scholarly journals Global and Regional High-Resolution VTEC Modelling Using a Two-Step B-Spline Approach

2020 ◽  
Vol 12 (7) ◽  
pp. 1198 ◽  
Author(s):  
Andreas Goss ◽  
Michael Schmidt ◽  
Eren Erdogan ◽  
Florian Seitz
Keyword(s):  
Real Time ◽  
Spectral Resolution ◽  
The State ◽  
Single Frequency ◽  
External Information ◽  
Electron Content ◽  
Intermediate Step ◽  
Total Electron ◽  
B Spline ◽  
Hourly Data

The ionosphere is one of the largest error sources in GNSS (Global Navigation Satellite Systems) applications and can cause up to several meters of error in positioning. Especially for single-frequency users, who cannot correct the ionospheric delay, the information about the state of the ionosphere is mandatory. Dual- and multi-frequency GNSS users, on the other hand, can correct the ionospheric effect on their observations by linear combination. However, real-time applications such as autonomous driving or precision farming, require external high accuracy corrections for fast convergence. Mostly, this external information is given in terms of grids or coefficients of the vertical total electron content (VTEC). Globally distributed GNSS stations of different networks, such as the network of the International GNSS Services (IGS), provide a large number of multi-frequency observations which can be used to determine the state of the ionosphere. These data are used to generate Global Ionosphere Maps (GIM). Due to the inhomogeneous global distribution of GNSS real-time stations and especially due to the large data gaps over oceanic areas, the global VTEC models are usually limited in their spatial and spectral resolution. Most of the GIMs are mathematically based on globally defined radial basis functions, i.e., spherical harmonics (SH), with a maximum degree of 15 and provided with a spatial resolution of 2.5 ° × 5 ° in latitude and longitude, respectively. Regional GNSS networks, however, offer dense clusters of observations, which can be used to generate regional VTEC solutions with a higher spectral resolution. In this study, we introduce a two-step model (TSM) comprising a global model as the first step and a regional model as the second step. We apply polynomial and trigonometric B-spline functions to represent the global VTEC. Polynomial B-splines are used for modelling the finer structures of VTEC within selected regions, i.e., the densification areas. The TSM provides both, a global and a regional VTEC map at the same time. In order to study the performance, we apply the developed approach to hourly data of the global IGS network as well as the EUREF network of the European region for St. Patrick storm in March 2015. For the assessment of the generated maps, we use the dSTEC analysis and compare both maps with different global and regional products from the IGS Ionosphere Associated Analysis Centers, e.g., the global product from CODE (Berne, Switzerland) and from UPC (Barcelona, Spain), as well as the regional maps from ROB (Brussels, Belgium). The assessment shows a significant improvement of the regional VTEC representation in the form of the generated TSM maps. Among all other products used for comparison, the developed regional one is of the highest accuracy within the selected time span. Since the numerical tests are performed using hourly data with a latency of one to two hours, the presented procedure is seen as an intermediate step for the generation of high precision regional real-time corrections for modern applications.

scholarly journals Real-Time Global Ionospheric Map and Its Application in Single-Frequency Positioning

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 1138 ◽  
Author(s):  
Liang Zhang ◽  
Yibin Yao ◽  
Wenjie Peng ◽  
Lulu Shan ◽  
Yulin He ◽  
...  
Keyword(s):  
Real Time ◽  
Total Electron Content ◽  
Precise Point Positioning ◽  
Single Frequency ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Time Service ◽  
Point Positioning ◽  
Raw Observations

The prevalence of real-time, low-cost, single-frequency, decimeter-level positioning has increased with the development of global navigation satellite systems (GNSSs). Ionospheric delay accounts for most errors in real-time single-frequency GNSS positioning. To eliminate ionospheric interference in real-time single-frequency precise point positioning (RT-SF-PPP), global ionospheric vertical total electron content (VTEC) product is designed in the next stage of the International GNSS Service (IGS) real-time service (RTS). In this study, real-time generation of a global ionospheric map (GIM) based on IGS RTS is proposed and assessed. There are three crucial steps in the process of generating a real-time global ionospheric map (RTGIM): estimating station differential code bias (DCB) using the precise point positioning (PPP) method, deriving slant total electron content (STEC) from PPP with raw observations, and modeling global vertical total electron content (VTEC). Experiments were carried out to validate the algorithm’s effectiveness. First, one month’s data from 16 globally distributed IGS stations were used to validate the performance of DCB estimation with the PPP method. Second, 30 IGS stations were used to verify the accuracy of static PPP with raw observations. Third, the modeling of residuals was assessed in high and quiet ionospheric activity periods. Afterwards, the quality of RTGIM products was assessed from two aspects: (1) comparison with the Center for Orbit Determination in Europe (CODE) global ionospheric map (GIM) products and (2) determination of the performance of RT-SF-PPP with the RTGIM. Experimental results show that DCB estimation using the PPP method can realize an average accuracy of 0.2 ns; static PPP with raw observations can achieve an accuracy of 0.7, 1.2, and 2.1 cm in the north, east, and up components, respectively. The average standard deviations (STDs) of the model residuals are 2.07 and 2.17 TEC units (TECU) for moderate and high ionospheric activity periods. Moreover, the average root-mean-square (RMS) error of RTGIM products is 2.4 TECU for the one-month moderate ionospheric period. Nevertheless, for the high ionospheric period, the RMS is greater than the RMS in the moderate period. A sub-meter-level horizontal accuracy and meter-level vertical accuracy can be achieved when the RTGIM is employed in RT-SF-PPP.

Real-time regional VTEC modeling based on B-splines using real-time GPS and GLONASS observations

2021 ◽  
Author(s):  
Eren Erdogan ◽  
Andreas Goss ◽  
Michael Schmidt ◽  
Denise Dettmering ◽  
Florian Seitz ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Carrier Phase ◽  
Background Information ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
B Spline ◽  
B Splines ◽  
Cycle Slips

<p>The project OPTIMAP is at the current stage a joint initiative of BGIC, GSSAC and DGFI-TUM. The development of an operational tool for ionospheric mapping and prediction is the main goal of the project.</p><p>The ionosphere is a dispersive medium. Therefore, GNSS signals are refracted while they pass through the ionosphere. The magnitude of the refraction rate depends on the frequencies of the transmitted GNSS signals. The ionospheric disturbance on the GNSS signals paves the way of extracting Vertical Total Electron Content (VTEC) information of the ionosphere.</p><p>In OPTIMAP, the representation of the global and regional VTEC signal is based on localizing B-spline basis functions. For global VTEC modeling, polynomial B-splines are employed to represent the latitudinal variations, whereas trigonometric B-splines are used for the longitudinal variations. The regional modeling in OPTIMAP relies on a polynomial B-spline representation for both latitude and longitude.</p><p>The VTEC modeling in this study relies on both a global and a regional sequential estimator (Kalman filter) running in a parallel mode. The global VTEC estimator produces VTEC maps based on data from GNSS receiver stations which are mainly part of the global real-time IGS network. The global estimator relies on additional VTEC information obtained from a forecast procedure using ultra-rapid VTEC products. The regional estimator makes use of the VTEC product of the real-time global estimator as background information and generates high-resolution VTEC maps using real-time data from the EUREF Permanent GNSS Network. EUREF provides a network of very dense GNSS receivers distributed alongside Europe.</p><p>Carrier phase observations acquired from GPS and GLONASS, which are transmitted in accordance with RTCM standard, are used for real-time regional VTEC modeling. After the acquisition of GNSS data, cycle slips for each satellite-receiver pair are detected, and ionosphere observations are constructed via the linear combination of carrier-phase observations in the data pre-processing step. The unknown B-spline coefficients, as well as the biases for each phase-continuous arc belonging to each receiver-satellite pair, are simultaneously estimated in the Kalman filter.</p><p>Within this study, we compare the performance of regional and global VTEC products generated in real-time using the well-known dSTEC analysis.</p>

scholarly journals A Refinement Method of Real-Time Ionospheric Model for China

2020 ◽  
Vol 12 (20) ◽  
pp. 3354
Author(s):  
Yang Wang ◽  
Yibin Yao ◽  
Liang Zhang ◽  
Mingshan Fang
Keyword(s):  
Real Time ◽  
Total Electron Content ◽  
Global Navigation Satellite Systems ◽  
Single Frequency ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Ionospheric Model ◽  
Total Electron ◽  
Satellite Systems ◽  
Refinement Method

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.

scholarly journals High-Resolution Ionosphere Corrections for Single-Frequency Positioning

2020 ◽  
Vol 13 (1) ◽  
pp. 12
Author(s):  
Andreas Goss ◽  
Manuel Hernández-Pajares ◽  
Michael Schmidt ◽  
David Roma-Dollase ◽  
Eren Erdogan ◽  
...  
Keyword(s):  
Real Time ◽  
Basis Functions ◽  
High Spectral Resolution ◽  
Single Frequency ◽  
Satellite Orbits ◽  
Electron Content ◽  
Navigation Satellite ◽  
B Spline ◽  
Global Navigation ◽  
Global Navigation Satellite

The ionosphere is one of the main error sources in positioning and navigation; thus, information about the ionosphere is mandatory for precise modern Global Navigation Satellite System (GNSS) applications. The International GNSS Service (IGS) and its Ionosphere Associated Analysis Centers (IAAC) routinely provide ionospheric information in terms of global ionosphere maps (final GIM). Typically, these products are modeled using series expansion in terms of spherical harmonics (SHs) with a maximum degree of n=15 and are based on post processed observations from Global Navigation Satellite Systems (GNSS), as well as final satellite orbits. However, precise applications such as autonomous driving or precision agriculture require real-time (RT) information about the ionospheric electron content with high spectral and spatial resolution. Ionospheric RT-GIMs are disseminated via Ntrip protocol using the SSR VTEC message of the RTCM. This message can be streamed in RT, but it is limited for the dissemination of coefficients of SHs of lower degrees only. It allows the dissemination of SH coefficients up to a degree of n=16. This suits to most the SH models of the IAACs, but higher spectral degrees or models in terms of B-spline basis functions, voxels, splines and many more cannot be considered. In addition to the SHs, several alternative approaches, e.g., B-splines or Voxels, have proven to be appropriate basis functions for modeling the ionosphere with an enhanced resolution. Providing them using the SSR VTEC message requires a transfer to SHs. In this context, the following questions are discussed based on data of a B-spline model with high spectral resolution; (1) How can the B-spline model be transformed to SHs in order to fit to the RTCM requirements and (2) what is the loss of detail when the B-spline model is converted to SHs of degree of n=16? Furthermore, we discuss (3) what is the maximum necessary SH degree n to convert the given B-spline model and (4) how can the transformation be performed to make it applicable for real-time applications? For a final assessment, we perform both, the dSTEC analysis and a single-frequency positioning in kinematic mode, using the transformed GIMs for correcting the ionospheric delay. The assessment shows that the converted GIMs with degrees n≥30 coincide with the original B-spline model and improve the positioning accuracy significantly.

Real-time regional VTEC modeling based on B-splines using real-time GPS, GLONASS and GALILEO observations

2020 ◽  
Author(s):  
Eren Erdogan ◽  
Andreas Goss ◽  
Michael Schmidt ◽  
Denise Dettmering ◽  
Florian Seitz ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Carrier Phase ◽  
Background Information ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
B Spline ◽  
B Splines ◽  
Cycle Slips

<p>The project OPTIMAP is at the current stage a joint initiative of BGIC, GSSAC and DGFI-TUM. The development of an operational tool for ionospheric mapping and prediction is the main goal of the project.</p><p>The ionosphere is a dispersive medium. Therefore, GNSS signals are refracted while they pass through the ionosphere. The magnitude of the refraction rate depends on the frequencies of the transmitted GNSS signals. The ionospheric disturbance on the GNSS signals paves the way of extracting Vertical Total Electron Content (VTEC) information of the ionosphere.</p><p>In OPTIMAP, the representation of the global and regional VTEC signal is based on localizing B-spline basis functions. For global VTEC modeling, polynomial B-splines are employed to represent the latitudinal variations, whereas trigonometric B-splines are used for the longitudinal variations. The regional modeling in OPTIMAP relies on a polynomial B-spline representation for both latitude and longitude.</p><p>The VTEC modeling in this study relies on both a global and a regional sequential estimator (Kalman filter) running in a parallel mode. The global VTEC estimator produces VTEC maps based on data from GNSS receiver stations which are mainly part of the global real-time IGS network. The global estimator relies on additional VTEC information obtained from a forecast procedure using ultra-rapid VTEC products. The regional estimator makes use of the VTEC product of the real-time global estimator as background information and generates high-resolution VTEC maps using real-time data from the EUREF Permanent GNSS Network. EUREF provides a network of very dense GNSS receivers distributed alongside Europe.</p><p>Carrier phase observations acquired from GPS, GLONASS and GALILEO constellations, which are transmitted in accordance with RTCM standard, are used for real-time regional VTEC modeling. After the acquisition of GNSS data, cycle slips for each satellite-receiver pair are detected, and ionosphere observations are constructed via the linear combination of carrier-phase observations in the data pre-processing step. The unknown B-spline coefficients, as well as the biases for each phase-continuous arc belonging to each receiver-satellite pair, are simultaneously estimated in the Kalman filter.</p><p>Within this study, we compare the performance of regional and global VTEC products generated in real-time using the well-known dSTEC analysis.</p>

scholarly journals Near real-time estimation of ionosphere vertical total electron content from GNSS satellites using B-splines in a Kalman filter

2017 ◽  
Vol 35 (2) ◽  
pp. 263-277 ◽  
Author(s):  
Eren Erdogan ◽  
Michael Schmidt ◽  
Florian Seitz ◽  
Murat Durmaz
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Data Distribution ◽  
Time Estimation ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Unknown Parameters ◽  
Total Electron ◽  
B Spline ◽  
Real Time Estimation

Abstract. Although the number of terrestrial global navigation satellite system (GNSS) receivers supported by the International GNSS Service (IGS) is rapidly growing, the worldwide rather inhomogeneously distributed observation sites do not allow the generation of high-resolution global ionosphere products. Conversely, with the regionally enormous increase in highly precise GNSS data, the demands on (near) real-time ionosphere products, necessary in many applications such as navigation, are growing very fast. Consequently, many analysis centers accepted the responsibility of generating such products. In this regard, the primary objective of our work is to develop a near real-time processing framework for the estimation of the vertical total electron content (VTEC) of the ionosphere using proper models that are capable of a global representation adapted to the real data distribution. The global VTEC representation developed in this work is based on a series expansion in terms of compactly supported B-spline functions, which allow for an appropriate handling of the heterogeneous data distribution, including data gaps. The corresponding series coefficients and additional parameters such as differential code biases of the GNSS satellites and receivers constitute the set of unknown parameters. The Kalman filter (KF), as a popular recursive estimator, allows processing of the data immediately after acquisition and paves the way of sequential (near) real-time estimation of the unknown parameters. To exploit the advantages of the chosen data representation and the estimation procedure, the B-spline model is incorporated into the KF under the consideration of necessary constraints. Based on a preprocessing strategy, the developed approach utilizes hourly batches of GPS and GLONASS observations provided by the IGS data centers with a latency of 1 h in its current realization. Two methods for validation of the results are performed, namely the self consistency analysis and a comparison with Jason-2 altimetry data. The highly promising validation results allow the conclusion that under the investigated conditions our derived near real-time product is of the same accuracy level as the so-called final post-processed products provided by the IGS with a latency of several days or even weeks.

IGS RTS for real-time global ionospheric total electron content modeling: Method and Applications

2020 ◽  
Author(s):  
Ningbo Wang ◽  
Zishen Li ◽  
Liang Wang
Keyword(s):  
Real Time ◽  
Sampling Rate ◽  
Global Scale ◽  
Global Network ◽  
Single Frequency ◽  
Space Representation ◽  
Electron Content ◽  
Time Data ◽  
Total Electron ◽  
Real Time Mode

<p>To enable GNSS applications with low or no time latency, real-time services (RTS) of the International GNSS Services (IGS) has been launched since 2013. The IGS RTS provides real-time data streams with latencies of less than few seconds, containing multi-frequency and multi-constellation GNSS measurements from a global network of high-quality GNSS receivers, which provides the opportunity to reconstruct global ionospheric models in real-time mode. For the computation of real-time global ionospheric maps (RT-GIM), a 2-day predicted global ionospheric model is introduced along with real-time slant ionospheric delays extracted from real-time IGS global stations. GPS and GLONASS L1+L2, BeiDou B1+B2 and Galileo E1+E5a signals with a sampling rate of 1 Hz are used to extract slant TEC (STEC) estimates. Spherical harmonic expansion up to degree and order 15 is employed for global vertical TEC (VTEC) modeling by combining the observed and predicted ionospheric data in real-time mode. Real-time ionospheric State Space Representation (SSR) corrections are then distributed in RTCM 1264 message (123.56.176.228:2101/CAS05) aside from the generation of RT-GIM in IONEX v1.0 format (available at ftp://ftp.gipp.org.cn/product/ionex/). The quality of CAS RT-GIMs is assessed during an 18-month period starting from August 2017, by comparison with GPS differential slant TECs at the selected IGS stations over continental areas, Jason-3 VTECs over the oceans and IGS combined final GIMs on a global scale, respectively. Results show that CAS’s RT-GIM products exhibit a relative error of 13.9%, which is only approximately 1-2% worse than the final ones during the test period. Additionally, the application of RT-GIM on the single-frequency precise point positioning (PPP) of smartphones is also presented.</p>

Dissemination of High-Resolution Ionosphere Information from VTEC B-spline Expansions for Single-Frequency Positioning

2021 ◽  
Author(s):  
Andreas Goss ◽  
Manuel Hernández-Pajares ◽  
Michael Schmidt ◽  
Eren Erdogan
Keyword(s):  
High Resolution ◽  
Series Expansion ◽  
Single Frequency ◽  
Space Representation ◽  
Model Parameters ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
B Spline ◽  
Voxel Representation

<p>The ionospheric signal delay is one of the largest error sources in GNSS applications and may cause in case of a single-frequency receiver a positioning error of up to several meters. To avoid such an inaccuracy some of the Ionosphere Associated Analysis Centers (IAAC) of the International GNSS Service (IGS) provide the user the Vertical Total Electron Content (VTEC) as Real-Time Global Ionosphere Maps (RT-GIM) via streaming formats. Currently, the only data format used for the dissemination of these ionospheric corrections is based on the State Space Representation (SSR) message and the RTCM standards.</p><p>Mathematically most of the RT-GIMs are based on modeling VTEC as series expansions in spherical harmonics (SH) up to a highest degree of n = 15 which corresponds to a spatial resolution of 12° in latitude and longitude and is therefore, too low for modern GNSS applications such as autonomous driving. However, the SSR VTEC message allows the dissemination of SH coefficients only up to a maximum degree of n = 16.</p><p>To avoid the drawbacks of expanding VTEC in SHs other approaches such as a voxel representation or a B-spline series expansion have been proven to be appropriate candidates for global and regional modelling with an enhanced resolution. In order to provide in these cases the significant model parameters to the user, the application of the SSR VTEC message requires a transformation of the model parameters into SH coefficients. In this contribution a methodology will be presented which describes a fast transformation of the B-spline approach into a SH representation with high accuracy by minimizing the information loss.</p><p>To test the method, a high-resolution VTEC GIM modeled as a series expansion in B-splines is transformed into SH representations of different highest degree values; the results are validated via dSTEC analysis as well as via an example of single frequency positioning and show a significantly improved accuracy compared to the IGS GIMs.</p>

Predicting total electron content in ionosphere using vector autoregression model during geomagnetic storm

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sumitra Iyer ◽  
Alka Mahajan
Keyword(s):  
Real Time ◽  
Total Electron Content ◽  
Vector Autoregression ◽  
Prediction Interval ◽  
Single Frequency ◽  
Percentage Error ◽  
Electron Content ◽  
Total Electron ◽  
Vector Autoregression Model ◽  
Autoregression Model

Abstract The ionospheric total electron content (TEC) severely impacts the positional accuracy of a single frequency Global Positioning System (GPS) receiver at the equatorial latitudes. The ionosphere causes a frequency-dependent group delay in the GPS-ranging signals, which reduces the receiver’s accuracy. Further, the variations in TEC due to various space weather phenomena make the ionosphere’s behaviour nonhomogeneous and complex. Hence, developing an accurate forecast model that can track the dynamic behaviour of the ionosphere remains a challenge. However, advances in emerging data-driven algorithms have been found helpful in tracking non-stationary behavior in TEC. These models help forecast the delays in advance. The multivariate Vector Autoregression model (VAR) predicts the Ionospheric TEC in the proposed model. The prediction model uses input data compiled in real-time from the lag values of incoming TEC data and features extracted from TEC. The TEC is predicted in real-time and tested for different prediction intervals. The metrics – Mean Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) are used for testing and validating the accuracy of the model statistically. Testing the predicted output accuracy is also done with the dynamic time warping (DTW) algorithm by comparing it with the actual value obtained from the dual-frequency receiver. The model is tested for storm days of the year 2015 for Bangalore and Hyderabad stations and found to be reliable and accurate. A prediction interval of twenty-minute shows the highest accuracy with an error within 10 TECU for all the storm days.

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