Center For Orbit Determination In Europe Research Articles

One‐Day Forecasting of Global TEC Using a Novel Deep Learning Model

AbstractIn this study, we make a global total electron content (TEC) forecasting using a novel deep learning method, which is based on conditional generative adversarial networks. For training, we use the International GNSS Service (IGS) TEC maps from 2003 to 2012 with 2‐h time cadence. Our model has two input images (IGS TEC map and 1‐day difference map between the present day and the previous day) and one output image (1‐day future map). The model is tested with two data sets: solar maximum period (2013–2014) and solar minimum period (2017–2018). Then, we compare the results of our model with those of 1‐day Center for Orbit Determination in Europe (CODE) prediction model. Our major results can be summarized as follows. First, we successfully apply our model to the forecast of global TEC maps. Second, our model well predicts daily TEC maps with 1 day in advance using only previous TEC maps. The averaged root mean square error, bias, and standard deviation between AI‐generated and IGS TEC maps are 2.74 TECU, −0.32 TECU, and 2.59 TECU, respectively. Third, our model generates some peak structures around equatorial regions. Fourth, our model shows better performance than 1‐day CODE prediction model during both solar maximum and minimum periods. Fifth, another model with additional input data Kp index gives a slight improvement of the results. Our study shows that our deep learning model based on an image translation method will be effective for forecasting of future images using previous data.

Performance evaluation of GIMs released by different IGS ionosphere associate analysis centers in ionospheric constrained single-frequency precise point positioning

Single-frequency precise point positioning (PPP) is widely used with the advantage of cost-efficient, while its further development and application are limited by the difficulty of ionospheric delay correction and the long-time convergence, especially for real-time positioning. And the development of high-accuracy ionospheric models plays an important role for the correction of ionospheric delay in single-frequency PPP. In this paper, the final and rapid global ionospheric map (GIM) products released by Chinese Academy of Science (CAS), Center for Orbit Determination in Europe (CODE), European Space Agency (ESA), Jet Propulsion Laboratory (JPL), Universitat Politècnica de Catalunya (UPC), Wuhan University (WHU) and International GNSS Service (IGS) were used as external constraints in static, simulation kinematic and kinematic single-frequency PPP respectively. The performance and practicality of each product were analyzed by using IGS station observation data (September 2017 and January 2018, with different ionospheric activity levels) and a kinematic experiment. The results indicate that GIM products may improve convergence time in most areas of middle and high latitudes of the globe. However, the improvement of convergence time of some regions in low latitudes or near the equator with dense and uniform distributed IGS stations show even better performance than the regions in middle and high latitudes. Comparing with standard PPP (S-PPP), the convergence time of static PPP is reduced about 14–42% and 13–29% with GIM final and rapid products respectively. In simulation kinematic PPP, the convergence time improves 10–43% and 12–25% for final and rapid products respectively. In the kinematic positioning, the addition of external ionospheric constraints may speed up the convergence in the early stage of positioning and improve the accuracy to a certain extent. Among all GIM products, the final products show better performance than that of the rapid products obviously. The GIM products from CAS and CODE and UQRG from UPC express the best performance are recommended to process ionospheric delay in the high-accuracy positioning.

Denoising ionospheric observables based on multipath error modelling with Tikhonov regularization

Multipath errors, as one of the manifest unmodelled error types introduced by code measurements, are absorbed in ionospheric observables, which results in ionospheric pollution. In this work, in order to cancel out random noise by an adjustment algorithm, the modelling of multipath errors derived from code measurement residuals in undifferentiated and uncombined precise point position (PPP) mode is realized by solving a regularization problem, in which Tikhonov regularization (i.e. the first order difference) is taken into account. Furthermore, the Thomas update algorithm is employed to find the solution and a bootstrap method is used to determine the optimal regularization parameter. After the multipath error model was constructed, it was used to extract the ionospheric observables, thereby enabling the correction of the code measurements. In this research, three ionosphere-retrieval schemes were designed, namely the the alignment of the carrier phase to the code (1) before and (2) after the multipath errors were corrected (CCBM and CCAM), and (3) a PPP solution (PPPS). Based on colocation experiments, the effects of removing errors arising from the multipath effect on the code were comparatively assessed. Large differences were found between the three schemes when used in a short-baseline experimental setting, but only small differences were found with a zero-baseline setup. In the short-baseline experiment, CCAM was more reliable than CCBM, with an improvement in accuracy of about 50%, and reached close agreement with PPPS. In addition, 14 continuously operating reference stations in Hong Kong were selected for ionosphere modelling with differential code bias (DCB) estimations. Similar results were seen, as follows: (1) compared with CCBM, CCAM and PPPS had better modelling accuracies, with an improvement of 60%; (2) CCAM and PPPS had better performance at five fitting stations with respect to CCBM, which resulted in improvements in the accuracies ranging from 60% to 80%; (3) taking five-day-average values of the satellite DCBs, the difference between Center for OrbitDetermination in Europe (CODE) and CCAM was around 0.5 ns, which is consistent with the difference between CODE and PPPS, but about a 2 ns difference was verified between CODE and CCBM.

Real-time GNSS precise point positioning using improved robust adaptive Kalman filter

Multi-constellation GNSS precise point positioning (PPP) typically uses the extended Kalman filter (EKF) for kinematic applications. Unfortunately, the obtained positioning accuracy in this approach is prone to errors caused by measurement outliers and the system’s dynamic model. An adaptive robust Kalman filter (RKF) was recently developed to mitigate these errors. However, RKF uses empirical values as detection thresholds for the outliers, which requires the measurements to be from the same constellation and of equal precision to obtain an optimal PPP solution. The classification robust adaptive Kalman filter (CAKF) has subsequently been developed to deal with measurements of different precisions, namely pseudorange and carrier-phase measurements. This paper proposes a real-time GPS/Galileo PPP system, which employs a modified version of CAKF called the Improved Robust adaptive Kalman Filter (IRKF). The positioning performance of GPS/Galileo PPP through the IRKF is initially verified in comparison with those obtained through the EKF, RKF, and CAKF using the Centre for Orbit Determination in Europe (CODE) final orbit and clock products in both of static and kinematic modes. The real-time GPS/Galileo PPP solution through the IRKF is then assessed in comparison with its near-real-time counterpart. The results indicate that when the IRKF approach is utilised, the positioning accuracy is significantly improved and the convergence behaviour is enhanced compared with results from EKF, conventional RKF, and CAKF. In the real-time mode, centimeter-level horizontal positioning accuracy is achieved under an open sky environment, while decimeter-level horizontal positioning accuracy is achieved under a challenging environment. On the other hand, decimeter-level accuracy is achieved for the vertical positioning component under all environmental scenarios. Moreover, the positioning accuracy of the real-time solution is comparable to the near-real-time counterpart.

A Least Squares Solution to Regionalize VTEC Estimates for Positioning Applications

A new approach is presented to improve the spatial and temporal resolution of the Vertical Total Electron Content (VTEC) estimates for regional positioning applications. The proposed technique utilises a priori information from the Global Ionosphere Maps (GIMs) of the Center for Orbit Determination in Europe (CODE), provided in terms of Spherical Harmonic (SH) coefficients of up to degree and order 15. Then, it updates the VTEC estimates using a new set of base-functions (with better resolution than SHs) while using the measurements of a regional GNSS network. To achieve the highest accuracy possible, our implementation is based on a transformation of the GIM/CODE VTECs to their equivalent coefficients in terms of (spherical) Slepian functions. These functions are band-limited and reflect the majority of signal energy inside an arbitrarily defined region, yet their orthogonal property is remained. Then, new dual-frequency GNSS measurements are introduced to a Least Squares (LS) updating step that modifies the Slepian VTEC coefficients within the region of interest. Numerical application of this study is demonstrated using a synthetic example and ground-based GPS data in South America. The results are also validated against the VTEC estimations derived from independent GPS stations (that are not used in the modelling), and the VTEC products of international centres. Our results indicate that, by using 62 GPS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the new VTEC estimates in a Precise Point Positioning (PPP) experiment improved the positioning accuracy compared to the usage of GIM/CODE and Klobuchar models. The reductions in the root mean squared of errors were ∼23% and 25% for a day with moderate solar activity while 26% and ∼35% for a day with high solar activity, respectively.

Epoch-by-epoch estimation and analysis of BeiDou Navigation Satellite System (BDS) receiver differential code biases with the additional BDS-3 observations

Abstract. The differential code bias (DCB) of the Global Navigation Satellite System (GNSS) is an important error source in ionospheric modeling, which was generally estimated as constants every day. However, the receiver DCB may be changing due to the varying spatial environments and temperatures. In this paper, a method based on the global ionospheric map (GIM) of the Center for Orbit Determination in Europe (CODE) is presented to estimate the BeiDou Navigation Satellite System (BDS) receiver DCB with epoch-by-epoch estimates. The BDS receiver DCBs are analyzed from 30 d of Multi-GNSS Experiment observations. The comparison of estimated receiver DCB of BDS with the DCB provided by the German Aerospace Center (DLR) and the Chinese Academy of Sciences (CAS) shows a good agreement. The root-mean-square (rms) values of receiver DCB are 0.43 and 0.80 ns with respect to the DLR and CAS estimates, respectively. In terms of the intraday variability of receiver DCB, most of the receiver DCBs show relative stability within 1 d with the intraday standard deviation (SD) of less than 1 ns. However, larger fluctuations with more than 2 ns of intraday receiver DCB are found. Besides, the intraday stability of receiver DCB calculated by the third-generation BDS (BDS-3) and the second-generation BDS (BDS-2) observations is compared. The result shows that the intraday stability of BDS-3 receiver DCB is better than that of BDS-2 receiver DCB.

Reply to Comment on Choi et al. Correlation between Ionospheric TEC and the DCB Stability of GNSS Receivers from 2014 to 2016. Remote Sens. 2019, 11, 2657

Choi et al. (2019) suggested that ionospheric total electron content (TEC) and receiver differential code bias (rDCB) stability have a strong correlation during a period of two years from 2014 to 2016. This article is a response to Zhong et al. (2020), who pointed out that the long-term variations of the GPS DCBs are mainly attributed to the satellite replacement rather than the ionospheric variability. In this issue, we investigated the center for orbit determination in Europe (CODE) Global Ionosphere Maps (GIM) products from 2000 to 2020. In this study, changes in TEC and receiver DCB (rDCB) root mean squares (RMS) at Bogota (BOGT) station still have a clear correlation. In addition, there was a moderate correlation between satellite DCB RMS and rDCB RMS. As a result, we suggest that rDCB can be affected simultaneously by GPS sDCB as well as ionospheric activity.

Investigating the GALILEO and BeiDou orbit accuracy derived from rapid products

In recent years, the advances of the new Global Navigation Satellite System (GNSS) constellations including, Galileo and BeiDou (BDS), have undergone dramatic changes. Some analysis centers (ACs) produce precise orbit and clock products of Galileo and BeiDou constellations. Currently, three types of Galileo and BeiDou satellite orbit and clock products are available – namely, precise, rapid and ultra-rapid products –. Ultra-rapid and rapid products are generally used for time-constrained applications. Precise orbit determination (POD) of Galileo and BeiDou is much challenging compared with GPS and GLONASS constellations due to the officially undetermined receiver phase center offset (PCO), variations (PCV) of Galileo and BeiDou constellations and, also some other not well-defined factors such as yaw-attitude models and solar radiation pressure. In this study, GALILEO orbit accuracy is investigated using rapid products produced by Center for Orbit Determination in Europe (CODE) GeoForschungsZentrum (GFZ) and Wuhan University (WUHAN), while GFZ and WUHAN rapid products are used for BeiDou constellation only. One month (January) of data in 2020 is used to compute errors of radial, along-track, and cross-track components of Galileo and BeiDou orbit derived by rapid products compared with the CODE final Multi-GNSS Experiment (MGEX) product which is assumed as the reference product. The results show that no significant differences between the products are found for Galileo orbit. For BeiDou orbit, WUHAN rapid product produced the smaller root mean square errors (RMSEs) of orbit components compared with the GFZ rapid product.

Dynamic GPS-based LEO orbit determination with 1 cm precision using the Bernese GNSS Software

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20% improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

A Refinement Method of Real-Time Ionospheric Model for China

Ionospheric delay is a crucial error source and determines the source of single-frequency precise point positioning (SF-PPP) accuracy. To meet the demands of real-time SF-PPP (RT-SF-PPP), several international global navigation satellite systems (GNSS) service (IGS) analysis centers provide real-time global ionospheric vertical total electron content (VTEC) products. However, the accuracy distribution of VTEC products is nonuniform. Proposing a refinement method is a convenient means to obtain a more accuracy and consistent VTEC product. In this study, we proposed a refinement method of a real-time ionospheric VTEC model for China and carried out experiments to validate the model effectiveness. First, based on the refinement method and the Centre National d’Études Spatiales (CNES) VTEC products, three refined real-time global ionospheric models (RRTGIMs) with one, three, and six stations in China were built via GNSS observations. Second, the slant total electron content (STEC) and Jason-3 VTEC were used as references to evaluate VTEC accuracy. Third, RT-SF-PPP was used to evaluate the accuracy in the positioning domain. Results showed that even if using only one station to refine the global ionospheric model, the refined model achieved a better performance than CNES and the Center for Orbit Determination in Europe (CODE). The refinement model with six stations was found to be the best of the three refinement models.

GNSS-Based Non-Negative Absolute Ionosphere Total Electron Content, its Spatial Gradients, Time Derivatives and Differential Code Biases: Bounded-Variable Least-Squares and Taylor Series.

Global navigation satellite systems (GNSS) allow estimating total electron content (TEC). However, it is still a problem to calculate absolute ionosphere parameters from GNSS data: negative TEC values could appear, and most of existing algorithms does not enable to estimate TEC spatial gradients and TEC time derivatives. We developed an algorithm to recover the absolute non-negative vertical and slant TEC, its derivatives and its gradients, as well as the GNSS equipment differential code biases (DCBs) by using the Taylor series expansion and bounded-variable least-squares. We termed this algorithm TuRBOTEC. Bounded-variable least-squares fitting ensures non-negative values of both slant TEC and vertical TEC. The second order Taylor series expansion could provide a relevant TEC spatial gradients and TEC time derivatives. The technique validation was performed by using independent experimental data over 2014 and the IRI-2012 and IRI-plas models. As a TEC source we used Madrigal maps, CODE (the Center for Orbit Determination in Europe) global ionosphere maps (GIM), the IONOLAB software, and the SEEMALA-TEC software developed by Dr. Seemala. For the Asian mid-latitudes TuRBOTEC results agree with the GIM and IONOLAB data (root-mean-square was < 3 TECU), but they disagree with the SEEMALA-TEC and Madrigal data (root-mean-square was >10 TECU). About 9% of vertical TECs from the TuRBOTEC estimates exceed (by more than 1 TECU) those from the same algorithm but without constraints. The analysis of TEC spatial gradients showed that as far as 10–15° on latitude, TEC estimation error exceeds 10 TECU. Longitudinal gradients produce smaller error for the same distance. Experimental GLObal Navigation Satellite System (GLONASS) DCB from TuRBOTEC and CODE peaked 15 TECU difference, while GPS DCB agrees. Slant TEC series indicate that the TuRBOTEC data for GLONASS are physically more plausible.

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.

Improving regional ionospheric TEC mapping based on RBF interpolation

Radial basis function (RBF) interpolation with multi-quadric is developed to perform ionospheric total electron content (TEC) mapping for the Chinese region between 15°N ~ 40°N and 100°E ~ 125°E. TEC measurements from the Centre for Orbit Determination in Europe (CODE) covering the solar maximum year 2011 are used to investigate the performance of the proposed RBF interpolation method. The differences between the RBF interpolated TEC and the CODE TEC are within 0.5 TECU and the root mean square error (RMSE) is very small when 49 data points are used. The maximum difference is ~5 TECU and the error is less than 1 TECU with 25 samples. Our study suggests that a random distribution of measurement points gives smaller RMSEs than a homogenous distribution when the number of sample points is low. The study indicates that RBF interpolation offers a powerful and reliable tool for ionospheric TEC mapping.

Analysis of Ionospheric TEC Anomalies during Super Typhoons Megi and Meranti

Sun, J.L.; Zhang, Z.Y.; Liu, X.; Zhang, C., Mou, Z.H., 2020. Analysis of ionospheric TEC anomalies during super typhoons Megi and Meranti. In: Bai, X. and Zhou, H. (eds.), Advances in Water Resources, Environmental Protection, and Sustainable Development. Journal of Coastal Research, Special Issue No. 115, pp. 692-695. Coconut Creek (Florida), ISSN 0749-0208.In this paper, we detected and analyzed ionospheric anomalies during the 2016 super typhoons Megi and Meranti using the sliding interquartile range method applied to the ionospheric total electron content (TEC) grid data from the Global Ionospheric Model (GIM) provided by the Center for Orbit Determination in Europe (CODE). We found that ionospheric TEC anomalies occurred 2 days before the origination of super typhoon Megi. The anomalies occurred from 02:00 to 12:00 local time over a period of 10 h, with a maximum outlier of 12 TEC units over the typhoon center. Anomalies occurred in the ionosphere over both the area near the typhoon center and the corresponding equatorial magnetic conjugate region. The anomalies in both areas showed approximately the same trends. It is very likely that the disturbances from the ionospheric anomalies over the typhoon center were one of the precursors for the typhoon event. Similar ionospheric anomalies also occurred in the ionosphere 2 days before the formation and development of super typhoon Meranti. The global ionospheric TEC distribution was even more complex on that day. The existence of multiple peaks and valleys in the maximum outlier near the typhoon center was possibly associated with the position of the typhoon center and the GIM grid points or the wind speeds over the typhoon center.

Validation of the EGSIEM-REPRO GNSS Orbits and Satellite Clock Corrections

In the framework of the European Gravity Service for Improved Emergency Management (EGSIEM) project, consistent sets of state-of-the-art reprocessed Global Navigation Satellite System (GNSS) orbits and satellite clock corrections have been generated. The reprocessing campaign includes data starting in 1994 and follows the Center for Orbit Determination in Europe (CODE) processing strategy, in particular exploiting the extended version of the empirical CODE Orbit Model (ECOM). Satellite orbits are provided for Global Positioning System (GPS) satellites since 1994 and for Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) since 2002. In addition, a consistent set of GPS satellite clock corrections with 30 s sampling has been generated from 2000 and with 5 s sampling from 2003 onwards. For the first time in a reprocessing scheme, GLONASS satellite clock corrections with 30 s sampling from 2008 and 5 s from 2010 onwards were also generated. The benefit with respect to earlier reprocessing series is demonstrated in terms of polar motion coordinates. GNSS satellite clock corrections are validated in terms of completeness, Allan deviation, and precise point positioning (PPP) using terrestrial stations. In addition, the products herein were validated with Gravity Recovery and Climate Experiment (GRACE) precise orbit determination (POD) and Satellite Laser Ranging (SLR). The dataset is publicly available.

Adopting the empirical CODE orbit model to Galileo satellites

In 2012 the Center for Orbit Determination in Europe (CODE) joined the Multi-GNSS-EXtension project (MGEX) of the International GNSS Service (IGS). Since the end of 2013 the CODE MGEX contributions were based on combined solutions of five already established and emerging GNSS: GPS, GLONASS, Galileo, BeiDou and QZSS. This undertaking was made possible thanks to the continuous development of new models and approaches and their introduction in our processing schemes in order to ensure the delivery of products of the highest quality.The European Galileo system with a total number of active satellites reaching the level of a nominal constellation is currently complete. Because of their relatively high area-to-mass ratio the Galileo spacecraft are more sensitive to non-gravitational forces than other GNSS satellites. The introduction of the extended empirical CODE orbit model (ECOM2) to the CODE MGEX solutions in early 2015 resulted in a significant improvement of the Galileo products. The use of the Galileo satellites metadata, which were made publicly available in the course of 2016 and 2017, has further enhanced the quality of the produced solutions. However, they still show significant degradations during eclipse seasons in particular for long-arc solutions (e.g., over three days), which are similarly observed in solutions of other IGS MGEX analysis centers to different extents. In particular this is reflected in elevated orbit misclosures, deterioration of the estimated satellite clock corrections and excessive satellite laser ranging (SLR) residuals during these periods. Since the ECOM2 parameters are designed to absorb the effect of solar radiation pressure, they are switched off during eclipses. Hence, there is no empirical force parameter left that can absorb any unmodelled perturbations (e.g., due to thermal radiation (TR)) during an eclipse period.In this study we take advantage of the satellites’ metadata to address the Galileo TR-induced accelerations and, therefore, to advance our orbit model further. By adjusting existing and introducing additional empirical parameters, as well as adopting a priori accelerations to account for unmodelled perturbations we achieve a significant improvement of our solutions. In particular, the use of a once-per-revolution sine term in the ECOM E3 direction (satellite-Sun), activation of the constant term in the ECOM E2 direction (along the solar panels) during the Earth’s shadow transitions as well as the use of a priori acceleration in the body-fixed +X direction substantially improve our solutions. The introduced modifications to the orbit model allow for an efficient adjustment of satellite velocity along the orbit that is necessary due to the apparent presence of unmodelled thermal radiation. The refinements lead to a substantial reduction of orbit misclosures and improvement of the radial orbital component accuracy during eclipse seasons up to 14% w.r.t. the solutions using ECOM2.

Higher order ionospheric delay and derivation of regional total electron content over Ethiopian global positioning system stations

The Global Positioning System (GPS) is a space-based radio positioning system which is capable of providing continuous position, velocity and time information to users anywhere on, or near, the surface of the Earth. The positional accuracy of GPS is limited by several sources of error, such as satellite and receiver clock offsets, signal propagation delays (due to the ionosphere and troposphere), multipath, receiver measurement noise, and instrument bias. The ionospheric delay is the predominant error source. The main objective of this work was to estimate the regional vertical Total Electron Content (vTEC) densities, using a linear combination of L1 and L2 carrier phase for higher order time delays at different thin-shell layers of the ionosphere (i.e. 60 km, 90 km, 150 km, 200 km and 450 km) over GPS stations in Ethiopia. Due to the high equatorial ionization anomaly and irregularity of the electron density distribution, we selected four GPS stations across the country. We studied longitudinal, latitudinal, and altitudinal variations in the ionosphere using GPS observables extracted by precise geodetic GAMIT-GLOBK software package. We obtained data from the 2013 to 2015 period for all stations. For daily data processing in GAMIT, we switched the International Geomagnetic Reference Field 2012 (IGRF-12) model (which consists of spherical harmonic coefficients) on and off, representing the Earth’s main field and its secular variation and ionospheric electron content along the signal path (available from the Centre for Orbit Determination in Europe (CODE)).Our results confirmed that there is latitudinal, longitudinal and altitudinal variation in the ionosphere. The density of total electron content and GPS positional error due to higher-order time delays have a positive correlation (more than 95%). The positional error, due to the higher order ionospheric delay, exceeds 4 mm for all GPS stations and reached up to 8 mm. Finally, we observed that the time delay due to the higher-order ionospheric effect in the L2 signal is twice that in the L1.We conclude that the GPS signal is affected by the higher order ionospheric delay by up to several centimetres due to its electron content and the Earth’s magnetic field.

Seismic-ionospheric effects prior to four earthquakes in Indonesia detected by the China seismo-electromagnetic satellite

In this study, we investigated the characteristics of pre-earthquake ionospheric effects related to four successive shallow-focus earthquakes (M6.4 on July 28, 2018, M6.8, 5.9, 6.9 on August 05, 09 and 19, 2018) in Indonesia by the China Seismo-Electromagnetic Satellite (CSES). By adopting the moving median method (MMM), the ionospheric electron density (Ne) detected by the Langmuir probe (LAP) onboard CSES presented remarkable enhancements along the orbits #2660-0 on July 27, #2721-0 and #2728-1 on July 31, #2827-0 and #2735-1 on August 7, #2934-0 on August 14, respectively, which were just 1, 5, 2 and 5 days before the four earthquakes. Moreover, the disturbances mainly appeared in the north and north-east within the distance of 2000 km from each epicenter. By comparing the disturbed orbits with their corresponding four nearest and four revisiting orbits as well as the predicted values from the International Reference Ionosphere 2016 model (IRI-2016), the results powerfully illustrated that CSES observed the ionospheric precursors preceding the four Indonesian earthquakes. To make the space-borne results more convincing, we further studied the grid total electron content (TEC) data from the Center for Orbit Determination in Europe (CODE), which exhibited similar anomalies in both the temporal and spatial distributions. In the end, the superposed epoch analyses (SEA) method was conducted on 35 M ⩾ 5.8, depth⩽50 km earthquakes in Indonesia during 2007–2017 by using CODE TEC. The statistical results demonstrated that there were significant positive anomalies 1–7 days before earthquakes within 2000 km from the epicenters in this region. The positive plasma perturbations detected by CSES were highly suggested as the seismic-ionospheric effects before earthquakes.

Empirical orthogonal function analysis and modeling of global ionospheric spherical harmonic coefficients

We developed a global empirical model for computing spherical harmonic (SH) coefficients based on the empirical orthogonal function (EOF) method and periodic functions by utilizing global ionospheric SH coefficients data provided by Center for Orbit Determination in Europe (CODE) during the years 2005–2016. Results show that the first four-order base functions and corresponding associated coefficients can represent 97.15% of the basic characteristics of the original data. The first four-order associated coefficients have noticeable periodic variations, and the correlation between these coefficients and the solar activity intensity is high. By fitting the associated coefficients with the periodic function that takes into account the influence of solar activity, it is possible to establish an EOF model to characterize the variations of the ionospheric SH coefficients with few model parameters and further calculate the global vertical total electron content (VTEC). Relative to the existing global VTEC EOF models, this EOF method can achieve high-accuracy modeling of global VTEC with a smaller number of model coefficients. By comparing the SH coefficients and the global VTEC between the EOF model and CODE, results demonstrate that the EOF model can achieve high accuracy and reliability under different solar activities. The difference between the EOF model and CODE is basically at the same level as that between the individual ionospheric analysis centers and CODE. In the extreme event of magnetic storms, the EOF model can also present higher accuracy than the international reference ionosphere (IRI) model.

Assessment and Comparison of Broadcast Ionospheric Models: NTCM-BC, BDGIM, and Klobuchar

For single-frequency Global Navigation Satellite Systems (GNSSs) users, ionospheric delay is the main error source affecting the accuracy of positioning. Applying a broadcast ionospheric correction model to mitigate the ionospheric delay is essential for meter-to-decimeter-level accuracy positioning. To provide support for real-time single-frequency operations, particularly in the China area, we assessed the performance of three broadcast ionospheric correction models, namely, the Neustrelitz total electron content (TEC) broadcast model (NTCM-BC), the BeiDou global broadcast ionospheric delay correction model (BDGIM), and the Klobuchar model. In this study, the broadcast coefficients of Klobuchar and BDGIM are obtained from the navigation data files directly. Two sets of coefficients of NTCM-BC for China and global areas are estimated. The slant total electron contents (STEC) data from more than 80 validation stations and the final vertical TEC (VTEC) data of the Center for Orbit Determination in Europe (CODE) are used as independent benchmarks for comparison. Compared to GPS STEC during the period of Day of Year (DOY) 101~199, 2019, the ionospheric correction ratio of NTCM-BC, BDGIM, and Klobuchar are 79.4%, 64.9%, and 57.7% in China, respectively. For the global area, the root-mean-square (RMS) errors of these three models are 3.67 TECU (1 TECU = 1016 electrons/m2), 5.48 TECU, and 8.92 TECU, respectively. Compared to CODE VTEC in the same period, NTCM-BC, BDGIM, and Klobuchar can correct 72.6%, 69.8%, and 61.7% of ionospheric delay, respectively. Hence, NTCM-BC is recommended for use as the broadcast ionospheric model for the new-generation BeiDou satellite navigation system (BDS) and its satellite-based augmentation system.