北斗系统硬件延迟解算及精度分析

差分码偏差(differential code bias,DCB)又称硬件延迟,是影响用户导航定位授时(pointing navigation timing,PNT)服务的主要误差源之一。GPS卫星的硬件延迟通常是在电离层建模过程中和电离层模型系数一起解得的,但是北斗系统目前仅是一个区域导航定位系统,无法通过单系统获得高精度的硬件延迟解。提出通过联合GPS和北斗卫星观测数据用低阶球谐模型建模的方式确定北斗卫星和接收机的DCB。实验数据表明在现有条件下采用该方式解算北斗卫星的DCB的精度在0.3ns左右,稳定性较好,且北斗地球静止轨道卫星(GEO)、倾斜同步轨道(IGSO)卫星DCB稳定性好于中轨道(MEO)卫星,北斗卫星DCB的稳定性要优于接收机。     

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%。     

多频多模GNSS接收机差分相位偏差的短期时变特性

随着中国北斗三号全球导航卫星系统(BeiDou-3 Navigation Satellite System,BDS-3)的建成、欧盟伽利略系统(Galileo)及日本准天顶卫星系统(quasi-zenith satellite system,QZSS)的发展,越来越多的卫星可用于反演大气电离层.通常,接收机差分码偏差(differential code biases,DCB)的短时变化被认为是利用全球导航卫星系统(Global Navigation Satellite System,GNSS)反演电离层的重要误差来源,然而,有研究表明,接收机差分相位偏差(differential phase biases,DPB)的短时变化也有可能影响电离层反演的精度和可靠性.为此,本文提出了基于站间单差模型并采用不变换参考星策略来估计接收机DPB的方法,可实现接收机DPB的连续估计.基于几台可跟踪BDS-3信号的多频多模接收机采集的数据,对BDS-3、Galileo、GPS和QZSS重叠频率组合的DPB进行了分析.结果表明,四系统的接收机DPB日变化都是很明显的,并且和温度有很强的相关性;基于不同系统重叠频率组合的DPB之间存在强相关;基于相同类型接收机的DPB的变化也存在明显的相关性.     

多模多频GNSS差分码偏差估计及电离层建模研究EI北大核心CSCD

电离层延迟是GNSS导航定位中重要的误差源,对电离层进行监测和建模具有重要的意义。GNSS具有覆盖范围广、观测时间长、反演精度高等特点,为电离层监测和建模提供了一种有效的手段。差分码偏差(differential code bias,DCB)包含在电离层观测值中,与电离层总电子含量(total electron content,TEC)参数相互耦合,在电离层建模时需要被精确分离和确定。     

Swarm低轨卫星星座的GPS接收机差分码偏差估计

差分码偏差(differential code bias,DCB)是指由全球导航卫星系统(global navigation satellite system, GNSS)信号接收和发射硬件导致的频率相关的偏差项,对电离层估计有显著的影响,在利用GNSS观测数据提取电离层总电子含量时需要被精确修正,研究利用低轨卫星的星载GNSS观测数据估计DCB尤为重要。使用Swarm星座3颗卫星GPS接收机2016年1月的双频观测值,设计了独立估计和联合估计两种估计方案,采用附加限制条件的间接平差方法对GPS卫星以及星载接收机的DCB进行估计。以中国科学院和德国宇航中心的DCB产品作为参考,分析了两种估计方案的精度和稳定性,相较于独立估计方案,联合估计方案得到的GPS卫星DCB的稳定性较独立估计方案提高了16.6%,且与参考DCB具有更好的一致性。     

基于河北省CORS的区域电离层模型精度分析

为提高区域电离层模型和导航定位服务的精度,利用河北省连续运行参考站系统（CORS） 6个基准站的GPS卫星观测数据进行区域电离层建模和接收机差分码偏差（DCB）估计,并引入中国科学院（CAS）发布的电离层产品内插得到的垂直总电子含量（VTEC）进行区域电离层模型精度验证。实验结果表明,估计的单日GPS卫星DCB与产品值精度相当,偏差控制在0.5 ns以内;河北省CORS站GPS系统接收机DCB稳定性较好,5 d的标准偏差均小于0.1 ns;利用河北省CORS建立的区域电离层TEC在地磁平静期与磁暴期均与CAS产品值具有较高的一致性,TEC偏差控制在2 TECU以内。河北省区域电离层模型能有效监测电离层TEC在不同地磁状态下的时空变化,提高区域导航定位服务水平。     

GNSS差分码偏差处理方法及全球广播电离层模型研究

<正>针对当前多模GNSS应用对多系统差分码偏差(differential code bias,DCB)产品的需求以及DCB研究仍多局限于GPS及GLONASS的现状,本文首先开展多模GNSS DCB参数精确确定研究;进而结合BDS全球系统建设的实际应用需求,深入开展了GPS、Galileo及BDS全球广播电离层模型研究,并采用大量实测数据对相关     

多频多模接收机差分码偏差的精密估计与特性分析

全球导航卫星系统（Global Navigation Satellite System,GNSS）探测大气电离层需要精确处理由接收机差分码偏差（differential cade bias,DCB）引起的系统误差。准确掌握接收机DCB的多时间尺度精细变化等特性是联合美国GPS、中国北斗卫星导航系统（BeiDou navigation satellite system,BDS）和欧盟Galileo等多GNSS技术监测电离层所面临的主要科学问题之一。为此,提出了基于零基线精密估计站间单差接收机DCB的方法,并对站间单差接收机DCB的日加权平均值进行了分析。基于4台多模接收机采集于2013年的双频观测值,揭示了站间单差接收机DCB的变化可能受3种因素的影响,即接收机内置软件的版本升级（实验中引起了约3 ns的显著增加）、拆卸个别接收机所导致的观测条件改变（实验中引起了约1.3 ns的显著减少）和估计方法的误差（引起了与导航系统卫星几何结构重复性相一致的周期性变化）等。     

基于球谐函数模型的GPS差分码延迟估计

电离层延迟是GNSS观测值中最大的误差源,因此如何利用GNSS观测值确定高精度电离层模型逐渐成为实时导航、定位及大气相关研究的重要内容。在通常采用组合观测值建立模型的方法中,精确估计电离层总电子含量（TEC）的重要误差之一是差分码硬件延迟（DCBs）。为了实时得到P1、P2、C2相互间硬件差分码延迟偏差,本文采用IGS跟踪站的观测数据并利用载波平滑后的差分伪距建立观测方程,对卫星和接收机硬件差分码延迟偏差进行实时解算。经比较模型解算DCB值与IGS最大差异不超过0.8 ns,C1、P1码延迟偏差72%差异值小于0.3 ns,P1、P2的74%差异值小于0.3 ns。     

利用非组合精密单点定位技术确定斜向电离层总电子含量和站星差分码偏差

联合双频GPS数据,利用相位平滑伪距算法,可得到包含斜向电离层总电子含量（slant total electron content,sTEC）、测站和卫星差分码偏差（differential code bias,DCB）的电离层观测值（称之为＂平滑伪距电离层观测值＂）,常应用于与电离层有关的研究。然而,平滑伪距电离层观测值易受平滑弧段长度和与测站有关的误差影响。提出一种新算法：利用非组合精密单点定位技术（precise point positioning,PPP）计算电离层观测值（称之为＂PPP电离层观测值＂）,进而估计sTEC和站星DCB。基于短基线试验,先用一台接收机按上述两种方法估计sTEC,用于改正另一接收机观测值的电离层延迟以实施单频PPP,结果表明,利用PPP电离层观测值得到的sTEC精度较高,定位结果的可靠性较强。随后,选取全球分布的8个IGS（internationalGNSS service）连续跟踪站2009年1月内某四天的观测数据,利用上述两种电离层观测值计算所有卫星的DCB,并将计算结果与CODE发布的月平均值进行比较,其中,平滑伪距电离层观测值的卫星DCB估值与CODE（Centre for Orbit Deter mination in Europe）发布值的差别较大,部分卫星甚至可达0.2～0.3 ns,而PPP电离层观测值而言,绝大多数卫星对应的差异均在0.1 ns以内。     

A two-step ionospheric modeling algorithm considering the impact of GLONASS pseudo-range inter-channel biases

The Global Navigation Satellite System presents a plausible and cost-effective way of computing the total electron content (TEC). But TEC estimated value could be seriously affected by the differential code biases (DCB) of frequency-dependent satellites and receivers. Unlike GPS and other satellite systems, GLONASS adopts a frequency-division multiplexing access mode to distinguish different satellites. This strategy leads to different wavelengths and inter-frequency biases (IFBs) for both pseudo-range and carrier phase observations, whose impacts are rarely considered in ionospheric modeling. We obtained observations from four groups of co-stations to analyze the characteristics of the GLONASS receiver P1P2 pseudo-range IFB with a double-difference method. The results showed that the GLONASS P1P2 pseudo-range IFB remained stable for a period of time and could catch up to several meters, which cannot be absorbed by the receiver DCB during ionospheric modeling. Given the characteristics of the GLONASS P1P2 pseudo-range IFB, we proposed a two-step ionosphere modeling method with the priori IFB information. The experimental analysis showed that the new algorithm can effectively eliminate the adverse effects on ionospheric model and hardware delay parameters estimation in different space environments. During high solar activity period, compared to the traditional GPS + GLONASS modeling algorithm, the absolute average deviation of TEC decreased from 2.17 to 2.07 TECu (TEC unit); simultaneously, the average RMS of GPS satellite DCB decreased from 0.225 to 0.219 ns, and the average deviation of GLONASS satellite DCB decreased from 0.253 to 0.113 ns with a great improvement in over 55%.     

On the short-term temporal variations of GNSS receiver differential phase biases

As a first step towards studying the ionosphere with the global navigation satellite system (GNSS), leveling the phase to the code geometry-free observations on an arc-by-arc basis yields the ionospheric observables, interpreted as a combination of slant total electron content along with satellite and receiver differential code biases (DCB). The leveling errors in the ionospheric observables may arise during this procedure, which, according to previous studies by other researchers, are due to the combined effects of the code multipath and the intra-day variability in the receiver DCB. In this paper we further identify the short-term temporal variations of receiver differential phase biases (DPB) as another possible cause of leveling errors. Our investigation starts by the development of a method to epoch-wise estimate between-receiver DPB (BR-DPB) employing (inter-receiver) single-differenced, phase-only GNSS observations collected from a pair of receivers creating a zero or short baseline. The key issue for this method is to get rid of the possible discontinuities in the epoch-wise BR-DPB estimates, occurring when satellite assigned as pivot changes. Our numerical tests, carried out using Global Positioning System (GPS, US GNSS) and BeiDou Navigation Satellite System (BDS, Chinese GNSS) observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, suggest two major findings. First, epoch-wise BR-DPB estimates can exhibit remarkable variability over a rather short period of time (e.g. 6 cm over 3 h), thus significant from a statistical point of view. Second, a dominant factor driving this variability is the changes of ambient temperature, instead of the un-modelled phase multipath.     

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.     

Ionospheric and receiver DCB-constrained multi-GNSS single-frequency PPP integrated with MEMS inertial measurements

Single-frequency precise point positioning (SF-PPP) is a potential precise positioning technique due to the advantages of the high accuracy in positioning after convergence and the low cost in operation. However, there are still challenges limiting its applications at present, such as the long convergence time, the low reliability, and the poor satellite availability and continuity in kinematic applications. In recent years, the achievements in the dual-frequency PPP have confirmed that its performance can be significantly enhanced by employing the slant ionospheric delay and receiver differential code bias (DCB) constraint model, and the multi-constellation Global Navigation Satellite Systems (GNSS) data. Accordingly, we introduce the slant ionospheric delay and receiver DCB constraint model, and the multi-GNSS data in SF-PPP modular together. In order to further overcome the drawbacks of SF-PPP in terms of reliability, continuity, and accuracy in the signal easily blocking environments, the inertial measurements are also adopted in this paper. Finally, we form a new approach to tightly integrate the multi-GNSS single-frequency observations and inertial measurements together to ameliorate the performance of the ionospheric delay and receiver DCB-constrained SF-PPP. In such model, the inter-system bias between each two GNSS systems, the inter-frequency bias between each two GLONASS frequencies, the hardware errors of the inertial sensors, the slant ionospheric delays of each user-satellite pair, and the receiver DCB are estimated together with other parameters in a unique Kalman filter. To demonstrate its performance, the multi-GNSS and low-cost inertial data from a land-borne experiment are analyzed. The results indicate that visible positioning improvements in terms of accuracy, continuity, and reliability can be achieved in both open-sky and complex conditions while using the proposed model in this study compared to the conventional GPS SF-PPP.     

Calibration errors on experimental slant total electron content (TEC) determined with GPS

The Global Positioning System (GPS) has become a powerful tool for ionospheric studies. In addition, ionospheric corrections are necessary for the augmentation systems required for Global Navigation Satellite Systems (GNSS) use. Dual-frequency carrier-phase and code-delay GPS observations are combined to obtain ionospheric observables related to the slant total electron content (sTEC) along the satellite-receiver line-of-sight (LoS). This observable is affected by inter-frequency biases [IFB; often called differential code biases (DCB)] due to the transmitting and the receiving hardware. These biases must be estimated and eliminated from the data in order to calibrate the experimental sTEC obtained from GPS observations. Based on the analysis of single differences of the ionospheric observations obtained from pairs of co-located dual-frequency GPS receivers, this research addresses two major issues: (1) assessing the errors translated from the code-delay to the carrier-phase ionospheric observable by the so-called levelling process, applied to reduce carrier-phase ambiguities from the data; and (2) assessing the short-term stability of receiver IFB. The conclusions achieved are: (1) the levelled carrier-phase ionospheric observable is affected by a systematic error, produced by code-delay multi-path through the levelling procedure; and (2) receiver IFB may experience significant changes during 1 day. The magnitude of both effects depends on the receiver/antenna configuration. Levelling errors found in this research vary from 1.4 total electron content units (TECU) to 5.3 TECU. In addition, intra-day vaiations of code-delay receiver IFB ranging from 1.4 to 8.8 TECU were detected.     

Revisit the calibration errors on experimental slant total electron content (TEC) determined with GPS

The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.     

确定卫星与接收机信号延迟偏差的新方法及其应用

单频ＧＰＳ接收机用户通常需要进行电离层延迟改正,电离层延迟改正量通常来源于电离层延迟改正模型或双频ＧＰＳ基准站信息,后者即是利用双频ＧＰＳ观测值估计电子含量总数,求解电离层延迟改正量。利用双频ＧＰＳ观测值估计电子含量总数,一个关键总是是去掉卫星与接收信号延迟偏差。     

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。     

Improving performance of GPS satellite DCB estimation for regional GPS networks using long-term stability

Compensation for differential code bias (DCB) is necessary because it is the major source of errors in total electron content (TEC) measurements. The DCB estimation performance is degraded when only the regional GPS network is used. Because DCB estimation is highly correlated with ionospheric modeling, this degradation is particularly evident for measurements concentrated in an area of high TEC concentration. This study proposes a DCB estimation method that uses the long-term stability of the DCB to improve the estimation performance of the regional GPS network. We estimate satellite DCBs by assuming their constancy over seven months. This extended period increases the number of measurements used in DCB estimation and changes the local time distribution of collected measurements. As a result, the unbalanced distribution of specific ionospheric conditions disappears. Tests are performed using both global and regional networks, and the estimation performance is evaluated based on the position error and pseudorange residuals. First, the difference between the global and regional networks when using the conventional method is analyzed. Second, proposed methods are applied to regional networks. The proposed method can improve the DCB estimation performance, and the results are similar to those obtained using one-day global network data.