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%。     

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。     

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%。     

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      

GPS精密卫星钟差估计研究

随着精密单点定位技术的发展,对于精确的卫星坐标以及卫星钟差改正精度的要求越来越高,精密卫星星历以及精密卫星钟差的求解成为制约精密单点定位技术发展的瓶颈。本文基于修复周跳的载波相位观测值与相位平滑伪距观测值,采用无电离层延迟星间单差精密卫星钟差估计模型,在先估计出整周模糊度后,进行了精密卫星钟差的估计,并采用与IGS事后精密钟差作二次差的方法进行精度分析,这对于提高精密单点定位精度具有一定的意义。     

BDS-3新频点PPP模糊度固定研究

针对BDS-3新频点在精密单点定位解算中的模糊度固定问题，该文采用绝对信号偏差(OSB)改正的方法，对B2a频点在精密单点定位方面的性能进行了研究。首先通过与整数钟差法进行对比实验，验证OSB改正法在模糊度固定方面的可靠性，之后采用该方法对B2a频点构建的双频无电离层组合进行精密单点定位-模糊度固定(PPP-AR)实验，与B1I/B3I的PPP-AR结果进行比较，评估定位精度。结果表明，OSB改正原始观测值的模糊度固定方法有较好的可靠性，收敛速度提升20%,模糊度固定成功率在90%以上；新频点B2a的精密单点定位性能较好，收敛速度和定位精度与B1I、B3I频点相当，采用B2a频点得到的双频无电离层组合在PPP-AR解算时能完成模糊度的快速固定，收敛时间在25 min以内，收敛后误差小于2 cm, B2a频点可用于PPP-AR解算。     

整数相位钟法精密单点定位模糊度固定模型及效果分析

精密单点定位(PPP)模糊度固定方法有3种:星间单差法、整数相位钟法和钟差解耦法,但目前仅法国CNES公开发布用于整数相位钟法PPP模糊度固定的产品,因此研究基于整数相位钟法的用户端PPP模糊度固定模型很有必要.本文分析了整数相位钟法PPP模糊度固定模型,着重指出该模型与传统浮点解PPP模型的区别;提出一种顾及质量控制的逐级模糊度固定策略用于具体实施PPP模糊度固定.大量动态PPP解算试验表明:与浮点解PPP相比,固定解PPP具有更快的收敛速度且定位精度和稳定性更好.     

模糊度线性约束的消电离层多频模糊度解算

针对传统多频模糊度解算方法受到电离层延迟影响造成窄巷模糊度解算可靠性降低的问题,提出一种基于模糊度线性约束的消电离层MCAR方法。该方法通过模型等价性原理构建了基于几何相关-消电离层组合模型,并凭借能够可靠解算的超宽巷/宽巷模糊度值形成线性约束,进而构造窄巷模糊度解算模型,最终求解窄巷模糊度及精密定位结果。多组北斗三频实际数据测试结果表明,即使双差电离层延迟达到73.2 cm,所提出方法也可实现模糊度解算成功率高于96%,定位精度优于15 cm。     

实时模式下UPD产品计算及PPPAR定位性能分析

针对目前实时精密单点定位(PPP)收敛速度还相对较慢的问题，该文提出了一种适用于实时模式的宽巷及窄巷相位小数偏差(UPD)估计算法。采用180个全球均匀分布的多模实验跟踪网(MGEX)站，分析了基于实时轨道钟差产品进行实时UPD解算及实时精密单点定位模糊度固定(PPPAR)定位的可行性。实验结果表明，GPS和BDS-3的相邻两天宽巷UPD相减所得偏差的均值以及标准差基本上在0.025周左右，因此采用宽巷UPD预报值进行后续解算是可靠的。GPS浮点PPP和PPPAR定位结果表明，PPPAR的定位误差相较于浮点解PPP在E、N、U方向分别提升了36.4%、25.0%和22.2%,定位收敛时间也从31.9 min下降到24.8 min。GPS+BDS-3的PPPAR定位结果表明，定位时加入BDS-3可以缩短PPPAR的首次固定时间，最终的三维定位误差也从单GPS系统的2.55 cm下降到了GPS+BDS-3的2.17 cm。基于实时模式UPD解算和PPPAR定位实验结果表明，该文提出的UPD实时估计算法是可靠的，估计出的实时UPD产品应用于PPPAR可以获得较好的定位效果。     

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%。     

A new differential code bias (C1–P1) estimation method and its performance evaluation

The current satellite clock products are computed using the ionosphere-free phase (L1/L2) and code (P1/P2) observations. Thus, if users conduct undifferenced positioning using these clock products together with C1 and P2 observations, the differential code bias (DCB) (C1–P1) should be properly compensated. The influence of DCB (C1–P1) on the undifferenced ambiguity solutions is investigated. Based on the investigation, we propose a new DCB (C1–P1) estimation method. Using it, the satellite DCB (C1–P1) can be computed. A 30-day (DOY 205–234, 2012) dual-frequency GPS data set is processed to estimate the DCB (C1–P1). Comparing the estimated results with that of IGS DCB products, the accuracy is better than 0.13 m. The performances of DCB (C1–P1) in the code-based single-point positioning, precise point positioning (PPP) convergence and wide-lane uncalibrated phase delay (UPD) estimation are investigated using the estimated DCB (C1–P1). The results of the code-based single-point positioning show that the influence of DCB (C1–P1) on the up direction is more evident than on the horizontal directions. The accuracy is improved by 50 % and reaches to decimeter level with DCB (C1–P1) application. The performance of DCB (C1–P1) in PPP shows that it can accelerate PPP convergence through improving the accuracy of the code observation. The computed UPD values show that influence of DCB (C1–P1) on UPD of each satellite is different, and some values are larger than 0.3 cycles.     

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%。     

历元差分模型在北斗卫星钟差实时解算中的应用

卫星钟差是影响卫星定位精度的重要误差源之一,而实时精密单点定位又要求卫星钟差实时更新。卫星钟差的解算可通过非差模型或历元差分模型实现,但非差模型涵盖较多的载波相位模糊度参数,相比消掉模糊度参数的历元差分模型,计算效率要慢许多。历元差分模型仅利用载波相位观测量就可获得高精度卫星钟差历元间差,恢复后的卫星钟差仍可达到一定精度水平。利用历元差分模型可实现北斗卫星钟差的实时解算,试验结果表明:通过滤波得到的卫星钟差历元间差精度优于0.02 ns,恢复后的卫星钟差精度优于0.25 ns.      

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.     

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.     

Impact of GPS differential code bias in dual- and triple-frequency positioning and satellite clock estimation

The features and differences of various GPS differential code bias (DCB)s are discussed. The application of these biases in dual- and triple-frequency satellite clock estimation is introduced based on this discussion. A method for estimating the satellite clock error from triple-frequency uncombined observations is presented to meet the need of the triple-frequency uncombined precise point positioning (PPP). In order to evaluate the estimated satellite clock error, the performance of these biases in dual- and triple-frequency positioning is studied. Analysis of the inter-frequency clock bias (IFCB), which is a result of constant and time-varying frequency-dependent hardware delays, in ionospheric-free code-based (P1/P5) single point positioning indicates that its influence on the up direction is more pronounced than on the north and east directions. When the IFCB is corrected, the mean improvements are about 29, 35 and 52% for north, east and up directions, respectively. Considering the contribution of code observations to PPP convergence time, the performance of DCB(P1–P2), DCB(P1–P5) and IFCB in GPS triple-frequency PPP convergence is investigated. The results indicate that the DCB correction can accelerate PPP convergence by means of improving the accuracy of the code observation. The performance of these biases in positioning further verifies the correctness of the estimated dual- and triple-frequency satellite clock error.     

快速星历代替最终星历的可行性研究

精密单点定位中卫星星历误差和卫星钟差是影响定位精度的重要误差。基于传统的消电离层模型,编制相应的程序,然后对目前IGS提供的2种精密星历（IGF、IGR）及其钟差进行实验分析。结果表明,快速星历及其钟差可以代替最终星历及其钟差进行定位。