GPS slant total electron content accuracy using the single layer model under different geomagnetic regions and ionospheric conditions

The use of observations from the Global Positioning System (GPS) has significantly impacted the study of the ionosphere. As it is widely known, dual-frequency GPS observations can provide very precise estimation of the slant Total Electron Content (sTEC—the linear integral of the electron density along a ray-path) and that the precision level is bounded by the carrier-phase noise and multi-path effects on both frequencies. Despite its precision, GPS sTEC estimations can be systematically affected by errors in the estimation of the satellites and receivers by Inter-Frequency Biases (IFB) that are simultaneously determined with the sTEC. Thus, the ultimate accuracy of the GPS sTEC estimation is determined by the errors with which the IFBs are estimated. This contribution attempts to assess the accuracy of IFBs estimation techniques based on the single layer model for different ionospheric regions (low, mid and high magnetic latitude); different seasons (summer and winter solstices and spring and autumn equinoxes); different solar activity levels (high and low); and different geomagnetic conditions (quiet and very disturbed). The followed strategy relies upon the generation of a synthetic data set free of IFB, multi-path, measurement noise and of any other error source. Therefore, when a data set with such properties is used as the input of the IFB estimation algorithms, any deviation from zero on the estimated IFBs should be taken as indications of the errors introduced by the estimation technique. The truthfulness of this assessment work is warranted by the fact that the synthetic data sets resemble, as realistically as possible, the different conditions that may happen in the real ionosphere. The results of this work show that during the high solar activity period the accuracy for the estimated sTEC is approximately of ±10 TECu for the low geomagnetic region and of ±2.2 TECu for the mid-latitude. During low solar activity the accuracy can be assumed to be in the order of ±2 TECu. For the geomagnetic high-disturbed period, the results show that the accuracy is degraded for those stations located over the region where the storm has the strongest impact, but for those stations over regions where the storm has a moderate effect, the accuracy is comparable to that obtained in the quiet period.     

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.     

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.     

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%.     

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。     

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。     

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.     

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.     

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。     

Instantaneous Precise GPS Positioning under Geomagnetic Storm Conditions

Due to the maximum of the solar cycle, ionospheric activity increased considerably last year. At frequent times warning were sent out announcing geomagnetic storms disturbing the ionospheric electron content. In this article the influence of such geomagnetic storms on fast and precise GPS positioning (for surveying applications at midlatitude regions) is studied. And here with “fast” it is aimed at the shortest observation time possible: carrier ambiguity resolution and position estimation using only one single epoch of data. To apply this instantaneous data processing technique successfully to GPS baselines of medium length (up to 50 km), additional ionospheric information is inevitable, not only under geomagnetic storm but also under more quiet conditions. However, in this article it will be shown that under geomagnetic storm conditions, even for rather short baselines (<10 km), for which the ionospheric delays under more quiet conditions could be neglected, one has to account for significant relative ionospheric delays. Therefore an important facet of this contribution is the investigation of how to process baselines of varying length in a more uniform way, making use of a permanent GPS network (if available in the surveying area) and a stochastic modeling technique of the ionospheric delays. ? 2001 John Wiley & Sons, Inc.     

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.     

On the optimal height of ionospheric shell for single-site TEC estimation

The ionospheric shell height has an impact on the estimated differential code bias (DCB) and total electron content (TEC) obtained by global navigation satellite system (GNSS) data, especially for a single site. However, the shell height is generally considered as a fixed value. Based on data from the international GNSS service (IGS), we propose the concept of optimal ionospheric shell height, which minimizes |ΔDCB| when compared to the DCB provided by Center for Orbit Determination in Europe (CODE). Based on the data from five IGS stations at high, middle, and low latitudes during the time 2003–2013, we investigate the variation in the optimal ionospheric shell height and its relation with the solar activity. Results indicate that the relation between the mean of the optimal ionospheric shell height and the latitude is N-shaped. At the three stations at midlatitude, the mean value almost increases linearly with the latitude. The optimal ionospheric shell heights show 11-year and 1-year periods. The influences of the solar activity are related to the means of the optimal ionospheric shell height during the time 2003–2013. The slope of the linear fitting decreases with the mean value. Using the data from 2003 to 2013, we estimate the daily optimal ionospheric shell heights for 2014 by using the Fourier fitting method and then calculate the daily average of ΔDCB of the observed satellites by comparing to CODE results. The statistical results of the daily average in 2014 show that the optimal ionospheric shell height is much better than the fixed one. From the high-latitude station to the low-latitude station, the improvements in the mean value are about 75, 92, 96, 50, and 88% and the root-mean-squares are reduced by about 0.16, 2.09, 2.01, 1.01, and 0.02 TECu, respectively.     

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.     

EEMD-Holt-Winters的电离层TEC预报模型

利用IGS中心提供的全球电离层TEC数据,建立集合经验模态分解与Holt-Winters组合的预报模型。根据地磁活动情况,选取地磁平静时段和地磁活跃时段的低、中纬度TEC序列,分别采用EEMD-Holt-Winters组合模型和单一Holt-Winters模型进行建模预报。实验结果表明,地磁平静期文中模型的相对精度最优可达91.71%,均方根误差最优可达1.54 TECu,地磁活跃期文中模型的相对精度最优可达86.83%,均方根误差最优可达2.18 TECu,预报结果较单一模型有显著提高。     

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.     

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。     

Performance evaluation of different ionospheric models in single-frequency code-based differential GPS positioning

Differential ionospheric slant delays are obtained from a quiet-time, three-dimensional ionospheric electron density model, called the TaiWan Ionosphere Model (TWIM), to be used in code-based differential GPS positioning. The code observations are acquired from nine continuously operating GPS stations around Taiwan whose baseline ranged from 19 to 340 km. Daily 24-hour epoch-per-epoch positioning obtained for 70 most geomagnetic quiet days (2008–2010) for each of the 72 baselines. The performance of TWIM has been compared with the standard operational Klobuchar model (KLB) used by typical single-frequency receivers and the IGS global ionospheric model (GIM). Generally, TWIM performed well in reducing the differential ionospheric delay especially for long baselines and different levels of low solar activity. It has a much better performance compared to the operational KLB model. TWIM also performed similarly with GIM, though GIM has the best performance overall. GIM has the best ionospheric gradient estimates among the three models whose differential ionospheric delay-to-horizontal error ratio is more than 0.25. This is followed closely by TWIM with about 0.20. KLB only has a ratio of <0.10. The similarity of the performance of TWIM and GIM demonstrates the feasibility of TWIM in correcting for differential ionospheric delays in the C/A code pseudorange that is caused by electron density gradients in the ionosphere. It can provide decimeter-to-centimeter level accuracy in differential GPS positioning for single-frequency receivers during geomagnetic quiet conditions across all seasons and different levels of low solar activities.     

Two-step method for the determination of the differential code biases of COMPASS satellites

The differential code bias (DCB) in satellites of the Global Navigation Satellite Systems (GNSS) should be precisely corrected when designing certain applications, such as ionospheric remote sensing, precise point positioning, and time transfer. In the case of COMPASS system, the data used for estimating DCB are currently only available from a very limited number of global monitoring stations. However, the current GPS/GLONASS satellite DCB estimation methods generally require a large amount of geographically well-distributed data for modeling the global ionospheric vertical total electron content (TEC) and are not particularly suitable for current COMPASS use. Moreover, some satellites with unstable DCB (i.e., relatively large scatter) may affect other satellite DCB estimates through the zero-mean reference that is currently imposed on all satellites. In order to overcome the inadequacy of data sources and to reduce the impact of unstable DCB, a new approach, designated IGGDCB, is developed for COMPASS satellite DCB determination. IGG stands for the Institute of Geodesy and Geophysics, which is located in Wuhan, China. In IGGDCB, the ionospheric vertical TEC of each individual station is independently modeled by a generalized triangular series function, and the satellite DCB reference is selected using an iterative DCB elimination process. By comparing GPS satellite DCB estimates calculated by the IGGDCB approach based on only a handful (e.g., seven) of tracking stations against that calculated by the currently existing methods based on hundreds of tracking stations, we are able to demonstrate that the accuracies of the IGGDCB-based DCB estimates perform at the level of about 0.13 and 0.10?ns during periods of high (2001) and low (2009) solar activity, respectively. The iterative method for DCB reference selection is verified by statistical tests that take into account the day-to-day scatter and the duration that the satellites have spent in orbit. The results show that the impact of satellites with unstable DCB can be considerably reduced using the IGGDCB method. It is also confirmed that IGGDCB is not only specifically valid for COMPASS but also for all other GNSS.     

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.