非差FCB估计及其在PPP模糊度固定中的应用

模糊度固定能够显著提高精密单点定位(PPP)的精度和收敛速度,是国内外卫星导航定位领域的研究热点．本文通过最小二乘法分离接收机端和卫星端小数周偏差(FCB),恢复非差模糊度的整数特性,将得到的卫星端FCB提供给用户,能够实现非差模糊度固定的PPP．采用全球IGS跟踪站的观测数据进行非差FCB解算,实验结果表明,宽巷FCB的稳定性较好,一周内变化小于0.1周,而窄巷FCB一天内变化较大．将获得的FCB用于模糊度固定PPP实验,E、N、U三个方向的定位精度分别为0.7 cm、0.8 cm和2.1 cm,与浮点解PPP相比,分别提高68％、51％和37％,验证了本文估计的FCB用于模糊度固定PPP的定位性能      

一种顾及先验约束的窄巷FCB估计方法

精密单点定位(PPP)技术由于作业灵活,目前在多领域得到了广泛的应用,其中整周模糊度固定是精密单点定位的核心问题。由于北斗三号全球卫星导航系统(BDS-3)的测站分布大多数集中在亚太区域,因此BDS-3的窄巷小数周偏差(FCB)受观测环境和观测条件的影响,各时段估计值差异较大,窄巷FCB的估计精度严重制约了BDS-3精密单点定位的整周模糊度固定。针对此问题,本文提出了采用最小方差估计算法,加入先验信息估计窄巷FCB的方法。首先对各观测站的观测数据进行粗差探测与隔离,在处理“干净”的数据的基础上,依据先验方差和均值进行最小方差估计,最后采用亚太地区38个观测站数据进行验证。试验结果表明,新方法估计的窄巷FCB月稳定性在0.2周以内,利用估计的窄巷FCB在进行BDS-3精密单点定位时,静态条件下固定率可达95.1%,定位精度在东向、北向和天向3个方向的均方根误差(RMS)分别为1.1、1.3和3.9 cm。     

北斗小数周偏差时变特性分析及应用

小数周偏差可用于精密单点定位的模糊度固定,其时变特性对于FCB的播发间隔、数据总量有着重要影响。当前北斗应用进入成熟期,对北斗FCB时变特性及其变化进行研究,有利于推广北斗PPP模糊度固定应用。本文基于单差FCB的生成方法,对2017年和2019年的北斗FCB时变特性展开研究,并改进了IGSO卫星窄巷FCB的播发间隔,通过已知测站固定解PPP解算,验证了改进后的北斗FCB产品。试验表明：2019年北斗FCB的稳定性相比2017年大幅提高;IGSO卫星可每天播发一组窄巷FCB,相比原有播发间隔减小73.4%的数据总量;改进后FCB可有效应用于北斗固定解PPP,收敛速度相比浮点解提升43.1%。     

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%。     

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。     

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%。     

针对消电离层组合FCB的非组合PPP部分模糊度固定方法

非差模糊度经过未校准硬件延迟小数部分(fractional cycle bias,FCB)产品改正后恢复整周特性,能够显著缩短精密单点定位(precise point positioning,PPP)的初始化时间。服务端采用非组合模型估计FCB产品时,由于电离层误差的影响,原始频点L1和L2的FCB无法准确分离,因此提出一种基于消电离层组合FCB产品的非组合PPP部分模糊度固定方法。由于传统服务端消电离层组合FCB产品算法与用户端非组合模糊度固定算法具有一致性,可采用星间单差的宽巷和原始频点模糊度构建窄巷模糊度,利用消电离层组合FCB产品进行分步模糊度固定。采用全球120个MGEX(multi-GNSS experiment)测站作为服务端生成消电离层组合FCB和非组合FCB产品,再选取全球未参与服务端解算的10个测站进行评估验证。实验结果表明,相对于使用传统非组合FCB的模糊度固定方法,静态情况下,所提方法收敛精度平均提升25.0%,收敛时间缩短21.1%;仿动态条件下,所提方法收敛精度平均提升26.7%,收敛时间缩短17.9%。     

精密单点定位模糊度快速固定算法

精密单点定位非差模糊度解算和收敛时间是制约其应用和发展的主要因素。本文从基本观测模型出发,将消电离层模糊度分解为宽巷和窄巷分别固定,并对固定方法做了改进,削弱了初始历元相关性对收敛速度的影响;提出非差相位延迟估计(PDE)解算模型,在不利用区域或全球参考站的前提下解算卫星与接收机相位延迟。通过对中国6个IGS站数据处理结果显示,93%的模糊度可以在20 min内固定。固定后定位精度在E,N和U方向上分别提高了63%,53%和24%;定位精度可以达到毫米至厘米级。对于数据质量较好的站点(如上海站)平面精度可达3 mm,模糊度固定后精密单点定位有了很大提高。     

基于整数钟的PPP非差模糊度固定方法

非差模糊度固定能够有效提高精密单点定位(PPP)的定位精度和收敛速度,是国内外卫星导航定位领域的研究热点。基于整数钟实现了PPP非差模糊度固定,在非差模糊度逐级固定中分别估计接收机宽巷偏差和窄巷偏差;对宽巷和窄巷模糊度进行改正,从而消除了接收机硬件延迟对模糊度的影响;同时采用取整成功率检验和ratio值检验,保证模糊度固定的可靠性。将以上方法应用到动态精密单点定位中,实验结果表明:仿动态条件下,模糊度正确固定后,东、北向定位精度达到mm级、天向定位精度优于5 cm;动态解算条件下,采用1 s采样间隔数据16 min左右即可实现模糊度的首次固定。PPP固定解在东、北、天3个方向的定位精度分别为1.5、2.7和1.3 cm,相比于浮点解分别提升了61%、40%和38%。     

北斗中长基线三频模糊度解算的自适应抗差滤波算法

针对经典TCAR(three carrier ambiguity resolution)算法受电离层延迟及测量噪声的影响,在中长基线下难以正确固定模糊度的问题,提出一种顾及电离层延迟影响并具有良好自适应抗差特性的改进TCAR算法。在无几何TCAR模型的基础上,通过对模糊度固定的超宽巷进行线性组合得到电离层延迟,再求解宽巷模糊度,通过构造最优组合观测量后用自适应抗差滤波求解窄巷模糊度,以提高窄巷模糊度固定正确率,减小粗差的不利影响。试验结果表明,改进TCAR算法可保证较高的宽巷模糊度固定正确率,有效提高了窄巷模糊度固定正确率,并具有良好抵抗粗差的能力。     

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.     

Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP

The main challenge of ambiguity resolution in precise point positioning (PPP) is that it requires 30 min or more to succeed in the first fixing of ambiguities. With the full operation of the BeiDou (BDS) satellite system in East Asia, it is worthwhile to investigate the performance of GPS + BDS PPP ambiguity resolution, especially the improvements of the initial fixing time and ambiguity-fixing rate compared to GPS-only solutions. We estimated the wide- and narrow-lane fractional-cycle biases (FCBs) for BDS with a regional network, and PPP ambiguity resolution was carried out at each station to assess the contribution of BDS. The across-satellite single-difference (ASSD) GPS + BDS combined ambiguity-fixed PPP model was used, in which the ASSD is applied within each system. We used a two-day data set from 48 stations. For kinematic PPP, the percentage of fixing within 10 min for GPS only (Model A) is 17.6 %, when adding IGSO and MEO of BDS (Model B), the percentage improves significantly to 42.8 %, whereas it is only 23.2 % if GEO is added (Model C) due to the low precision of GEO orbits. For static PPP, the fixing percentage is 32.9, 53.3 and 28.0 % for Model A, B and C, respectively. In order to overcome the limitation of the poor precision of GEO satellites, we also used a small network of 10 stations to analyze the contribution of GEO satellites to kinematic PPP. We took advantage of the fact that for stations of a small network the GEO satellites appear at almost the same direction, such that the GEO orbit error can be absorbed by its FCB estimates. The results show that the percentage of fixing improves from 39.5 to 57.7 % by adding GEO satellites.     

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.     

Improving the estimation of fractional-cycle biases for ambiguity resolution in precise point positioning

Ambiguity resolution dedicated to a single global positioning system (GPS) station can improve the accuracy of precise point positioning. In this process, the estimation accuracy of the narrow-lane fractional-cycle biases (FCBs), which destroy the integer nature of undifferenced ambiguities, is crucial to the ambiguity-fixed positioning accuracy. In this study, we hence propose the improved narrow-lane FCBs derived from an ambiguity-fixed GPS network solution, rather than the original (i.e. previously proposed) FCBs derived from an ambiguity-float network solution. The improved FCBs outperform the original FCBs by ensuring that the resulting ambiguity-fixed daily positions coincide in nature with the state-of-the-art positions generated by the International GNSS Service (IGS). To verify this improvement, 1?year of GPS measurements from about 350 globally distributed stations were processed. We find that the original FCBs differ more from the improved FCBs when fewer stations are involved in the FCB estimation, especially when the number of stations is less than 20. Moreover, when comparing the ambiguity-fixed daily positions with the IGS weekly positions for 248 stations through a Helmert transformation, for the East component, we find that on 359 days of the year the daily RMS of the transformed residuals based on the improved FCBs is smaller by up to 0.8?mm than those based on the original FCBs, and the mean RMS over the year falls evidently from 2.6 to 2.2?mm. Meanwhile, when using the improved rather than the original FCBs, the RMS of the transformed residuals for the East component of 239 stations (i.e. 96.4% of all 248 stations) is clearly reduced by up to 1.6?mm, especially for stations located within a sparse GPS network. Therefore, we suggest that narrow-lane FCBs should be determined with ambiguity-fixed, rather than ambiguity-float, GPS network solutions.     

3种PPP模型的统一模糊度固定方法

精密单点定位(PPP)的模糊度经未校准硬件延迟小数部分(FCB)产品改正后,可恢复整周特性,能够显著缩短PPP的初始化时间。然而由于用户端模糊度固定模型需与服务端FCB产品保持一致,不仅造成了用户端面临不同FCB产品无法使用的问题,而且加重了服务端的链路传输压力。本文提出一种基于用户端3种PPP模型(消电离层组合、无电离层约束的非组合以及先验电离层约束的非组合模型)的统一模糊度固定方法,不同用户端可采用同一种FCB产品实现模糊度的快速固定。选取全球116个MGEX测站作为服务端生成3种FCB产品,选取未参与服务端解算的50个测站作为用户端进行验证。试验结果表明,本文方法解决了用户端面临不同FCB产品的PPP模糊度固定问题,在定位精度、收敛时间、固定率方面与传统方法保持一致。     

Assessment of PPP integer ambiguity resolution using GPS,GLONASS and BeiDou (IGSO,MEO) constellations

Although integer ambiguity resolution (IAR) can improve positioning accuracy considerably and shorten the convergence time of precise point positioning (PPP), it requires an initialization time of over 30 min. With the full operation of GLONASS globally and BDS in the Asia–Pacific region, it is necessary to assess the PPP–IAR performance by simultaneous fixing of GPS, GLONASS, and BDS ambiguities. This study proposed a GPS + GLONASS + BDS combined PPP–IAR strategy and processed PPP–IAR kinematically and statically using one week of data collected at 20 static stations. The undifferenced wide- and narrow-lane fractional cycle biases for GPS, GLONASS, and BDS were estimated using a regional network, and undifferenced PPP ambiguity resolution was performed to assess the contribution of multi-GNSSs. Generally, over 99% of a posteriori residuals of wide-lane ambiguities were within ±0.25 cycles for both GPS and BDS, while the value was 91.5% for GLONASS. Over 96% of narrow-lane residuals were within ±0.15 cycles for GPS, GLONASS, and BDS. For kinematic PPP with a 10-min observation time, only 16.2% of all cases could be fixed with GPS alone. However, adding GLONASS improved the percentage considerably to 75.9%, and it reached 90.0% when using GPS + GLONASS + BDS. Not all epochs could be fixed with a correct set of ambiguities; therefore, we defined the ratio of the number of epochs with correctly fixed ambiguities to the number of all fixed epochs as the correct fixing rate (CFR). Because partial ambiguity fixing was used, when more than five ambiguities were fixed correctly, we considered the epoch correctly fixed. For the small ratio criteria of 2.0, the CFR improved considerably from 51.7% for GPS alone, to 98.3% when using GPS + GLONASS + BDS combined solutions.