Determining receiver biases in GPS-derived total electron content in the auroral oval and polar cap region using ionosonde measurements

Global Positioning System (GPS) total electron content (TEC) measurements, although highly precise, are often rendered inaccurate due to satellite and receiver differential code biases (DCBs). Calculated satellite DCB values are now available from a variety of sources, but receiver DCBs generally remain an undertaking of receiver operators and processing centers. A procedure for removing these receiver DCBs from GPS-derived ionospheric TEC at high latitudes, using Canadian Advanced Digital Ionosonde (CADI) measurements, is presented. Here, we will test the applicability of common numerical methods for estimating receiver DCBs in high-latitude regions and compare our CADI-calibrated GPS vertical TEC (vTEC) measurements to corresponding International GNSS Service IONEX-interpolated vTEC map data. We demonstrate that the bias values determined using the CADI method are largely independent of the topside model (exponential, Epstein, and α-Chapman) used. We further confirm our results via comparing bias-calibrated GPS vTEC with those derived from incoherent scatter radar (ISR) measurements. These CADI method results are found to be within 1.0 TEC units (TECU) of ISR measurements. The numerical methods tested demonstrate agreement varying from within 1.6 TECU to in excess of 6.0 TECU when compared to ISR measurements.     

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.     

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.     

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.     

Accuracy assessment of the GPS-TEC calibration constants by means of a simulation technique

During the last 2 decades, Global Positioning System (GPS) measurements have become a very important data-source for ionospheric studies. However, it is not a direct and easy task to obtain accurate ionospheric information from these measurements because it is necessary to perform a careful estimation of the calibration constants affecting the GPS observations, the so-called differential code biases (DCBs). In this paper, the most common approximations used in several GPS calibration methods, e.g. the La Plata Ionospheric Model (LPIM), are applied to a set of specially computed synthetic slant Total Electron Content datasets to assess the accuracy of the DCB estimation in a global scale scenario. These synthetic datasets were generated using a modified version of the NeQuick model, and have two important features: they show a realistic temporal and spatial behavior and all a-priori DCBs are set to zero by construction. Then, after the application of the calibration method the deviations from zero of the estimated DCBs are direct indicators of the accuracy of the method. To evaluate the effect of the solar activity radiation level the analysis was performed for years 2001 (high solar activity) and 2006 (low solar activity). To take into account seasonal changes of the ionosphere behavior, the analysis was repeated for three consecutive days close to each equinox and solstice of every year. Then, a data package comprising 24 days from approximately 200 IGS permanent stations was processed. In order to avoid unwanted geomagnetic storms effects, the selected days correspond to periods of quiet geomagnetic conditions. The most important results of this work are: i) the estimated DCBs can be affected by errors around ±8 TECu for high solar activity and ±3 TECu for low solar activity; and ii) DCB errors present a systematic behavior depending on the modip coordinate, that is more evident for the positive modip region.     

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.     

北斗三号卫星多频多通道差分码偏差估计与分析

差分码偏差(DCB)是电离层建模与导航定位授时的主要误差源,北斗多频多通道信号衍生出一系列新的DCB。本文首先分析了北斗三号卫星的码观测值组合及可估的DCB类型,建立了北斗三号卫星多频码偏差估计的数学模型,利用IGS实测数据首次估计得到了22种不同类型的北斗DCB。在此基础上,全面比较分析了各类DCB的内符合精度、外符合精度及月稳定度。结果表明,北斗三号卫星各类DCB的闭合差基本都在0.2 ns以内,具有较好的内符合精度;估计结果与中科院(CAS)、德国宇航中心(DLR)提供的DCB产品具有一致性,与CAS的6种DCB偏差基本在0.1 ns以内,与DLR的4种DCB偏差基本在0.2 ns以内;由于误差传递的影响,通过线性转换得到DCB值的精度和可靠性不及DCB直接估计量;北斗三号卫星各类DCB的月平均标准差为0.083 ns,具有较好的中长期稳定性;相较于北斗二号卫星,北斗三号卫星的DCB稳定性相对更优。     

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%.     

A new algorithm for single receiver DCB estimation using IGS TEC maps

A new algorithm for single receiver DCB estimation using GIM vertical TEC gridded values is proposed. It estimates receiver DCB and vertical residual ionospheric delays using the least squares approach with linear constraints. The performance of the proposed algorithm was assessed by comparing estimated receiver DCBs with those provided by the IGS. The same comparisons were done using two other algorithms for receiver DCB estimation. It is demonstrated that the proposed algorithm is capable of reproducing IGS DCB values at the level of 0.1?C0.3?ns, which is better than the level of agreement observed for the other two algorithms. For our tests, we considered data from more than 100 IGS stations, daily, such that all major regions of the world were covered. Besides, both ionospherically quiet and disturbed days were considered. It provides some evidence that the aforementioned level of agreement with IGS receiver DCB values does not significantly dependent on geographical region and the state of the ionosphere. The algorithm is easy to implement and can be considered for online use.     

Absolute Positioning with Single-Frequency GPS Receivers

The use of precise post-processed satellite orbits and satellite clock corrections in absolute positioning, using one GPS receiver only, has proven to be an accurate alternative to the more commonly used differential techniques for many applications in georeferencing. The absolute approach is capable of centimeter accuracy when using state-of-the-art, dual-frequency GPS receivers. When using observations from single-frequency receivers, however, the accuracy, especially in height, decreases. The obvious reason for this degradation in accuracy is the effect of unmodeled ionospheric delay. This paper discusses the availability of some empirical ionospheric models that are publicly available and quantifies their usefulness for absolute positioning using single-frequency GPS receivers. The Global Ionospheric Model supplied by International GPS Service (IGS) is the most accurate one and is recommended for absolute positioning using single-frequency GPS receivers. Using high-quality single-frequency observations, a horizontal epoch-to-epoch accuracy of better than 1 m and a vertical accuracy of approximately 1 m is demonstrated. ? 2002 Wiley Periodicals, Inc.     

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。     

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%。     

Anomalies in broadcast ionospheric coefficients recorded by GPS receivers over the past two solar cycles (1992–2013)

The anomaly phenomenon of broadcast ionospheric model coefficients of the Global Positioning System (GPS) is revealed after analyzing the navigation file data collected from all the IGS (International GNSS Service) stations worldwide over a 22-year period (1992–2013). GPS broadcast ionospheric coefficients widely used by many single-frequency users to correct the ionosphere errors for numerous GPS applications are usually believed to have only one set/version per day. However, it is found that GPS receivers from the IGS network can report as many as eight sets/versions of ionospheric coefficients in a day. In order to investigate the possible factors for such an anomalous phenomenon, the relationship between the number of coefficient sets and solar cycle, the receiver geographic locations, and receiver types/models are analyzed in detail. The results indicate that most of the coefficients show an annual variation. During the active solar cycle period from mid-1999 to mid-2001, all of the coefficients extracted from IGS navigation files behaved anomalously. Our analysis shows that the anomaly is also associated with GPS receiver types/models. Some types/models of GPS receivers report one set/version of ionospheric coefficients daily, while others report multiple sets. Our analysis also suggests that the ionospheric coefficient anomaly is not necessarily related to ionospheric scintillations. No correlation between the anomaly and geographic location of GPS receivers has been found in the analysis. Using the ionospheric coefficient data collected from 1998 to 2013, the impact of ionospheric coefficient anomaly on vertical total electron content (VTEC) calculation using the Klobuchar model has been evaluated with respect to the Global Ionospheric Maps generated by the Center for Orbit Determination in Europe. With different sets of coefficients recorded on the same day, the resulting VTEC values are dramatically different. For instance on June 1, 2000, the largest VTEC at one of our test stations can be as large as 153.3 TECu (total electron content unit) using one set of coefficients, which is 16.36 times larger than the smallest VTEC of 9.37 TECu computed from using another set of coefficients.     

Estimation and analysis of GPS satellite DCB based on LEO observations

The Global Positioning System (GPS) satellite differential code bias (DCB) should be precisely calibrated when obtaining ionospheric slant total electron content (TEC). So far, it is ground-based GPS observations that have been used to estimate GPS satellite DCB. With the increased Low Earth Orbit (LEO) missions in the near future, the real-time satellite DCB estimation is a crucial factor in real-time LEO GPS data applications. One alternative way is estimating GPS DCB based on the LEO observations themselves, instead of using ground observations. We propose an approach to estimate the satellite DCB based on Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) and Challenging Minisatellite Payload (CHAMP) GPS observations during the years 2002–2012. The results have been validated through comparisons with those issued by Center for Orbit Determination in Europe (CODE). The evaluations indicate that: The approach can estimate satellite DCB in a reasonable way; the DCB estimated based on CHAMP observations is much better than those on COSMIC observations; the accuracy and precision of DCB show a possible dependency on the ionospheric ionization level. This method is significance for the real-time processing of LEO-based GNSS TEC data from the perspective of real-time applications.     

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.     

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。     

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。     

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％      

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     

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.