Estimation of GPS instrumental biases from small scale network

With 4 GPS receivers located in the equatorial anomaly region in southeast China, this paper proposes a grid-based algorithm to determine the GPS satellites and receivers biases, and at the same time to derive the total electron content (TEC) with time resolution of 15 min and spatial resolution of 1° by 3.5° in latitude and longitude. By assuming that the TEC is identical at any point within a given grid block and the biases do not vary within a day, the algorithm arranges unknown biases and TECs with slant path TEC from the 4 receivers’ observations into a set of equations. Then the instrumental biases and the TECs are determined by using the least squares fitting technique. The performance of the method is examined by applying it to the GPS receiver chain observations selected from 16 geomagnetically quiet days in four seasons of 2006. It is found that the fitting agrees with the data very well, with goodness of fit ranging from 0.452 TECU to 1.914 TECU. Having a mean of 0.9 ns, the standard deviations for most of the GPS satellite biases are less than 1.0 ns for the 16 days. The GPS receiver biases are more stable than that of the GPS satellites. The standard deviation in the 4 receiver bias is from 0.370 ns to 0.855 ns, with a mean of 0.5 ns. Moreover, the instrumental biases are highly correlated with those derived from CODE and JPL with independent methods. The typical precision of the derived TEC is 5 TECU by a conservative estimation. These results indicate that the proposed algorithm is valid and qualified for small scale GPS network.     

Estimation of QZSS differential code biases using QZSS/GPS combined observations from MGEX

As an important error source in Global Navigation Satellite System (GNSS) positioning and ionospheric modeling, the differential code biases (DCB) need to be estimated accurately, e.g., the regional Quasi-Zenith satellite system (QZSS). In this paper, the DCB of QZSS is estimated by adopting the global ionospheric modeling method based on QZSS/GPS combined observations from Multi-GNSS experiment (MGEX). The performance of QZSS satellite and receiver DCB is analyzed with observations from day of year (DOY) 275–364, 2018. Good agreement between our estimated QZSS satellite DCB and the products from DLR and CAS is obtained. The bias and root mean square (RMS) of DCB are mostly within ±0.3 ns. The day-to-day fluctuation of the DCB time series is less than 0.5 ns with about 96% of the cases for all satellites. However, the receiver DCB is a little less stable than satellite DCB, and their standard deviations (STDs) are within 1.9 ns. The result shows that the stability of the receiver DCBs is not significantly related to the types of receiver or antenna.     

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

Estimation of differential code biases with Jason-2/3 onboard GPS observations

With the continuous deployment of Low Earth Orbit (LEO) satellites, the estimation of differential code biases (DCBs) based on GNSS observations from LEO has gained increasing attention. Previous studies on LEO-based DCB estimation are usually using the spherical symmetry ionosphere assumption (SSIA), in which a uniform electron density is assumed in a thick shell. In this study, we propose an approach (named the SHLEO method) to simultaneously estimate the satellite and LEO onboard receiver DCBs by modeling the distribution of the global plasmaspheric total electron content (PTEC) above the satellite orbit with a spherical harmonic (SH) function. Compared to the commonly used SSIA method, the SHLEO model improves the GPS satellite DCB estimation accuracy by 13.46% and the stability by 22.34%, respectively. Compared to the GPS satellite DCBs estimated based on the Jason-3-only observations, the accuracy and monthly stability of the satellite DCBs can be improved by 14.42% and 26.8% when both Jason-2 and Jason-3 onboard observations are jointly processed. Compared with the Jason-2 solutions, the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations have an improved consistency of better than 18.26% and 9.71% with the products provided by the Center for Orbit Determination in Europe (CODE) and Chinese Academy of Sciences (CAS). Taking the DCB products provided by the German Aerospace Center (DLR) as references, there is no improvement in accuracy of the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations than the Jason-2 solutions alone. A periodic variation is found in the time series of both the Jason-3 and Jason-2 onboard receiver DCB estimates. Preliminary analysis of the PTEC distribution based on the estimated SH coefficients are also presented.     

A method of estimating GPS instrumental biases with a convolution algorithm

This paper presents a method of deriving the instrumental differential code biases (DCBs) of GPS satellites and dual frequency receivers. Considering that the total electron content (TEC) varies smoothly over a small area, one ionospheric pierce point (IPP) and four more nearby IPPs were selected to build an equation with a convolution algorithm. In addition, unknown DCB parameters were arranged into a set of equations with GPS observations in a day unit by assuming that DCBs do not vary within a day. Then, the DCBs of satellites and receivers were determined by solving the equation set with the least-squares fitting technique. The performance of this method is examined by applying it to 361?days in 2014 using the observation data from 1311 GPS Earth Observation Network (GEONET) receivers. The result was crosswise-compared with the DCB estimated by the mesh method and the IONEX products from the Center for Orbit Determination in Europe (CODE). The DCB values derived by this method agree with those of the mesh method and the CODE products, with biases of 0.091?ns and 0.321?ns, respectively. The convolution method's accuracy and stability were quite good and showed improvements over the mesh method.     

一种地基GNSS接收机差分码偏差估算方法

GNSS不同频点间的码伪距作差会引入信号的差分码偏差(DCB),包括GNSS卫星及地面接收机的DCB.本文提出一种地基GNSS接收机差分码偏差参数估算方法,首先由电离层文件参数作线性插值,计算出电离层延迟误差.之后对IGS站观测文件进行加权最小二乘法估计,得到GPS卫星和地面GNSS接收机的L1C频点和L2P频点间码偏...     

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%。     

电离层周日变化对解算GPS硬件延迟稳定性的影响

针对电离层周日变化特征分析了其可能对SCORE方法估算的硬件延迟稳定性的影响. 利用BJFS以及XIAM台站的GPS观测数据, 解算了位于太阳活动高年(2001年)和太阳活动低年(2009年)的卫星硬件延迟并分析了估算的硬件延迟的稳定性. 研究发现, 电离层周日变化对估算的硬件延迟稳定性具有一定影响, 但是利用不同台站所得到的卫星硬件延迟稳定性在昼夜不同时间上的解算结果存在一定差异. 电离层周日变化对利用 BJFS台站数据解算的硬件延迟稳定性日夜差异较为明显, 在太阳活动高年利用XIAM 台站数据解算的硬件延迟日夜稳定性差异不很明显, 由于XIAM台站处于电离层赤道异常峰附近, 夜间电离层变化很大, 因此对比中纬度地区, 电离层周日变化对赤道异常峰附近地区硬件延迟稳定性解算结果的影响相对较小, 但在太阳活动低年, 其影响仍较为显著.      

Multi-GNSS contributions to differential code biases determination and regional ionospheric modeling in China

Due to the limited number and uneven distribution globally of Beidou Satellite System (BDS) stations, the contributions of BDS to global ionosphere modeling is still not significant. In order to give a more realistic evaluation of the ability for BDS in ionosphere monitoring and multi-GNSS contributions to the performance of Differential Code Biases (DCBs) determination and ionosphere modeling, we select 22 stations from Crustal Movement Observation Network of China (CMONOC) to assess the result of regional ionospheric model and DCBs estimates over China where the visible satellites and monitoring stations for BDS are comparable to those of GPS/GLONASS. Note that all the 22 stations can track the dual- and triple-frequency GPS, GLONASS, and BDS observations. In this study, seven solutions, i.e., GPS-only (G), GLONASS-only (R), BDS-only (C), GPS + BDS (GC), GPS + GLONASS (GR), GLONASS + BDS (RC), GPS + GLONASS + BDS (GRC), are used to test the regional ionosphere modeling over the experimental area. Moreover, the performances of them using single-frequency precise point positioning (SF-PPP) method are presented. The experimental results indicate that BDS has the same ionospheric monitoring capability as GPS and GLONASS. Meanwhile, multi-GNSS observations can significantly improve the accuracy of the regional ionospheric models compared with that of GPS-only or GLONASS-only or BDS-only, especially over the edge of the tested region which the accuracy of the model is improved by reducing the RMS of the maximum differences from 5–15 to 2–3 TECu. For satellite DCBs estimates of different systems, the accuracy of them can be improved significantly after combining different system observations, which is improved by reducing the STD of GPS satellite DCB from 0.243 to 0.213, 0.172, and 0.165 ns after adding R, C, and RC observations respectively, with an increment of about 12.3%, 29.4%, and 32.2%. The STD of GLONASS satellite DCB improved from 0.353 to 0.304, 0.271, and 0.243 ns after adding G, C, and GC observations, respectively. The STD of BDS satellite DCB reduced from 0.265 to 0.237, 0.237 and 0.229 ns with the addition of G, R and GR systems respectively, and increased by 10.6%, 10.4%, and 13.6%. From the experimental positioning result, it can be seen that the regional ionospheric models with multi-GNSS observations are better than that with a single satellite system model.     

基于硬件信号模拟器的电离层TEC监测仪 差分码偏差长期变化

利用硬件信号模拟器可以标定电离层TEC监测仪的差分码偏差.通过对相同接收机时隔近41.5月进行的两次差分码偏差标定实验,以GPS系统为例分析了硬件标定法得到的差分码偏差随时间的长期变化情况.结果表明:接收机差分码偏差均值从第一次实验的16.122ns增加至第二次实验的16.749ns,在约41.5月的时间内增加约0.627ns,月增量为0.0151ns,增加比较缓慢;第二次实验的差分码偏差标准差也有所增加,但增量也不大（均值分别为0.05ns和0.07ns）.此外,两次标定实验的TEC测量精度（均方根误差）均达到约0.3TECU,对应的差分码偏差误差约0.1ns,这说明该接收机差分码偏差变化的一致性较好.若不加以再次标定,第二次实验时TEC测量误差将增加至约1.8TECU,月增量约为0.0434TECU.      

基于双频GPS观测的电离层TEC与硬件延迟反演方法

利用全球定位系统（Global Positioning System,GPS）的双频观测数据反演得到电离层的总电子含量（Total Electron Content,TEC）,使得广域甚至全球范围高时空分辨率的电离层观测研究成为可能,但由于GPS卫星和接收机对信号的硬件延迟可导致TEC测量系统偏差,因此,需要探索反演TEC并估测GPS卫星与接收机硬件延迟的有效算法.本文根据电离层电波传播理论,阐述了基于双频GPS观测提取电离层TEC的方法,给出TEC与硬件延迟的基本关系.综合研究了TEC与硬件延迟的反演方法,进行分析与归纳分类,在此基础上提出了有待深入研究的问题.      

单接收机GNSS数据组合硬件延迟的联合求解方法

利用GNSS观测数据解算TEC的最大误差源是硬件延迟,包括卫星硬件延迟和接收机硬件延迟.在单接收机情况下,由于数据稀疏以及接收到的卫星信号时间不对齐等特点,已有的解算硬件延迟方法的求解结果往往不理想.在应用局域模式拟合方法和SCORE方法求解单接收机数据基础上,利用局域模型拟合法在电离层平静期拟合较准确的优点,提出一种联合改进方法,同时改正了SCORE方法解算过程中约束过强的缺点.通过利用GPStation-6接收机的GPS和BDS实际观测数据进行解算分析,验证了所提方法的有效性与准确性.      

GPS derived TEC and foF2 variability at an equatorial station and the performance of IRI-model

The ionosphere induces a time delay in transionospheric radio signals such as the Global Positioning System (GPS) signal. The Total Electron Content (TEC) is a key parameter in the mitigation of ionospheric effects on transionospheric signals. The delay in GPS signal induced by the ionosphere is proportional to TEC along the path from the GPS satellite to a receiver. The diurnal monthly and seasonal variations of ionospheric electron content were studied during the year 2010, a year of extreme solar minimum (F10.7 = 81 solar flux unit), with data from the GPS receiver and the Digisonde Portable Sounder (DPS) collocated at Ilorin (Geog. Lat. 8.50°N, Long. 4.50°E, dip −7.9°). The diurnal monthly variation shows steady increases in TEC and F2-layer critical frequency (foF2) from pre-dawn minimum to afternoon maximum and then decreases after sunset. TEC show significant seasonal variation during the daytime between 0900 and 1900 UT (LT = UT + 1 h) with a maximum during the March equinox (about 35 TECU) and minimum during the June solstice (about 24 TECU). The GPS-TEC and foF2 values reveal a weak seasonal anomaly and equinoctial asymmetry during the daytime. The variations observed find their explanations in the amount of solar radiation and neutral gas composition. The measured TEC and foF2 values were compared with last two versions of the International Reference Ionosphere (IRI-2007 and IRI-2012) model predictions using the NeQuick and CCIR (International Radio Consultative Committee) options respectively in the model. In general, the two models give foF2 close to the experimental values, whereas significant discrepancies are found in the predictions of TEC from the models especially during the daytime. The error in height dependent thickness parameter, daytime underestimation of equatorial drift and contributions of electrons from altitudes above 2000 km have been suggested as the possible causes.     

A real-time ionospheric model based on GNSS Precise Point Positioning

This paper proposes a method of real-time monitoring and modeling the ionospheric Total Electron Content (TEC) by Precise Point Positioning (PPP). Firstly, the ionospheric TEC and receiver’s Differential Code Biases (DCB) are estimated with the undifferenced raw observation in real-time, then the ionospheric TEC model is established based on the Single Layer Model (SLM) assumption and the recovered ionospheric TEC. In this study, phase observations with high precision are directly used instead of phase smoothed code observations. In addition, the DCB estimation is separated from the establishment of the ionospheric model which will limit the impacts of the SLM assumption impacts. The ionospheric model is established at every epoch for real time application. The method is validated with three different GNSS networks on a local, regional, and global basis. The results show that the method is feasible and effective, the real-time ionosphere and DCB results are very consistent with the IGS final products, with a bias of 1–2 TECU and 0.4 ns respectively.     

A morphological study of GPS-TEC data at Agra and their comparison with the IRI model

The temporal and seasonal variations of Total Electron Content (TEC) are studied at Agra (Geographic Lat. 27.17°N, Long. 78.89°E, Dip: 41.4°), India, which is in the equatorial anomaly region, for a period of 12 months from 01 January to 31 December, 2007 using a Global Positioning System (GPS) receiver. The mean TEC values show a minimum at 0500 h LT (LT = UT + 5.5 h) and a peak value at about 1400 h LT. The lowest TEC values are observed in winter whereas largest values are observed in equinox and summer. Anomalous variations are found during the period of magnetic disturbances. These results are compared with the TEC derived from IRI-2007 using three different options of topside electron density, NeQuick, IRI01-corr, and IRI-2001. A good agreement is found between the TEC obtained at Agra and those derived from IRI models.     

Calibration errors in determining slant Total Electron Content (TEC) from multi-GNSS data

The global navigation satellite system (GNSS) is presently a powerful tool for sensing the Earth's ionosphere. For this purpose, the ionospheric measurements (IMs), which are by definition slant total electron content biased by satellite and receiver differential code biases (DCBs), need to be first extracted from GNSS data and then used as inputs for further ionospheric representations such as tomography. By using the customary phase-to-code leveling procedure, this research comparatively evaluates the calibration errors on experimental IMs obtained from three GNSS, namely the US Global Positioning System (GPS), the Chinese BeiDou Navigation Satellite System (BDS), and the European Galileo. On the basis of ten days of dual-frequency, triple-GNSS observations collected from eight co-located ground receivers that independently form short-baselines and zero-baselines, the IMs are determined for each receiver for all tracked satellites and then for each satellite differenced for each baseline to evaluate their calibration errors. As first derived from the short-baseline analysis, the effects of calibration errors on IMs range, in total electron content units, from 1.58 to 2.16, 0.70 to 1.87, and 1.13 to 1.56 for GPS, Galileo, and BDS, respectively. Additionally, for short-baseline experiment, it is shown that the code multipath effect accounts for their main budget. Sidereal periodicity is found in single-differenced (SD) IMs for GPS and BDS geostationary satellites, and the correlation of SD IMs over two consecutive days achieves the maximum value when the time tag is around 4?min. Moreover, as byproducts of zero-baseline analysis, daily between-receiver DCBs for GPS are subject to more significant intra-day variations than those for BDS and Galileo.     

Low-latitude ionospheric scintillations and total electron content obtained with the CITRIS instrument on STPSat1 using radio transmissions from DORIS ground beacons

The primary objective of the Scintillation and Tomography Receiver in Space (CITRIS) is to detect ionospheric irregularities from space at low latitude. For this purpose, the satellite receiver uses the UHF and S-Band transmissions of the ground network of Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) beacons. CITRIS, developed at the Naval Research Laboratory, differs from the normal DORIS receiver by being able to capture and store the complex amplitude of the 401.25 and 2036.25 MHz transmissions at 200 Hz sample rate. Ground processing of the CITRIS data yields total electron content (TEC) and both phase and amplitude scintillations. With CITRIS flying on the US Space Test Program (STP) satellite STPSat1, 2 years of data were collected and processed to determine the fluctuations in ionospheric TEC and radio scintillations associated with equatorial irregularities. CITRIS flights over DORIS transmitters yield direct measurements of the horizontal plasma density fluctuations associated with equatorial plasma bubbles. Future flights of CITRIS can provide valuable complements to other satellite instruments such as GPS occultation receivers used to estimate vertical electron density profiles in the ionosphere.     

Night-time total electron content enhancements at equatorial anomaly region in China

This paper presents small scale (duration ?1 h, ΔTEC ? 1TECU) night-time total electron content (TEC) enhancements observed at the equatorial anomaly region in China, for the first time. The data is from a GPS receiver chain established in 2005 by Institute of Center for Space Science and Applied Research, Chinese Academy of Sciences and a GPS receiver of International GPS Service (IGS), located between Fuzhou (26.1°N, 119.3°E) and Nanning (22.8°N, 108.3°E). Two other GPS observations of IGS taken at higher latitude were also used to investigate the localization of such phenomenon. The characteristics of the night-time TEC enhancement are examined with two case studies. The TEC increases about 1–3TECU, intermittently. While the night-time TEC enhancement mainly occurs at the equatorial anomaly region, it can be observed at middle latitude as well. The spatial size of the enhancement region is less than 5° in longitude. The primary statistical study shows that the TEC enhancement is more often observed in spring and autumn, but rarely in summer. It has no dependence on geomagnetic activity. The enhancement can occur both before and after midnight.     

Towards a GPS-based TEC prediction model for Southern Africa with feed forward networks

In this paper, first results from a national Global Positioning System (GPS) based total electron content (TEC) prediction model over South Africa are presented. Data for 10 GPS receiver stations distributed through out the country were used to train a feed forward neural network (NN) over an interval of at most five years. In the NN training, validating and testing processes, five factors which are well known to influence TEC variability namely diurnal variation, seasonal variation, magnetic activity, solar activity and the geographic position of the GPS receivers were included in the NN model. The database consisted of 1-min data and therefore the NN model developed can be used to forecast TEC values 1 min in advance. Results from the NN national model (NM) were compared with hourly TEC values generated by the earlier developed NN single station models (SSMs) at Sutherland (32.38°S, 20.81°E) and Springbok (29.67°S, 17.88°E), to predict TEC variations over the Cape Town (33.95°S, 18.47°E) and Upington (28.41°S, 21.26°E) stations, respectively, during equinoxes and solstices. This revealed that, on average, the NM led to an improvement in TEC prediction accuracy compared to the SSMs for the considered testing periods.     

The effect of total solar eclipse of October 3, 2005, on the total electron content over Europe

GPS observations from EUREF permanent GPS network were used to observe the response of TEC (Total Electron Content) to the total solar eclipse on October 3, 2005, under quiet geomagnetic conditions of the daytime ionosphere. The effect of the eclipse was detected in diurnal variations and more distinctly in the variations of TEC along individual satellite passes. The trough-like variations with a gradual decrease and followed by an increase of TEC at the time of the eclipse were observed over a large region. The depression of TEC amounted to 3–4 TECU. The maximum depression was observed over all stations located at the maximum path of the solar eclipse. The delay of a minimum level of TEC with respect to the maximum phase of the eclipse was about 20–30 min.