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。     

Computation of GPS P1–P2 Differential Code Biases with JASON-2

GPS Differential Code Biases (DCBs) computation is usually based on ground networks of permanent stations. The drawback of the classical methods is the need for the ionospheric delay so that any error in this quantity will map into the solution. Nowadays, many low-orbiting satellites are equipped with GPS receivers which are initially used for precise orbitography. Considering spacecrafts at an altitude above the ionosphere, the ionized contribution comes from the plasmasphere, which is less variable in time and space. Based on GPS data collected onboard JASON-2 spacecraft, we present a methodology which computes in the same adjustment the satellite and receiver DCBs in addition to the plasmaspheric vertical total electron content (VTEC) above the satellite, the average satellite bias being set to zero. Results show that GPS satellite DCB solutions are very close to those of the IGS analysis centers using ground measurements. However, the receiver DCB and VTEC are closely correlated, and their value remains sensitive to the choice of the plasmaspheric parametrization.     

M_DCB: Matlab code for estimating GNSS satellite and receiver differential code biases

Global navigation satellite systems (GNSS) have been widely used to monitor variations in the earth’s ionosphere by estimating total electron content (TEC) using dual-frequency observations. Differential code biases (DCBs) are one of the important error sources in estimating precise TEC from GNSS data. The International GNSS Service (IGS) Analysis Centers have routinely provided DCB estimates for GNSS satellites and IGS ground receivers, but the DCBs for regional and local network receivers are not provided. Furthermore, the DCB values of GNSS satellites or receivers are assumed to be constant over 1?day or 1?month, which is not always the case. We describe Matlab code to estimate GNSS satellite and receiver DCBs for time intervals from hours to days; the software is called M_DCB. The DCBs of GNSS satellites and ground receivers are tested and evaluated using data from the IGS GNSS network. The estimates from M_DCB show good agreement with the IGS Analysis Centers with a mean difference of less than 0.7?ns and an RMS of less than 0.4?ns, even for a single station DCB estimate.     

Estimation and analysis of Galileo differential code biases

When sensing the Earth’s ionosphere using dual-frequency pseudorange observations of global navigation satellite systems (GNSS), the satellite and receiver differential code biases (DCBs) account for one of the main sources of error. For the Galileo system, limited knowledge is available about the determination and characteristic analysis of the satellite and receiver DCBs. To better understand the characteristics of satellite and receiver DCBs of Galileo, the IGGDCB (IGG, Institute of Geodesy and Geophysics, Wuhan, China) method is extended to estimate the satellite and receiver DCBs of Galileo, with the combined use of GPS and Galileo observations. The experimental data were collected from the Multi-GNSS Experiment network, covering the period of 2013–2015. The stability of both Galileo satellite and receiver DCBs over a time period of 36 months was thereby analyzed for the current state of the Galileo system. Good agreement of Galileo satellite DCBs is found between the IGGDCB-based DCB estimates and those from the German Aerospace Center (DLR), at the level of 0.22 ns. Moreover, high-level stability of the Galileo satellite DCB estimates is obtained over the selected time span (less than 0.25 ns in terms of standard deviation) by both IGGDCB and DLR algorithms. The Galileo receiver DCB estimates are also relatively stable for the case in which the receiver hardware device stays unchanged. It can also be concluded that the receiver DCB estimates are rather sensitive to the change of the firmware version and that the receiver antenna type has no great impact on receiver DCBs.     

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.     

基于球谐函数区域电离层模型建立

利用GPS双频观测数据建立高精度、准实时的区域电离层总电子含量(TEC)模型是电离层研究的一个重要手段。文中探讨IGS观测站数据结合4阶球谐函数建立区域电离层格网模型的方法,并对硬件延迟(DCB)和TEC建模结果的可靠性进行分析,结果表明,DCB解算精度在0.4ns以内,TEC内外精度优于1.4TECU(1TECU=1016电子数/m2)和1.5TECU,满足导航定位中电离层改正的需要。     

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.     

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。     

一种精确估计区域北斗接收机硬件延迟的方法

提出了一种精确估计区域北斗接收机硬件延迟(DCB)的方法。该方法不需要传统复杂的电离层模型,在已知一个参考站接收机硬件延迟的条件下,利用正常情况下电离层延迟量和卫星-接收机几何距离强相关这一特点,采用站间单差法来精确估计区域内BDS接收机的硬件延迟。试验结果表明,该方法单站估计的单站北斗接收机连续30d的硬件延迟RMS在0.3ns左右。通过GEO卫星双频观测值扣除已知卫星DCB和本文方法估计的接收机DCB,计算对应穿刺点一天的VTEC并和GIM格网内插结果并进行比对分析,二者大小和变化趋势均符合较好,进一步验证了本文提出的方法具有可靠性。     

Is the long-term variation of the estimated GPS differential code biases associated with ionospheric variability?

The global positioning system (GPS) differential code biases (DCB) provided by the International GNSS Service (IGS) show solar-cycle-like variation during 2002–2013. This study is to examine whether this variation of the GPS DCBs is associated with ionospheric variability. The GPS observations from low earth orbit (LEO) satellites including CHAMP, GRACE and Jason-1 are used to address this issue. The GPS DCBs estimated from the LEO-based observations at different orbit altitudes show a similar tendency as the IGS DCBs. However, this solar-cycle-like dependency is eliminated when the DCBs of 13 continuously operating GPS satellites are constrained to zero-mean. Our results thus revealed that ionospheric variation is not responsible for the long-term variation of the GPS DCBs. Instead, it is attributed to the GPS satellite replacement with different satellite types and the zero-mean condition imposed on all satellite DCBs.     

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.     

Spherical cap harmonic model for mapping and predicting regional TEC

An approach to modeling the regional ionospheric total electron content (TEC) based on spherical cap harmonic analysis is presented. This approach not only provides a better regional TEC mapping accuracy, but also the capability for ionospheric model prediction based on spectrum analysis and least squares collocation. Unlike conventional approaches, which predict the immediate TEC with models using current observations, the spherical cap harmonic approach utilizes models using past observations to predict a model which will provide future TEC values. A significant advantage in comparison with conventional approaches is that the spherical cap harmonic approach can be used to predict the long-term TEC with reasonable accuracy. This study processes a set of GPS data with an observation time span of 1 year from two GPS networks in China. The TEC mapping accuracy of the spherical cap harmonic model is compared with the polynomial model and the global ionosphere model from IGS. The results show that the spherical cap harmonic model has a better TEC mapping accuracy with smoother residual distributions in both temporal and spatial domains. The TEC prediction with the spherical cap harmonic model has been investigated for both short- and long-term intervals. For the short-term interval, the prediction accuracies for the latencies of 1-day, 2-days, and 3-days are 2.5 TECU, 3.5 TECU, and 4.5 TECU, respectively. For the long-term interval, the prediction accuracy is 4.5 TECU for a 2-month latency.     

卫星VLBI测轨资料处理中的电离层延迟改正

结合我国探月项目卫星VLBI测轨资料分析中的实际需求讨论了两个问题：一是在S、X波段时延测量精度均为1ns情况下，电离层延迟改正所能够达到的精度；二是在飞行器VLBI测轨过程中，不能确保S、X波段双频观测情况下获取电离层时延改正的可能途径，包括借助于相关电离层模型、利用常规VLB1历史观测资料积累、借助于局域GPS观测网和IGS网单站GPS测量以及借助于专门设计的单站GPS测量等。最后对电离层VLB1和GPS技术实测结果进行了比较和问题分析。     

A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver

This paper develops a new automated cycle slip detection and repair method that is based on only one single dual-frequency GPS receiver. This method jointly uses the ionospheric total electron contents (TEC) rate (TECR) and Melbourne–Wübbena wide lane (MWWL) linear combination to uniquely determine the cycle slip on both L1 and L2 frequencies. The cycle slips are inferred from the information of ionospheric physical TECR and MWWL ambiguity at the current epoch and that at the previous epoch. The principle of this method is that when there are cycle slips, the MWWL ambiguity will change and the ionospheric TECR will usually be significantly amplified, the part of artificial TECR (caused by cycle slips) being significantly larger than the normal physical TECR. The TECR is calculated based on the dual-frequency carrier phase measurements, and it is highly accurate. We calculate the ionospheric change information (including TECR and TEC acceleration) using the previous epochs (30 epochs in this study) and use the previous data to predict the TECR for the epoch needing cycle slip detection. If the discrepancy is larger than our defined threshold 0.15 TECU/s, cycle slips are regarded to exist at that epoch. The key rational of method is that during a short period (1.0 s in this study) the TECR of physical ionospheric phenomenon will not exceed the threshold. This new algorithm is tested with eight different datasets (including one spaceborne GPS dataset), and the results show that the method can detect and correctly repair almost any cycle slips even under very high level of ionospheric activities (with an average Kp index 7.6 on 31 March 2001). The only exception of a few detected but incorrectly repaired cycle slip is due to a sudden increased pseudorange error on a single satellite (PRN7) under very active ionosphere on 31 March 2001. This method requires dual-frequency carrier phase and pseudorange data from only one single GPS receiver. The other requirement is that the GPS data rate ideally is 1 Hz or higher in order to detect small cycle slips. It is suitable for many applications where one single receiver is used, e.g. real-time kinematic rover station and precise point positioning. An important feature of this method is that it performs cycle slip detection and repair on a satellite-by-satellite basis; thus, the cycle slip detection and repair for each satellite are completely independent and not affected by the data of other satellites.     

GPS differential code biases considering the second-order ionospheric term

GPS Solutions - Differential code biases (DCBs) of the global positioning system (GPS) are generally estimated together with total electron content (TEC) along the signal transmission path through...     

Eye on the Ionosphere: The Correlation between Solar 10.7 cm Radio Flux and Ionospheric Range Delay

Patricia Doherty joins the regular contributors of this column to discuss the correlation between measurements of solar 10.7 cm radio flux and ionospheric range delay effects on GPS. Mrs. Doherty has extensive experience in the analysis of ionospheric range delays from worldwide systems and in the utilization and development of analytical and theoretical models of the Earth's ionosphere. Ionospheric range delay effects on GPS and other satellite ranging systems are directly proportional to the Total Electron Content (TEC) encountered along slant paths from a satellite to a ground location. TEC is a highly variable and complex parameer that is a function of geographic location, local time, season, geomagnetic activity, and solar activity. When insufficiently accounted for, ionospheric TEC can seriously limit the performance of satellite ranging applications. Since the ionosphere is a dispersive medium, dual-frequency Global Positoning System (GPS) users can make automatic corrections for ionospheric range delay by computing the apparent difference in the time delays between the two signals. Single-frequency GPS users must depend on alternate methods to account for the ionospheric range delay. Various models of the ionosphere have been used to provide estimates of ionospheric range delay. These models range from the GPS system's simple eight-coefficient algorithm designed to correct for approximately 50% rms of the TEC, to state-of-the-art models derived from physical first principles, which can correct for up to 70 to 80% rms of the TEC but at a much greater computational cost. In an effort to improve corrections for the day-to-day variability of the ionosphere, some attempts have been made to predict the TEC by using the daily values of solar 10.7 cm radio flux (F_10,7). The purpose of this article is to show that this type of prediction is not useful due to irregular, and sometimes very poor, correlation between daily values of TEC and F_10.7. Long-term measurements of solar radio flux, however, have been shown to be well correlated with monthly mean TEC, as well as with the critical frequency of the inonospheric F2 region (foF2), which is proportional to the electron density at the peak of the ionospheric F2 region. ? 2000 John Wiley & Sons, Inc.     

Total electron content processing from GPS observations to facilitate ionospheric modeling

With the increasing global distribution of high rate dual-frequency global positioning system (GPS) receivers, the production of a real-time atmospheric constituent definition, total electron content (TEC), has become a beneficial contributor to the modeling applications used in the assessment of GPS position accuracy and the composition of the ionosphere, plasmasphere, and troposphere. Historically, TEC measurements have been obtained through post processing techniques to produce the quality of data necessary for modeling applications with rigorous error estimate requirements. These procedures necessitated the collection of large volumes of data to address the various abnormalities in the computation of TEC associated with the use of greater data quality controls and source selection while real-time modeling environments must rely on autonomous controls and filtration techniques to prevent the production of erroneous model results. In this paper we present methods for processing TEC in real time, which utilize several procedures including the application of an ionospheric model to automatically perform quality control on the TEC output and the computational techniques used to address receiver multipath, faulty receiver observations, cycle-slips, segmented processing, and receiver calibrations. The resulting TEC measurements are provided with rigorous error estimates validated using the vertical TEC from the Jason satellite mission.

Global Ionosphere Maps of VTEC from GNSS,satellite altimetry,and formosat-3/COSMIC data

For space geodetic techniques, operating in microwave band, ionosphere is a dispersive medium; thus signals traveling through this medium are in the first approximation affected proportional to inverse of the square of their frequencies. This effect allows gaining information about the parameters of the ionosphere in terms of Total Electron Content (TEC) or the electron density (N _e ). TEC or electron density can then be expressed by means of spherical harmonic base functions to provide a Global Ionosphere Map (GIM). The classical input data for development of GIMs are obtained from dual-frequency observations carried out at Global Navigation Satellite Systems (GNSS) stations. However, GNSS stations are in-homogeneously distributed around the world, with large gaps particularly over the oceans; this fact reduces the precision of the GIM over these areas. On the other hand, dual-frequency satellite altimetry missions such as Jason-1 provide information about the ionosphere precisely above the oceans; and furthermore Low Earth Orbiting (LEO) satellites, such as Formosat-3/COSMIC (F/C) provide well-distributed information of ionosphere globally. This study investigates on global modeling of TEC through combining GNSS and satellite altimetry data with global TEC data derived from the occultation measurements of the F/C mission. The combined GIMs of vertical TEC (VTEC) show a maximum difference of 1.3–1.7 TEC units (TECU) with respect to the GNSS-only GIMs in the whole day. The root mean square error (RMS) maps of combined solution show a reduction of about 0.1 TECU in the whole day. This decrease of RMS can reach up to 0.5 TECU in areas where no or few GNSS observations are available, but high number of F/C measurement is carried out. This proves that the combined GIMs provide a more homogeneous global coverage and higher reliability than results of each single method. All comparisons and validations made within this study provide vital information regarding combination and integration of various observation techniques in the Global Geodetic Observing System of the International Association of Geodesy.     

The activities of the Ionosphere Working Group of the International GPS Service (IGS)

This article is based on a position paper presented at the IGS Network, Data and Analysis Center Workshop 2002 in Ottawa, Canada, 8–11 April 2002, and introduces the IGS Ionosphere Working Group (Iono_WG). Detailed information about the IGS in general can be found on the IGS Central Bureau Web page: http://igscb.jpl.nasa.gov. The Iono_WG commenced working in June 1998. The working group's main activity currently is the routine production of ionosphere Total Electron Content (TEC) maps with a 2-h time resolution and daily sets of GPS satellite and receiver hardware differential code bias (DCB) values. The TEC maps and DCB sets are derived from GPS dual-frequency tracking data recorded with the global IGS tracking network. In the medium- and long-term, the working group intends to refine algorithms for the mapping of ionospheric parameters from GPS measurements and to realize near–real–time availability of IGS ionosphere products. The paper will give an overview of the Iono_WG activities that include a summary of activities since its establishment, achievements and future plans. Electronic Publication