星座单差FCB。选取IGS监测站网15 d的数据生成改进后的FCB产品,并进行固定解PPP验证。试验结果表明,仅播发单参考星改进后的单差FCB即可满足应用需求,改进FCB与现有的FCB产品相差小于0.04周,稳定性与可用性均优于传统的单差FCB。利用单参考星的合并FCB进行固定解PPP：静态解算的水平精度优于1 cm,垂直精度优于2 cm;动态解算时可在15 min左右实现5 cm以内的三维定位精度。     

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.