单频到五频多系统GNSS精密单点定位参数估计与应用

全球导航卫星系统(GNSS)已发展至多频多系统时代,特别以我国北斗卫星导航系统(BDS)为代表的四大全球导航卫星系统可全天时、全天候播发十几个频率的伪距、相位和多普勒等观测信息。多频多系统GNSS为用户提供更多的观测数据和组合选择,为精密定位、导航和授时(PNT)应用带来了新的机遇,如高精度位置服务、大地测量、空间天气和灾害监测等。但多频多系统GNSS观测为精密单点定位(PPP)组合模型和系统偏差及大气延迟估计等带来诸多问题和挑战。本文给出了单频到五频多系统GNSS精密单点定位(PPP)模型,估计和评估了单频到五频多系统GNSS PPP定位精度、接收机钟差、对流层延迟、卫星和接收机硬件延迟,以及频间偏差。给出了GNSS PPP最新应用进展,包括GNSS气象学、电离层模拟、时间频率传递、建筑物安全和地震监测及其应用。结果表明,多频多系统极大地提高了GNSS PPP参数估计的精度和可靠性,具有重要的应用价值。最后给出了多频多系统GNSS PPP应用前景与展望。     

几种附电离层约束GNSS单频PPP性能评估

针对单频精密单点定位(PPP)两种常用的定位模型:非组合模型和附加电离层约束模型,同时综合考虑电离层约束模型三种不同约束策略(常数约束,时空约束,逐步松弛),对比分析了其使用GPS单系统及GPS+BDS双系统观测值的定位收敛时间,定位精度及其优缺点. 实验结果表明:使用GPS单系统,附加不同电离层约束对单频PPP收敛时间缩短效果显著,其中逐步松弛约束平均收敛时间最短,其平均收敛时间为32.36 min,四种定位模型收敛后的定位精度基本相当. 加入北斗卫星导航系统(BDS)后,四种定位模型的收敛时间均有不同程度的缩短,其中时空约束模型缩短最为显著,收敛时间缩短为单系统的59.22%. 在定位精度方面,加入BDS观测值后水平方向定位精度可提升0.5～1.3 cm,垂直方向定位精度略有下降.      

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%。     

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%。     

几种电离层模型对单频单点定位的影响分析

针对实时GNSS单频定位中电离层延迟改正问题,本文采用可用于实时GNSS单频定位的几种电离层模型对电离层延迟进行改正并分析其对GNSS单频单点定位性能的影响。其中,对单频SPP的电离层延迟采用模型直接进行改正,采用Klobuchar模型、CODE的预报产品c1pg、原国家测绘地理信息局的实时球谐电离层产品cosong和CODE事后产品codg计算的电离层精度依次提高;采用不同电离层模型作为电离层估计的先验约束进行单频PPP定位。结果表明:采用精度较好的电离层产品作为先验约束可加快单频PPP收敛。     

GPS接收机硬件延迟时变特性分析

在全球定位系统(Global Positioning System,GPS)中,接收机硬件延迟引起的码偏差和相位偏差是影响精密授时、电离层建模以及非差模糊度解算的重要因素。利用GPS对电离层总电子含量进行估计和建模时,通常假定GPS接收机硬件延迟偏差是稳定不变的量,对其可能存在的波动及影响因素考虑不充分。因此,对GPS接收机硬件延迟偏差的时变特性进行分析,有助于提高电离层电子含量估值的准确性和可靠性。分析了GPS接收机差分码偏差(differential code bias,DCB)和差分相位偏差(differential phase bias,DPB)单历元及单天解的时间变化特性,并对温度变化与接收机DCB、DPB变化之间的相关性进行了实验探究。结果表明,接收机重启前后其DCB值会发生突变,重启之后接收机DCB和DPB大约需要25 min才能趋于稳定。接收机DCB和DPB并不能长期保持稳定,实验数据显示,在2~3 h内,DCB的变化量可以达到0.8 m左右,DPB的变化量可以达到4 mm左右,接收机DCB和DPB的波动与周围环境温度的变化具有较强相关性。     

Multifrequency algorithms for precise point positioning: MAP3

We present the new MAP3 algorithms to perform static precise point positioning (PPP) from multifrequency and multisystem GNSS observations. MAP3 represents a two-step strategy in which the least squares theory is applied twice to estimate smoothed pseudo-distances, initial phase ambiguities, and slant ionospheric delay first, and the absolute receiver position and its clock offset in a second adjustment. Unlike the classic PPP technique, in our new approach, the ionospheric-free linear combination is not used. The combination of signals from different satellite systems is accomplished by taking into account the receiver inter-system bias. MAP3 has been implemented in MATLAB and integrated within a complete PPP software developed on site and named PCube. We test the MAP3 performance numerically and contrast it with other external PPP programs. In general, MAP3 positioning accuracy with low-noise GPS dual-frequency observations is about 2.5 cm in 2-h observation periods, 1 cm in 10 h, and 7 mm after 1 day. This means an improvement in the accuracy in short observation periods of at least 7 mm with respect to the other PPP programs. The MAP3 convergence time is also analyzed and some results obtained from real triple-frequency GPS and GIOVE observations are presented.     

GNSS接收机DCB短期时变特征分析和估计方法

提出一种使用非差非组合精密单点定位(PPP)估计和分析接收机DCB短时时变特征的方法。首先利用非差非组合PPP得到包含接收机DCB的重构电离层参数估值;然后通过IGS电离层GIMs格网模型内插剥离各历元站星斜向电离层距离延迟;最后通过最小二乘约束得到各历元接收机DCB解。由于格网本身精度(2~8 TECU)和插值精度限制,解算出来的接收机DCB并不能真实反映其短期时变特征。为此,提出利用站间单差或者历元间差分的方法还原其真实的变化态势。实验结果表明,所提出的方法能够正确估计接收机DCB,并能真实还原其短期时变特征,具有良好的适用性。     

北斗/GPS实时精密卫星钟差融合解算模型及精度分析

实时GNSS精密单点定位(PPP)技术必须使用实时的高精度卫星精密轨道和钟差。本文研究了精密卫星钟差融合解算模型及策略,并利用滤波算法实现了北斗/GPS实时精密卫星钟差融合估计算法。仿真实时试验结果显示:获得的北斗/GPS实时钟差与GFZ事后多GNSS精密钟差(GBM)的标准差在0.15 ns左右;使用该钟差进行GPS动态PPP试验,收敛后水平精度优于5 cm,高程精度优于10 cm;使用仿真实时钟差进行的北斗动态PPP与使用GFZ事后多GNSS精密钟差开展的试验相比精度相当,可实现分米级定位。     

多系统非差非组合精密单点定位电离层延迟约束权阵的确定

非差非组合精密单点定位需要估计电离层延迟参数,采用电离层先验改正模型约束可以辅助电离层参数解算。针对先验电离层改正量与实际观测量之间权比关系难以确定的问题,本文提出一种电离层约束权因子搜索算法,采用权因子对先验电离层改正量的方差进行调整,根据验后残差加权平方和最小原则通过搜索找出较优的权因子,利用验后残差动态调整先验电离层改正量的方差从而达到改善定位结果的目的。采用8个MGEX跟踪站的GPS/BDS观测数据对该算法进行验证。静态结果表明：对比传统约束方法,采用搜索算法后平均三维定位精度由3.96 cm提高到3.40 cm,平均收敛时间由76.3 min缩短为59.9 min。     

Evaluation of three ionospheric delay computation methods for ground-based GNSS receivers

GNSS observables for ionospheric estimation are commonly based on carrier-to-code leveling (CCL) and precise point positioning (PPP) methods. The CCL method is a geometry-free method which uses carrier phase to level pseudorange observation for decreasing multipath error and observation noise. However, the ionospheric observable based on the CCL has been proven to be affected by leveling errors. The leveling errors are caused by pseudorange multipath and intraday variation of receiver DCB. To obtain more accurate ionospheric observable, the PPP method takes advantage of precise satellite-to-ground range for retrieving slant total electron content and is less affected by the leveling errors. Previous studies have only proven that the ionospheric observables extracted by the two methods are affected by the leveling errors. The influence on ionospheric observable by the pseudorange inter-receiver satellite bias (IRSB) of the receiver has not been taken into consideration. Also, the magnitude of the differences between the ionospheric observables extracted by the two methods has also not been given. In this work, three methods, namely, the CCL, the conventional ionospheric-free PPP method which uses the ionospheric-free Hatch–Melbourne–Wubbena (HMW) function, and the University of Calgary (UOFC) PPP method, are selected to analyze and compare the differences of ionospheric observables and the global ionospheric maps, using a large number of measured data from international GNSS service global stations. Experimental results show that the accuracy of ionospheric observables obtained by the three methods is not only related to the leveling error, but also pseudorange IRSB. The IRSB of the receiver exerts a major effect on the ionospheric observables obtained by the CCL method and a minor effect on the ionospheric observables obtained by the HMW and UOFC methods. The accuracies in the latter case are similar and superior to those obtained by the CCL. The differences of the ionospheric observables obtained by the CCL and UOFC methods, or the CCL and HMW methods, are at decimeter level, whereas the difference of the ionospheric observables obtained by the UOFC and HMW methods is at centimeter level. The UOFC method presented the highest single-frequency pseudorange positioning accuracy using estimated global ionospheric products, followed by the HMW and the CCL methods which presented the lowest positioning accuracy.     

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%。     

基于原始观测值的单频精密单点定位算法

研究了一种基于GPS原始观测值的单频PPP算法。该算法通过增加电离层延迟先验信息、空间和时间约束的虚拟观测方程,将电离层延迟当作未知参数与其他定位参数一并进行估计来高效修正电离层延迟误差。通过使用全球178个IGS站1d的实测数据对本算法的收敛速度、定位精度和电离层VTEC的精度进行检验与分析。结果表明,该算法的收敛速度和稳定性均得到了改善,其静态单频单天PPP解的精度可达2~3cm、模拟动态单频单天PPP解的精度可达2~3dm,并且单频PPP与双频PPP提取的电离层总电子含量平均偏差小于5个TECU,可作为一种附属定位产品使用。     

一种机载GNSS高精度定位算法

提出部分模糊度固定的加权电离层模型提高大范围全球卫星导航系统(GNSS)航空定位的精度、可靠性及连续性.该方法的主要思路包括:自适应调整大气扰动等误差影响以实现短基线与长基线两类解算模式之间的灵活切换;施加虚拟电离层观测约束信息,提高基线动态定位的浮点解精度;采用部分模糊度固定方法有效挖掘若干模糊度参数的整周约束.试验表明,提出的方法可提高模糊固定效率与定位精度,克服传统方法有效观测信息利用率不足、定位精度较差、可靠性不高以及连续性较差的问题.实验结果表明,部分模糊度固定算法可在2 min内固定95%以上宽巷模糊度解算与80%以上窄巷模糊度,约20 min后可固定所有模糊度.     

Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers

Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary approach to estimate VTEC along with SDCBs from dual-frequency GNSS data, hereinafter referred to as DF approach, consists of two sequential steps. The first step seeks to retrieve ionospheric observables through the carrier-to-code leveling technique. This observable, related to the slant total electron content (STEC) along the satellite–receiver line-of-sight, is biased also by the SDCBs and the receiver differential code biases (RDCBs). By means of thin-layer ionospheric model, in the second step one is able to isolate the VTEC, the SDCBs and the RDCBs from the ionospheric observables. In this work, we present a single-frequency (SF) approach, enabling the joint estimation of VTEC and SDCBs using low-cost receivers; this approach is also based on two steps and it differs from the DF approach only in the first step, where we turn to the precise point positioning technique to retrieve from the single-frequency GNSS data the ionospheric observables, interpreted as the combination of the STEC, the SDCBs and the biased receiver clocks at the pivot epoch. Our numerical analyses clarify how SF approach performs when being applied to GPS L1 data collected by a single receiver under both calm and disturbed ionospheric conditions. The daily time series of zenith VTEC estimates has an accuracy ranging from a few tenths of a TEC unit (TECU) to approximately 2 TECU. For 73–96% of GPS satellites in view, the daily estimates of SDCBs do not deviate, in absolute value, more than 1 ns from their ground truth values published by the Centre for Orbit Determination in Europe.     

基于北斗GEO的电离层延迟修正方法比较与分析

电离层延迟是影响导航定位精度的最主要因素。北斗卫星导航系统采用Klobuchar模型修正单频接收机用户的电离层延迟误差,对于双频接收机,可以利用不同频率信号的伪距观测数据解算得到电离层延迟值。为比较两种方法在天津地区的电离层延迟修正效果,利用NovAtel GPStation6接收机(GNSS电离层闪烁和TEC监测接收机)采集到的卫星实测数据进行计算。以国际全球导航卫星系统服务组织(IGS)发布的全球电离层格网数据为参考,对两种方法的修正效果进行比较分析。结果表明,在天津地区,利用双频观测值解算电离层延迟比Klobuchar模型计算结果更加精确,且平均每天的修正值达到IGS发布数据的82.11％,比Klobuchar模型计算值高948％      

电离层闪烁对卫星导航系统性能影响的仿真分析

电离层闪烁是影响卫星导航系统定位性能的重要因素之一。通过仿真方法对中国区域用户定位性能受电离层闪烁影响的情况进行分析研究。结合电离层闪烁模型、卫星导航接收机模型和用户定位算法,仿真了中国区域内卫星导航系统用户在电离层闪烁存在情况下的定位精度性能。仿真结果表明：电离层闪烁将引起用户接收机测量误差的增大,在受电离层闪烁影响严重的中国低纬地区,用户定位误差将有明显增大,严重时可能出现定位异常。     

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.     

Understanding the role of the ionospheric delay in single-point single-epoch GPS coordinates

The ionospheric delay is the main source of error for single-point single-epoch (SPSE) GPS positioning when using single-frequency receivers. In contrast to the common slant approach, in this article we focus on its effect in final coordinates through the study of bias propagation in SPSE positioning: we first show an analytical resolution for the propagation problem with highly symmetric satellite configurations. To overcome some of the disadvantages of this first method, we use Santerre’s technique and, finally, present a new numerical methodology that allows us to generalize for a real geometry and obtain an average ionospheric positioning error over a given site. From the results obtained, four working hypotheses that relate the ionospheric shape above the receiver with final position errors are presented and tested. These four hypotheses, which agree with average ionospheric positioning error in 95% of the studied cases, can be related to the construction of the design matrix. Finally, these hypotheses have been used to address a situation where the ionospheric delay is corrected with an ionospheric model.     

低成本μ-blox单频多系统GNSS接收机的定位性能分析

随着大众市场对高精度定位需求增加,基于低成本小型化设备的全球卫星导航系统(GNSS)高精度定位成为研究热点之一. 本文以低成本多系统GNSS接收机μ-blox M8P型号为例,分析其观测数据质量,研究其伪距单点定位和单频载波相对定位的定位性能和特点,为低成本GNSS接收机高精度定位应用提供参考. 实验结果表明,与测量型接收机相比,μ-blox输出GNSS观测值的载噪比略小,伪距和载波相位的测量噪声较大. 静态模式下,μ-blox的单频载波相对定位(基线长度约为430 m)可以提供厘米级的定位精度;城市环境动态模式下,其单频载波相对定位可提供亚米级至米级的定位精度. 信号受限环境下,GPS／GLONASS双系统能够提供更稳定的定位结果.