基于NTCM-BC模型的全球卫星导航系统单频电离层延迟修正

选择NTCM-BC模型作为单频电离层延迟修正模型,通过非线性最小二乘拟合的方法,利用提前一天预测的电离层图（COPG文件）,计算得到NTCM-BC模型修正系数;利用Klobuchar模型和IGS发布的GIM数据对NTCM-BC模型进行比较和分析.对太阳活动高、中、低年实测数据的分析结果表明:全球平均水平上,NTCM-BC模型的电离层延迟修正性能明显优于Klobuchar模型,NTCM-BC模型的TEC平均误差和均方根误差比Klobuchar模型分别下降了41%和30%;模型的TEC计算误差与太阳活动剧烈程度成正相关,即太阳活动高年模型误差较大,太阳活动低年误差相对较低.相较于磁静日,磁扰日期间Klobuchar模型和NCTM模型的误差均有一定程度的增加.此外,模型的电离层修正误差同时存在明显的纬度、季节和地方时差异.      

基于空间统计方法的电离层折射修正技术

针对中国上空电离层所具有的特殊性和GPS观测站在中国西部分布相对稀疏的特点, 尝试探索中国卫星增强系统电离层时延信息修正技术, 为卫星导航定位以及遥感、遥测等空间应用工程的电波修正提供数据. 利用中国地壳形变监测网提供的双频GPS数据, 以空间统计方法为主要工具, 给出了普通Kriging电离层估计算法, 构建了平静期和磁暴期电离层理论变异模型, 详细分析了电离层折射修正的精度. 结果表明, 将空间统计方法应用于卫星增强系统中的电离层时延改正问题, 有利于提高增强系统的电离层折射修正精度, 特别是在观测样点相对较少的情况下, 有利于系统完整性的实现.      

实时电离层格网数据精度评估

电离层延迟是制约单频接收机定位精度的重要误差源之一.为提高单频接收机的实时电离层改正精度，需要实时电离层数据.以中国科学院空天信息创新研究院提供的实时电离层数据为例，对比分析不同太阳活动期实时电离层数据及预报电离层数据与IGS最终电离层数据之间的差值以及不同太阳活动期、不同纬度测站的电离层数据对电离层延迟进行改正后得到的定位精度.结果表明:在低太阳活动期和高太阳活动期，实时电离层数据无法很好地反映大部分海洋上空的电离层变化特性；对不同太阳活动期，实时电离层数据在高纬度测站的定位精度优于预报数据和广播模型，在中纬度测站的定位精度略低于预报数据而与广播模型定位精度相当，在低纬度测站的定位精度略优于预报数据和广播模型.      

北斗三号系统广域差分服务精度评估

为了保证北斗系统广域差分服务的平稳过渡，北斗三号系统（BDS-3）通过GEO卫星B1I/B3I信号播发北斗二号协议广域差分改正信息，包括等效钟差改正数与格网点电离层信息。分析了增加BDS-3卫星后，等效钟差改正数和格网点电离层信息的特征，并对BDS-2和BDS-3的用户差分距离误差（UDRE）进行了对比。联合BDS-2和BDS-3实测数据，对BDS-3广域差分服务定位精度进行了评估。分析结果表明:BDS-2卫星广播星历空间信号用户等效距离误差（UERE）约为1 m，经过等效钟差改正数后，用户差分距离误差约为0.3 m；BDS-3卫星广播星历空间信号用户等效距离误差约为0.4 m，经过等效钟差改正数后，用户差分距离误差约为0.2 m。等效钟差改正数可以修正广播电文更新带来的空间信号阶跃误差，显著提升卫星空间信号精度。与基本导航系统播发的Klobuchar 8模型，广域差分系统所播发的格网点电离层信息可将电离层误差修正精度提高约18%。与单独BDS-2卫星相比，BDS-2/BDS-3卫星联合条件下，基本导航的单频用户和双频用户定位精度可分别提升26%和41%；广域差分服务的单频用户定位精度为2.4 m，双频用户定位精度为1.7 m，单频用户和双频用户定位精度分别提升13%和41%。      

北斗区域Klobuchar改进模型及其修正精度分析

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,由于此模型从亚洲地区应用角度考虑,在某一特定区域的修正精度甚至不足50%。为进一步提高区域电离层延迟修正精度,提出在原模型8个改正参数的基础上增加5个关键参数的Klobuchar改进模型,并采用松弛迭代与直线搜索法中的黄金分割相结合的算法对新增参数进行求解。以天津及其附近区域为例,利用GPStation6接收机采集到的实测数据对改进模型与原模型进行计算。将国际全球导航卫星系统服务组织（International GNSS Service,IGS）发布的全球电离层格网数据作为参考值,对比分析改进模型与原模型的修正精度。结果表明,区域Klobuchar改进模型在天津及其附近区域的电离层延迟平均修正精度比原模型提升了10.46%,平均修正精度达到77.51%。     

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.     

Klobuchar电离层模型误差分析及预测

电离层延迟误差是全球导航卫星系统（global navigation satellite system，GNSS）中的重要误差源之一。目前在电离层延迟改正模型中，应用最广泛的是Klobuchar参数模型，但是该模型的改正率仅能达到60%左右，无法满足日益增长的精度需求。将国际GNSS监测评估系统（international GNSS monitoring & assessment system，iGMAS）发布的高精度电离层格网数据作为对照，对Klobuchar电离层模型误差进行计算和分析，结果发现在中纬度区域误差存在明显的周期性特征。为进一步提高Klobuchar电离层模型在中纬度区域的改正精度，建立了基于粒子群优化反向传播（back propagation，BP）神经网络的Klobuchar电离层误差预测模型,并以2019年10月的采样数据为例进行误差预测。结果表明，用该模型对中纬度区域电离层延迟提供误差补偿，可将精度提高到90%左右。     

WAAS系统中电离层折射校正的新方法及计算结果

电离层介质的色散性是影响电磁波信号进行卫星导航定位精度的重要因素之一.配合北斗二代分系绩研制任务,提出了一种新的电离层折射校正算法,并利用2000年7月1日到3日的双频GPS观测数据对6个用户站进行试算,进一步将试算所得均方根误差和电离层网格算法得到的误差进行比较.结果表明,对于中纬区域的用户站,估算的TEC误差约为0.5 m左右;而低纬用户误差相对增大,为1 m左右.文中给出的算法与电离层网格模型所提供的精度相差不多,在未来中国自主的卫星增强系统中采用新方法进行电离层进行修正是可行的及有效的.      

GNSS电离层模型改正精度评估与分析

电离层时延误差是导航定位信号在空间传播路径上的主要误差源之一,因此全面了解GNSS电离层模型的改正精度具有一定现实意义.根据GPS,BDS和Galileo系统所采用的电离层修正模型,利用2014年电离层校正参数,以高精度全球电离层图为基准,评估分析了三大系统电离层时延的改正精度.结果表明:目前GNSS使用的几种电离层修正模型的改正率在65~75%左右;Galileo系统使用的第二版NeQuick模型与第一版NeQuick模型相比在修正精度上并无显著提高;GPS使用的Klobuchar 8参数模型在北半球25°-45°N的中纬度地区精度很高,但是在全球其他区域精度较低,分布性较差,而NeQuick模型全球改正率分布则较为平均且平滑.      

Klobuchar模型的实用分析与改进

电离层延迟误差是无线电信号传播中不可忽视的误差源.GPS特许用户利用双频接收机的双频观测值直接对电离层延迟进行实时测定,其所得结果精度很高.多数普通用户所使用的单频接收机依靠电离层模型对其进行误差修正,效果不很理想.本文通过WUHN观测站双频接收机10天的实测数据对GPS广播星历采用的Klobuchar模型进行了验证,其结果与前人论述相一致.此外,经由反映太阳活动强度的太阳相对黑子数对Klobuchar模型提出了新的改进方法.实验数据结果表明,该方法对此模型修正效果有大幅提升,对原模型修正效果>50%的修正率由60%左右提升至85%以上,>80%的修正率由10%左右提升至40%以上.在实际应用中单频接收机用户可以参考本文改进方法对Klobuchar模型进行修正.      

An improved approach to model regional ionosphere and accelerate convergence for precise point positioning

Given the severe effects of the ionosphere on global navigation satellite system (GNSS) signals, single-frequency (SF) precise point positioning (PPP) users can only achieve decimeter-level positioning results. Ionosphere-free combinations can eliminate the majority of ionospheric delay, but increase observation noise and slow down dual-frequency (DF) PPP convergence. In this paper, we develop a regional ionosphere modeling and rapid convergence approach to improve SF PPP (SFPPP) accuracy and accelerate DF PPP (DFPPP) convergence speed. Instead of area model, ionospheric delay is modeled for each satellite to be used as a priori correction. With the ionospheric, wide-lane uncalibrated phase delay (UPD) and residuals satellite DCBs product, the wide-lane observations for DF users change to be high-precision pseudorange observations. The validation of a continuously operating reference station (CORS) network was analyzed. The experimental results confirm that the approach considerably improves the accuracy of SFPPP. For DF users, convergence time is substantially reduced.     

Ionospheric correction using GPS Klobuchar coefficients with an empirical night-time delay model

We proposed an ionospheric correction approach called NKlob to mitigate the ionospheric delay errors. NKlob is a modification of the original GPS Ionospheric Correction Algorithm (ICA), which uses an empirical night-time model depending on the time, geomagnetic location and periodicities of the ionospheric behavior to replace the night-time constant delay in GPS ICA. Performance of NKlob was evaluated by the independent total electron contents (TECs) derived from Global Ionospheric Maps (GIMs) of the International GNSS Services (IGS) and Jason-2 altimetry satellite during 2013–2017. Compared to GIM TECs, NKlob corrects 51.5% of the ionospheric delay errors, which outperforms GPS ICA by 6.3%. Compared to Jason-2 TECs, NKlob mitigates the ionospheric errors by 58.1%, which is approximately 3.7% better than that of GPS ICA. NKlob shows significant improvement in low-latitude and equatorial regions with respect to GPS ICA, meanwhile exhibiting comparable performance at middle and high latitudes. Since NKlob only requires slight technical changes at the processing level of GPS receivers, we suppose that it can be easily implemented for better ionospheric delay corrections of real-time GPS single-frequency applications.     

An analysis on combined GPS/COMPASS data quality and its effect on single point positioning accuracy under different observing conditions

With the rapid development of the COMPASS system, it is currently capable of providing regional navigation services. In order to test its data quality and performance for single point positioning (SPP), experiments have been conducted under different observing conditions including open sky, under trees, nearby a glass wall, nearby a large area of water, under high-voltage lines and under a signal transmitting tower. To assess the COMPASS data quality, the code multipath, cycle slip occurrence rate and data availability were analyzed and compared to GPS data. The datasets obtained from the experiments have also been utilized to perform combined GPS/COMPASS SPP on an epoch-by-epoch basis using unsmoothed single-frequency code observations. The investigation on the regional navigation performance aims at low-accuracy applications and all tests are made in Changsha, China, using the “SOUTH S82-C” GPS/COMPASS receivers. The results show that adding COMPASS observations can significantly improve the positioning accuracy of single-frequency GPS-only SPP in environments with limited satellite visibility. Since the COMPASS system is still in an initial operational stage, all results are obtained based on a fairly limited amount of data.     

An improved approach to model ionospheric delays for single-frequency Precise Point Positioning

PPP with low-cost, single-frequency receivers has been receiving increasing interest in recent years because of its large amount of possible users. One crucial issue in single-frequency PPP is the mitigation of ionospheric delays which cannot be removed by combining observations on different frequencies. For this purpose, several approaches have been developed, such as, the approach using ionospheric model corrections with proper weight, the GRAPHIC (Group and Phase Ionosphere Calibration) approach, and the method to model ionospheric delays over a station with a low polynomial or stochastic process. From our investigation on the stochastic characteristics of the ionospheric delay over a station, it cannot be precisely represented by either a deterministic model in the form of a low-order polynomial or a stochastic process for each satellite, because of its strong irregular spatial and temporal variations. Therefore, a novel approach is developed accordingly in which the deterministic representation is further refined by a stochastic process for each satellite with an empirical model for its power density. Furthermore, ionospheric delay corrections from a constructed model using GNSS data are also included as pseudo-observations for a better solution. A large data set collected from about 200 IGS stations over one month in 2010 is processed with the new approach and several commonly adopted approaches for validation. The results show its significant improvements in terms of positioning accuracy and convergence time with a negligible extra processing time, which is also demonstrated by data collected with a low-cost, handheld, single-frequency receiver.     

基于CIT技术的广域增强系统电离层延迟修正算法

提出了一种基于电离层层析成像(CIT)技术的广域增强系统(WAAS)电离层延迟 修正算法. 该算法利用模式基函数与截断奇异值分解正则化组合的方式, 实现WAAS单频用户的电离层延迟误差修正. 基于中国区域23个广域基准站 和10个用户站的仿真结果分析表明, 传统的网格算法和基于CIT技术的电离 层延迟修正算法的电离层延迟修正精度与太阳活动、昼夜变化及地磁纬度 之间均存在明显的相关性. 基于CIT技术的电离层延迟修正算法精度优于网格算法, CIT算法的平均误差与标准差相比网格算法均有较大幅度的下降.      

一种基于系数择优的低阶球谐电离层延迟改正模型

针对单频接收机的电离层延迟改正问题, 提出了一种基于系数择优的低阶球谐电离层延迟改正模型. 按照电离层延迟改正模型参数择优问题的描述, 明确参数优化的目标和约束条件, 根据参数选择可编码的特点, 提出了利用遗传算法进行参数择优的方法及步骤. 以欧洲定轨中心(CODE)提供的电离层数据作为参考标准, 对参数择优模型、 低阶球谐模型和Klobuchar模型模拟的区域电离层VTEC精度进行了比较分析. 结果表明, 较之相同系数个数的低阶球谐模型, 参数择优模型精度平均改进了1～2TECU, 而且比Klobuchar模型及低阶球谐模型能更好地反映电离层的周日变化及纬度变化特征.      

基于三频数据的北斗卫星导航系统DCB参数精度评估方法

差分码偏差（Differential Code Biases,DCB）参数作为导航电文中重要的一项,是影响用户PNT服务的主要误差源之一。北斗卫星导航系统（后文简称“北斗系统”）发射三个频点的导航信号,在导航电文中需要发播卫星的2个TGD（Timing Group Delay）参数。文章首先介绍了北斗系统卫星DCB参数最小二乘解算与形式误差评估;其次根据北斗系统三频特点,提出了不同频点组合计算垂直方向电离层电子总含量（VTEC）互差的DCB精度定量评估方法,并与IGS(International GNSS Service)提供的GPS卫星DCB精度进行比较;最后,详细分析了DCB参数精度对用户等效距离误差（UERE）计算和定位计算的影响,分别采用卫星出场标定DCB参数和经过解算DCB参数进行评估。实测数据分析结果表明,北斗系统卫星DCB参数解算形式误差与IGS解算GPS卫星DCB参数形式误差相当,但受卫星类型和解算测站的几何分布限制,北斗系统卫星DCB参数解算不确定度相比IGS略差,估计精度优于0.5ns,不同频率组合计算VTEC互差绝对值均值优于0.6TECU。相比采用卫星出场标定值,采用系统解算DCB参数后,双频用户三维位置误差改善13.80%～47.42%。     

The use of ionospheric tomography and elevation masks to reduce the overall error in single-frequency GPS timing applications

Signals from Global Positioning System (GPS) satellites at the horizon or at low elevations are often excluded from a GPS solution because they experience considerable ionospheric delays and multipath effects. Their exclusion can degrade the overall satellite geometry for the calculations, resulting in greater errors; an effect known as the Dilution of Precision (DOP). In contrast, signals from high elevation satellites experience less ionospheric delays and multipath effects. The aim is to find a balance in the choice of elevation mask, to reduce the propagation delays and multipath whilst maintaining good satellite geometry, and to use tomography to correct for the ionosphere and thus improve single-frequency GPS timing accuracy. GPS data, collected from a global network of dual-frequency GPS receivers, have been used to produce four GPS timing solutions, each with a different ionospheric compensation technique. One solution uses a 4D tomographic algorithm, Multi-Instrument Data Analysis System (MIDAS), to compensate for the ionospheric delay. Maps of ionospheric electron density are produced and used to correct the single-frequency pseudorange observations. This method is compared to a dual-frequency solution and two other single-frequency solutions: one does not include any ionospheric compensation and the other uses the broadcast Klobuchar model. Data from the solar maximum year 2002 and October 2003 have been investigated to display results when the ionospheric delays are large and variable. The study focuses on Europe and results are produced for the chosen test site, VILL (Villafranca, Spain). The effects of excluding all of the GPS satellites below various elevation masks, ranging from 5° to 40°, on timing solutions for fixed (static) and mobile (moving) situations are presented. The greatest timing accuracies when using the fixed GPS receiver technique are obtained by using a 40° mask, rather than a 5° mask. The mobile GPS timing solutions are most accurate when satellites at lower elevations continue to be included: using a mask between 10° and 20°. MIDAS offers the most accurate and least variable single-frequency timing solution and accuracies to within 10 ns are achieved for fixed GPS receiver situations. Future improvements are anticipated by combining both GPS and Galileo data towards computing a timing solution.     

Refinement of global ionospheric coefficients for GNSS applications: Methodology and results

We developed the methodology for the optimal estimation of global ionospheric coefficients of the current Global Navigation Satellite Systems (GNSSs), including the eight- and ten-parameter Klobuchar-like as well as NeQuick models. The ionospheric coefficients of those correction models are calculated from two sets of globally distributed tracking stations of the International GNSS Services (IGS). Performance of the re-estimated Klobuchar-like and NeQuick coefficients are validated during 2002–2014 over the continental and oceanic areas, respectively. Over the continental areas, GPS TECs derived from 40 ground GPS receivers are selected as reference. The eight-, ten-parameter Klobuchar-like and NeQuick models can mitigate the ionospheric delay by 65.8, 67.3 and 75.0%, respectively. Over the global oceans, the independent TECs derived from Jason-1&2 altimeters are used as reference. The re-estimated ionospheric correction models can mitigate 56.1–66.7% of the delay errors. Compared to the original GPS Ionospheric Correction Algorithm (ICA), performance of those eight-, ten-parameter Klobuchar-like and NeQuick models has improved 3.4, 5.9 and 13.4% during the whole test period, respectively. The methodology developed here takes the advantage of high-quality ionospheric TECs derived from the global network of GNSS receivers. The re-estimated ionospheric coefficients can be used as precise ionospheric products to monitor and assess GNSS broadcast ionospheric parameters and to improve the performance of various single-frequency GNSS applications.     

45°(N)纬度带的Klobuchar like电离层延迟季节修正模型与评估

电离层延迟是全球卫星导航系统（GNSS）的主要误差源之一。对于装配GNSS单频接收机的航空器,选择简单有效的Klobuchar广播电离层模型来改正电离层延迟误差,其修正率为50%～60%。针对45°（N）纬度带,提出了更高电离层修正需求。考虑到季节因素对中高纬度地区电离层的显著影响,利用GIMs（Global Ionospheric Maps）分析了昼夜中TEC（Total Electron Content）的峰值和谷值随季节（年积日）的变化,建立了一种适用于45°（N）纬度带的Klobuchar like电离层模型。该模型不增加广播模型系数,新模型的夜间和VTEC高峰时电离层修正率分别达到了82%和80%,表明在穿刺点集中的45°(N)纬度地区使用该模型可以更精确地描述该地区的电离层,帮助航空器实现更高精度的定位。