北斗三号卫星差分码偏差稳定性分析及其对单点定位的影响

差分码偏差（differential code bias,DCB）是影响电离层监测和导航定位精度的重要因素之一,建立DCB改正模型对高精度定位有重要意义。针对北斗三号卫星的广播星历和精密星历钟差参数时间基准不统一的问题,首先介绍了多星座实验（multi-GNSS experiment,MGEX）发布的DCB产品的估计方法,给出了部分DCB产品的精度评估和分析结果;然后提出了北斗三号卫星单频和双频伪距单点定位以及双频精密单点定位的DCB改正模型;最后利用5个MGEX测站连续5 d的实测数据分别进行了DCB改正前后的定位实验。结果表明,MGEX发布的DCB产品均具有较高的稳定性,经卫星DCB改正后,单频和双频伪距单点定位的定位精度分别提高了48%~85%和71%~91%,双频静态精密单点定位的收敛时间减少了56%~83%。     

顾及卫星PCO改正的BDS-3卫星差分码偏差精确估计EI北大核心CSCD

精确的差分码偏差改正信息是实现全球导航卫星系统多频数据精密应用的基础,而现有DCB参数估计方法及数据产品中并未考虑天线相位中心偏移的误差影响。以BDS-3为例,本文在分析BDS-3卫星PCO变化特性及其对DCB估值理论影响的基础上,推导了DCB参数中的PCO误差经验校正方法,同时提出了顾及PCO误差改正的DCB参数估计方法。利用国际GNSS服务组织全球分布的BDS-3基准站数据,实现了PCO改正前后C2I-C6I/C1P-C5P两类DCB参数的精确估计,并在BDS-3 C2I/C1P单频标准单点定位中开展定位验证。结果表明,PCO改正前后的卫星DCB差异最大可达0.60 ns,引起不同类型卫星间的DCB差异最大可达1.17 ns,DCB参数中的PCO误差对BDS-3定位应用的影响不可忽略。与未改正PCO误差的DCB产品对应的定位结果相比,基于PCO-estimated-DCB和PCO-corrected-DCB两种方案的BDS-3 SPP精度增益相当,在水平与高程方向定位精度分别提升了5.7%和6.8%。     

BDS卫星端DCB不同表达对单点定位精度的影响

考虑到北斗卫星导航系统(BDS)的B1B2,B1B3及B2B3之间硬件延迟(DCB)值存在一个闭合差,分析BDS卫星端DCB改正公式不同表示方法在3种采样率下对定位精度的影响,分别进行了伪距定位和精密定位解算。结果表明,不同采样率的DCB改正后SPP下精度改善在m级,提高10%~80%;动态PPP下精度改善在dm~m级,提高50%~90%。改正公式的不同DCB表示方法对精度影响在cm量级,在SPP中可忽略该误差,动态PPP中建议取DCB改正均值作为最终改正值。     

估计接收机差分码偏差的GPS/BDS非组合精密单点定位模型

在传统多系统非差非组合精密单点定位（precise point positioning,PPP）模型中,电离层延迟会吸收部分接收机码硬件延迟,其估计值可能为负数。提出了一种估计接收机差分码偏差（differential code bias,DCB）参数的GPS（Global Positioning System）/BDS（BeiDou Navigation Satellite System）非组合PPP模型,将每个系统第1个频率上的接收机码硬件延迟约束为零,对接收机DCB进行参数估计,达到了分离电离层延迟和接收机码硬件延迟的目的,降低了接收机钟差和电离层延迟的相关程度。利用4个多星座实验（multi-GNSS experiment,MGEX）跟踪站的GPS/BDS数据进行了静态和动态PPP试验,结果表明,与不估计DCB参数的PPP模型相比,采用估计DCB参数PPP模型后,静态模式下定位精度和收敛速度平均提高了29.3%和29.8%,动态模式下定位精度和收敛速度平均提高了15.7%和21.6%。     

顾及TGD与DCB改正的单点定位研究

TGD是调制导航电文中的一个时延差参数,它反映了L1P（Y）信号与L2P（Y）信号内部时延间的差异,对于单频导航用户,必须进行TGD改正。DCB是一表征不同测距码间差异的参数,利用DCB参数可以将L1C／A码测距精度提升到L。P（Y）码水平。本文评估了TGD与DCB参数的量级,利用IGS站数据,分析了二者对GPS单点定位的影响,结果表明：进行TGD改正后,三维定位精度有平均约1．5m的提高,平均改善率为27．3％;在TGD改正的基础上进行DCB改正后,三维定位精度有平均约0．1m的提高,平均改善率为2．59／6．     

低轨增强北斗PPP-RTK定位方法与实验分析

低轨星座具有卫星数目多、几何构型变化快等优势，有利于精密单点定位(PPP)中模糊度参数的快速收敛，从而提升其收敛速度与定位精度.但由于未能精确消除大气误差的影响，难以实现瞬时厘米级定位.提出一种低轨增强北斗PPP-实时动态(RTK)方法，结合高精度大气增强信息与模糊度固定方法(AR)，进一步改进北斗快速精密定位性能.首先设计了包含192颗低轨卫星的极轨星座，仿真了22个地面测站的观测数据，在估计相位小数偏差与精密大气延迟改正数后，分别测试了低轨增强北斗PPP、PPP-AR与PPP-RTK的定位性能.结果表明：在低轨星座增强下，可视卫星数目增加6～8颗，22个测站北斗PPP的平均初始化时间由552.1 s缩短至102 s,提升了81.52%.模糊度固定后，初始化时间进一步缩短至1 min以内.通过180 km地面参考网增强后，低轨增强北斗PPP-RTK可以实现瞬时厘米级定位，定位精度相较于PPP提升98.5%.将地面参考网扩大至500 km后，低轨增强北斗PPP-RTK仍可以实现约10 s的快速收敛.     

基于伪距/相位OSB的多频多模PPP-AR及其性能评估

在进行多频多模全球导航卫星系统（global navigation satellite system,GNSS）精密单点定位（precise point positioning,PPP）时,以相对形式表达的伪距差分码偏差（differential code bias,DCB）和相位小数周偏差（fractional cycle bias,FCB）种类繁多且修正方法较为复杂。基于此,首先给出了相对形式的伪距/相位偏差与原始观测值上的绝对偏差（observable-specific signal bias,OSB）的转换方法,以及利用该偏差进行非差模糊度固定的具体流程;然后通过实测数据分析不同偏差形式下的PPP模糊度解算（PPP-ambiguity resolution,PPP-AR）定位性能。结果表明,无论是多系统PPP还是多频PPP,其基于OSB的PPP-AR定位精度、收敛时间及固定率均与相对形式DCB/FCB的PPP-AR定位结果相当。其中,三频PPP-AR的动态和静态收敛时间均优于双频,多系统PPP-AR定位的初始化时间和定位精度也均优于单系统。伪距/相位OSB可直接用于修正对应的观...     

基于DCB和OSB产品的GNSS精密单点定位性能对比与分析

随着全球卫星导航系统(GNSS)的不断建设，精密单点定位(PPP)可用频率和通道逐步多元化.文中在原始观测方程的基础上，分别推导出适用于差分码偏差(DCB)产品和绝对偏差(OSB)产品的双频无电离层组合(IF)PPP模型，并利用50个MGEX (Multi-GNSS Experiment)测站的10 d连续观测数据对两种策略对比分析了各GNSS系统PPP模型的定位性能.结果表明：采用OSB产品的PPP模型在性能上与传统的DCB产品差异可以忽略不计，而且OSB产品在使用时更便利，更适合未来多频PPP的应用前景.     

GNSS频间钟偏差时变特征分析及非组合PPP应用

针对卫星频间钟偏差(IFCB)导致传统精密钟差产品无法直接用于多频精密单点定位的问题，该文在顾及不同频率线性组合观测值噪声放大特性的基础上，推导并提出了包括BDS-3 B1C和B2a频点的多系统IFCB数据处理方法和附加IFCB改正的多频非组合PPP平差模型，研究了不同系统IFCB时变特性及其对三频非组合PPP定位影响。实验结果表明：Galileo和BDS-3系统IFCB振幅变化量级较小，平均分别约为0.4 cm和1.0 cm, GPS和BDS-2系统IFCB振幅变化量级较大，分别达20 cm和4 cm,必须加以考虑；相对于无IFCB改正，单GPS和单BDS-2静态和动态PPP解在水平和高程方向定位精度可显著提高，且PPP定位性能改善主要体现在收敛阶段。有效解决了多GNSS系统精密定位过程中多频观测数据有效融合的问题。     

精密单点定位估计GPS卫星的P1-C1码偏差及稳定性分析

给出了利用精密单点定位（PPP）技术估计GPS卫星P1-C1码偏差的数学模型,并以BRUS、GODE、SHAO和NIST四个跟踪站2010年10月份一个月的观测数据为例,采用PPP方法计算了所有GPS卫星的P1-C1码偏差,并与欧洲定轨中心提供的P1-C1码偏差进行了比较,结果表明：四个站估计的P1-C1码偏差精度均可达到几个厘米。一个月的计算结果表明：卫星的P1-C1码偏差在一个月内变化平缓。     

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.     

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.     

基于PPP技术估计的接收机P1-P2码偏差研究

提出了基于PPP技术估计接收机P1-P2码偏差的方法,并对全球分布IGS跟踪站的P1-P2码偏差进行了估计。结果表明,这种方法获取的P1-P2码偏差精度在中高纬度地区优于1dm,在低纬度地区为1～2dm。     

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%。     

Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.     

BDS/Galileo四频精密单点定位模型性能分析与比较

北斗卫星导航系统和Galileo卫星系统都可以提供4个频率信号上的服务。本文通过与双频无电离层模型（DF）比较,评估分析了4种BDS/Galileo四频PPP模型性能,即四频无电离层双组合模型（QF1）、四频无电离层组合模型（QF2）、四频非差非组合模型（QF3）和附加电离层约束四频非差非组合模型（QF4）,同时通过等价性原则理论上证明了QF1、QF2、QF3模型的等价性。此外,用1个月参考站的静态数据和1组动态数据分析了四频静态,仿动态和动态PPP性能。试验结果表明,BDS-3 B1C和B2a新频点伪距噪声要略大于B1I和B3I信号,Galileo卫星4个频率上的伪距噪声相差并不明显。对于静态和仿动态PPP模型,QF1、QF2和QF3模型定位性能基本上一致。通过附加外部电离层约束,四频PPP模型性能受到影响,BDS（BDS-2+BDS-3）静态QF4模型相比于QF1、QF2和QF3模型平均收敛时间分别减少了4.4%、4.4%和5.4%,Galileo静态Q4模型平均收敛时间相比于Q3模型增加了16.8 min。对于动态PPP,四频PPP模型相比于双频PPP性能得到提升显著,相比于QF1模型,BDS和Galileo单系统QF4模型三维定位精度分别提高了11.4%和31.4%。BDS/Galileo双系统PPP性能要优于单系统PPP。     

Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning

During past decades, precise point positioning (PPP) has been proven to be a well-known positioning technique for centimeter or decimeter level accuracy. However, it needs long convergence time to get high-accuracy positioning, which limits the prospects of PPP, especially in real-time applications. It is expected that the PPP convergence time can be reduced by introducing high-quality external information, such as ionospheric or tropospheric corrections. In this study, several methods for tropospheric wet delays modeling over wide areas are investigated. A new, improved model is developed, applicable in real-time applications in China. Based on the GPT2w model, a modified parameter of zenith wet delay exponential decay wrt. height is introduced in the modeling of the real-time tropospheric delay. The accuracy of this tropospheric model and GPT2w model in different seasons is evaluated with cross-validation, the root mean square of the zenith troposphere delay (ZTD) is 1.2 and 3.6 cm on average, respectively. On the other hand, this new model proves to be better than the tropospheric modeling based on water-vapor scale height; it can accurately express tropospheric delays up to 10 km altitude, which potentially has benefits in many real-time applications. With the high-accuracy ZTD model, the augmented PPP convergence performance for BeiDou navigation satellite system (BDS) and GPS is evaluated. It shows that the contribution of the high-quality ZTD model on PPP convergence performance has relation with the constellation geometry. As BDS constellation geometry is poorer than GPS, the improvement for BDS PPP is more significant than that for GPS PPP. Compared with standard real-time PPP, the convergence time is reduced by 2–7 and 20–50% for the augmented BDS PPP, while GPS PPP only improves about 6 and 18% (on average), in horizontal and vertical directions, respectively. When GPS and BDS are combined, the geometry is greatly improved, which is good enough to get a reliable PPP solution, the augmentation PPP improves insignificantly comparing with standard PPP.