scholarly journals High-resolution vertical total electron content maps based on multi-scale B-spline representations

2019 ◽  
Vol 37 (4) ◽  
pp. 699-717 ◽  
Author(s):  
Andreas Goss ◽  
Michael Schmidt ◽  
Eren Erdogan ◽  
Barbara Görres ◽  
Florian Seitz
Keyword(s):  
High Resolution ◽  
Spatial Resolution ◽  
Sampling Interval ◽  
Basis Functions ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Spectral Content ◽  
Total Electron ◽  
Multi Scale ◽  
Temporal Sampling

Abstract. For more than 2 decades the IGS (International GNSS Service) ionosphere associated analysis centers (IAACs) have provided global maps of the vertical total electron content (VTEC). In general, the representation of a 2-D or 3-D function can be performed by means of a series expansion or by using a discretization technique. While in the latter case, pixels or voxels are usually chosen for a spherical function such as VTEC, for a series expansion spherical harmonics (SH) are primarily used as basis functions. The selection of the best suited approach for ionosphere modeling means a trade-off between the distribution of available data and their possibility of representing ionospheric variations with high resolution and high accuracy. Most of the IAACs generate global ionosphere maps (GIMs) based on SH expansions up to the spectral degree n=15 and provide them with a spatial resolution of 2.5∘×5∘ with respect to the latitudinal and longitudinal directions, respectively, and a temporal sampling interval of 2 h. In recent years, it has frequently been claimed that the spatial resolution of the VTEC GIMs has to be increased to a spatial resolution of 1∘×1∘ and to a temporal sampling interval of about 15 min. Enhancing the grid resolution means an interpolation of VTEC values for intermediate points but with no further information about variations in the signal. n=15 in the SH case, for instance, corresponds to a spatial sampling of 12∘×12∘. Consequently, increasing the grid resolution concurrently requires an extension of the spectral content, i.e., to choose a higher SH degree value than 15. Unlike most of the IAACs, the VTEC modeling approach at Deutsches Geodätisches Forschungsinstitut der Technischen Universität München (DGFI-TUM) is based on localizing basis functions, namely tensor products of polynomial and trigonometric B-splines. In this way, not only can data gaps be handled appropriately and sparse normal equation systems be established for the parameter estimation procedure, a multi-scale representation (MSR) can also be set up to determine GIMs of different spectral content directly, by applying the so-called pyramid algorithm, and to perform highly effective data compression techniques. The estimation of the MSR model parameters is finally performed by a Kalman filter driven by near real-time (NRT) GNSS data. Within this paper, we realize the MSR and create multi-scale products based on B-spline scaling, wavelet coefficients and VTEC grid values. We compare these products with different final and rapid products from the IAACs, e.g., the SH model from CODE (Berne) and the voxel solution from UPC (Barcelona). In contrast to the abovementioned products, DGFI-TUM's products are based solely on NRT GNSS observations and ultra-rapid orbits. Nevertheless, we can conclude that the DGFI-TUM's high-resolution product (“othg”) outperforms all products used within the selected time span of investigation, namely September 2017.

scholarly journals High Resolution Vertical Total Electron Content Maps Based on Multi-Scale B-spline Representations

2019 ◽  
Author(s):  
Andreas Goss ◽  
Michael Schmidt ◽  
Eren Erdogan ◽  
Barbara Görres ◽  
Florian Seitz
Keyword(s):  
High Resolution ◽  
Spatial Resolution ◽  
Basis Functions ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Spectral Content ◽  
Total Electron ◽  
B Spline ◽  
Multi Scale ◽  
Temporal Sampling

Abstract. For more than two decades the IGS (International GNSS Service) Ionosphere Associated Analysis Centers (IAAC) provide global maps of the vertical total electron content (VTEC). In general, the representation of a two- or three-dimensional function can be performed by means of a series expansion or by using a discretization technique. Whereas in the latter case for a spherical function such as VTEC usually pixels or voxels are chosen, in case of a series expansion mostly spherical harmonics (SH) are used as basis functions. The selection of the best suited approach for ionosphere modelling means a trade-off between the distribution of available data and their possibility to represent ionospheric variations with high resolution and high accuracy. Most of the IAACs generate Global Ionosphere Maps (GIMs) based on SH expansions up to the spectral degree n = 15 and provide them with a spatial resolution of 2.5° × 5° with respect to latitude and longitude direction, and a temporal sampling of two hours. In the recent years it was frequently claimed to improve the spatial sampling of the VTEC GIMs to a spatial resolution of 1° × 1° and to a temporal sampling of about 15 minutes. Enhancing the grid resolution means a interpolation of VTEC values for intermediate points but with no further information about variations in the signal. A degree 15 in the SH case for instance corresponds to a spatial sampling of 12° × 12°. Consequently, increasing the grid resolution requires at the same time an extension of the spectral content, i.e. to choose a higher SH degree value than 15. Unlike most of the IAACs, the VTEC modelling approach at DGFI-TUM is based on localizing basis functions, namely tensor products of polynomial and trigonometric B-splines. This way, not only data gaps can be handled appropriately and sparse normal equation systems are established for the parameters estimation procedure, also a multi-scale-representation (MSR) can be set up, to determine GIMs of different spectral content directly by applying the so-called pyramid algorithm and to perform highly effective data compression techniques. The estimation of the MSR model parameters is finally performed by a Kalman-Filter driven by near real-time (NRT) GNSS data. Within this paper we realize the MSR and create multi-scale products based on B-spline scaling and wavelet coefficients and VTEC grid values. We compare these products with different final and rapid products of the IAACs, e.g., the SH model from CODE (Berne) and the voxel solution from UPC (Barcelona). In opposite to that, DGFI-TUM's products are solely based on NRT GNSS observations and ultra-rapid orbits. Nevertheless, we can conclude that DGFI-TUMs high-resolution product (`othg') outperforms all products used within the selected time span of investigation, namely September 2017.

Analysis of a new regional ionospheric assimilated H2PT model for Europe

2020 ◽  
Author(s):  
Paulina Woźniak ◽  
Anna Świątek ◽  
Mariusz Pożoga ◽  
Łukasz Tomasik
Keyword(s):  
Spatial Resolution ◽  
Negative Impact ◽  
Satellite System ◽  
Electron Content ◽  
Maximum Height ◽  
Vertical Total Electron Content ◽  
Dual Frequency ◽  
International Gnss Service ◽  
Statistical Parameters ◽  
Total Electron

<p>The signal emitted by the GNSS (<em>Global Navigation Satellite System</em>) satellite, on the way to the receiver located on the Earth’s surface, encounters a heterogeneous layer of ionized gas and free electrons, in which the radio wave is dispersed. As the ionosphere is the source of the highest-value errors among the different factors that affect GNSS positioning accuracy, it is necessary to minimize its negative impact. Various methods are used to compensate for the ionospheric delay, one of which is the usage of models.<br>The intensity of the processes occurring in the ionosphere is closely related to the Sun activity. As a consequence, with respect to a given location on the Earth's surface, the activity of the ionosphere changes throughout the year and day. Therefore, a model dedicated to a specific region is especially important in case of high-precision GNSS applications.<br>The assimilated H2PT model was based on the dual-frequency observations from GNSS stations belonging to EPN (<em>EUREF Permanent Network</em>), as well as on ionosondes participating in the DIAS (<em>European Digital Upper Atmosphere Server</em>) project. The H2PT model covers the Europe area, data with a 15-minutes interval were placed in similar to IONEX (<em>IONosphere Map EXchenge</em>) files in two versions of spatial resolution: 1- and 5-degree. Data provided by the H2PT model are the VTEC (<em>Vertical Total Electron Content</em>) values and the hmF2 (<em>maximum height of the F2 layer</em>) parameters.<br>The subject of this research is the comparison of the H2PT model with NeQuick-G model and IONEX data published by IGS (<em>International GNSS Service</em>) in the context of TEC values as well as determining differences between regional hmF2 data and its commonly used fixed value for the entire globe, amounting to 450 km. In order to perform the analysis, appropriate visualizations were made and statistical parameters determined. Additionally, data from selected periods of positive and negative disturbances were analysed in details based on the developed time series.<br>The relatively high temporal and spatial resolution is undoubtedly an advantage of the H2PT model, because unlike global models, the regional one allows conscientious analysis of the ionosphere characteristics for the area of Europe. Importantly, solutions regarding hmF2 show significant deviations from the fixed value approximated for the whole Earth. Taking into account the parameter appropriate for a given location and time during GNSS data processing may improve the obtained positioning quality. </p>

A Bayesian Approach to Improve Regional and Global Ionospheric Maps using GNSS Observations

2020 ◽  
Author(s):  
Saeed Farzaneh ◽  
Ehsan Forootan
Keyword(s):  
Total Electron Content ◽  
Spatial Resolution ◽  
Spherical Harmonics ◽  
Bayesian Approach ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Numerical Application ◽  
Total Electron ◽  
Base Functions ◽  
Gnss Measurements

<p>The Global Ionosphere Maps (GIMs) are generated on a daily basis at the Center for Orbit Determination in Europe (CODE) using the observations from about 200 Global Positioning System (GPS)/GLONASS sites of the International GNSS Service (IGS) and other institutions. These maps contain Vertical Total Electron Content (VTEC) values, which are estimated in a solar-geomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. Although these maps have wide applications, their relatively low spatial resolution limits the accuracy of many geodetic applications such as those related to Precise Point Positioning (PPP) and navigation. In this study, a novel Bayesian approach is proposed to improve the spatial resolution of VTEC estimations in regional and global scales. The proposed technique utilises GIMs as a prior information and updates the VTEC estimates using a new set of base-functions (with better resolution than that of spherical harmonics) and the GNSS measurements that are not included in the network of GIMs. To achieve the highest accuracy possible, our implementation is based on a transformation of spherical harmonics to the Slepian base-functions, where the latter is a set of bandlimited functions that reflect the majority of signal energy inside an arbitrarily defined region, yet they remain orthogonal within this region. The new GNSS measurements are considered in a Bayesian update estimation to modify those of GIMs. Numerical application of this study is demonstrated using the ground-based GPS data over South America. The results are also validated against the VTEC estimations derived from independent GPS stations.</p><p><strong>Key words:</strong> Spherical Slepian Base-Functions, Spherical Harmonics, Ionospheric modelling, Vertical Total Electron Content (VTEC)</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>

scholarly journals Characterization of multi-scale ionospheric irregularities using ground-based and space-based GNSS observations

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
YuXiang Peng ◽  
Wayne A Scales ◽  
Michael D Hartinger ◽  
Zhonghua Xu ◽  
Shane Coyle
Keyword(s):  
Formation Flying ◽  
Satellite System ◽  
Ionospheric Irregularities ◽  
Mission Design ◽  
Electron Content ◽  
Total Electron ◽  
Spatial And Temporal Scales ◽  
Multi Scale ◽  
Global Navigation Satellite ◽  
Gnss Observations

AbstractIonospheric irregularities can adversely affect the performance of Global Navigation Satellite System (GNSS). However, this opens the possibility of using GNSS as an effective ionospheric remote sensing tool. Despite ionospheric monitoring has been undertaken for decades, these irregularities in multiple spatial and temporal scales are still not fully understood. This paper reviews Virginia Tech’s recent studies on multi-scale ionospheric irregularities using ground-based and space-based GNSS observations. First, the relevant background of ionospheric irregularities and their impact on GNSS signals is reviewed. Next, three topics of ground-based observations of ionospheric irregularities for which GNSS and other ground-based techniques are used simultaneously are reviewed. Both passive and active measurements in high-latitude regions are covered. Modelling and observations in mid-latitude regions are considered as well. Emphasis is placed on the increased capability of assessing the multi-scale nature of ionospheric irregularities using other traditional techniques (e.g., radar, magnetometer, high frequency receivers) as well as GNSS observations (e.g., Total-Electron-Content or TEC, scintillation). Besides ground-based observations, recent advances in GNSS space-based ionospheric measurements are briefly reviewed. Finally, a new space-based ionospheric observation technique using GNSS-based spacecraft formation flying and a differential TEC method is demonstrated using the newly developed Virginia Tech Formation Flying Testbed (VTFFTB). Based on multi-constellation multi-band GNSS, the VTFFTB has been developed into a hardware-in-the-loop simulation testbed with external high-fidelity global ionospheric model(s) for 3-satellite formation flying, which can potentially be used for new multi-scale ionospheric measurement mission design.

scholarly journals Multi-Scale Ionospheric Anomalies Monitoring and Spatio-Temporal Analysis during Intense Storm

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 215
Author(s):  
Na Cheng ◽  
Shuli Song ◽  
Wei Li
Keyword(s):  
Magnetic Storm ◽  
Large Scale ◽  
Temporal Dynamics ◽  
Ionospheric Disturbance ◽  
Ionospheric Scintillation ◽  
Small Scale ◽  
Electron Content ◽  
Total Electron ◽  
Multi Scale ◽  
Intense Storm

The ionosphere is a significant component of the geospace environment. Storm-induced ionospheric anomalies severely affect the performance of Global Navigation Satellite System (GNSS) Positioning, Navigation, and Timing (PNT) and human space activities, e.g., the Earth observation, deep space exploration, and space weather monitoring and prediction. In this study, we present and discuss the multi-scale ionospheric anomalies monitoring over China using the GNSS observations from the Crustal Movement Observation Network of China (CMONOC) during the 2015 St. Patrick’s Day storm. Total Electron Content (TEC), Ionospheric Electron Density (IED), and the ionospheric disturbance index are used to monitor the storm-induced ionospheric anomalies. This study finally reveals the occurrence of the large-scale ionospheric storms and small-scale ionospheric scintillation during the storm. The results show that this magnetic storm was accompanied by a positive phase and a negative phase ionospheric storm. At the beginning of the main phase of the magnetic storm, both TEC and IED were significantly enhanced. There was long-duration depletion in the topside ionospheric TEC during the recovery phase of the storm. This study also reveals the response and variations in regional ionosphere scintillation. The Rate of the TEC Index (ROTI) was exploited to investigate the ionospheric scintillation and compared with the temporal dynamics of vertical TEC. The analysis of the ROTI proved these storm-induced TEC depletions, which suppressed the occurrence of the ionospheric scintillation. To improve the spatial resolution for ionospheric anomalies monitoring, the regional Three-Dimensional (3D) ionospheric model is reconstructed by the Computerized Ionospheric Tomography (CIT) technique. The spatial-temporal dynamics of ionospheric anomalies during the severe geomagnetic storm was reflected in detail. The IED varied with latitude and altitude dramatically; the maximum IED decreased, and the area where IEDs were maximum moved southward.

Analysis of ionospheric vertical total electron content before the 1 April 2014 Mw 8.2 Chile earthquake

2017 ◽  
Vol 21 (6) ◽  
pp. 1599-1612 ◽  
Author(s):  
Weiping Jiang ◽  
Yifang Ma ◽  
Xiaohui Zhou ◽  
Zhao Li ◽  
Xiangdong An ◽  
...  
Keyword(s):  
Total Electron Content ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Chile Earthquake

scholarly journals New GGOS JWG3 on Improved understanding of space weather events and their monitoring

2020 ◽  
Author(s):  
Alberto Garcia-Rigo ◽  
Benedikt Soja
Keyword(s):  
Electron Density ◽  
Space Weather ◽  
International Association ◽  
Real Data ◽  
Weather Conditions ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Weather Events ◽  
Space Geodetic Techniques

<p>Multiple space geodetic techniques are capable of measuring effects caused by space weather events. In particular, space weather events can cause ionospheric disturbances correlated with variations in the vertical total electron content (VTEC) or the electron density (Ne) of the ionosphere.</p><p>In this regard and in the context of the new Focus Area on Geodetic Space Weather Research within IAG’s GGOS (International Association of Geodesy; Global Geodetic Observing System), the Joint Working Group 3 on Improved understanding of space weather events and their monitoring by satellite missions has been created as part of IAG Commission 4, Sub-Commission 4.3 to run for the next four years.</p><p>Within JWG3, we expect investigating different approaches to monitor space weather events using the data from different space geodetic techniques and, in particular, combinations thereof. Simulations will be beneficial to identify the contribution of different techniques and prepare for the analysis of real data. Different strategies for the combination of data will also be investigated, in particular, the weighting of estimates from different techniques in order to increase the performance and reliability of the combined estimates. Furthermore, existing algorithms for the detection and prediction of space weather events will be explored and improved to the extent possible. Furthermore, the geodetic measurement of the ionospheric electron density will be complemented by direct observations from the Sun gathered from existing spacecraft, such as SOHO, ACE, SDO, Parker Solar Probe, among others. The combination and joint evaluation of multiple datasets with the measurements of space geodetic observation techniques (e.g. geodetic VLBI) is still a great challenge. In addition, other indications for solar activity - such as the F10.7 index on solar radio flux, SOLERA as EUV proxy or rate of Global Electron Content (dGEC)-, provide additional opportunities for comparisons and validation.</p><p>Through these investigations, we will identify the key parameters useful to improve real-time/prediction of ionospheric/plasmaspheric VTEC, Ne estimates, as well as ionospheric perturbations, in case of extreme solar weather conditions. In general, we will gain a better understanding of space weather events and their effect on Earth’s atmosphere and near-Earth environment.</p>

Validating the impact of various ionosphere correction on mid to long baselines and point positioning using GPS dual-frequency receivers

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alaa A. Elghazouly ◽  
Mohamed I. Doma ◽  
Ahmed A. Sedeek
Keyword(s):  
Geomagnetic Storms ◽  
Global Navigation Satellite Systems ◽  
Electron Content ◽  
Assessment Procedure ◽  
Vertical Total Electron Content ◽  
Dual Frequency ◽  
Total Electron ◽  
Satellite Systems ◽  
Point Positioning ◽  
The Impact

Abstract Due to the ionosphere delay, which has become the dominant GPS error source, it is crucial to remove the ionospheric effect before estimating point coordinates. Therefore, different agencies started to generate daily Global Ionosphere Maps (GIMs); the Vertical Total Electron Content (VTEC) values represented in GIMs produced by several providers can be used to remove the ionosphere error from observations. In this research, An analysis will be carried with three sources for VTEC maps produced by the Center for Orbit Determination in Europe (CODE), Regional TEC Mapping (RTM), and the International Reference Ionosphere (IRI). The evaluation is focused on the effects of a specific ionosphere GIM correction on the precise point positioning (PPP) solutions. Two networks were considered. The first network consists of seven Global Navigation Satellite Systems (GNSS) receivers from (IGS) global stations. The selected test days are six days, three of them quiet, and three other days are stormy to check the influence of geomagnetic storms on relative kinematic positioning solutions. The second network is a regional network in Egypt. The results show that the calculated coordinates using the three VTEC map sources are far from each other on stormy days rather than on quiet days. Also, the standard deviation values are large on stormy days compared to those on quiet days. Using CODE and RTM IONEX file produces the most precise coordinates after that the values of IRI. The elimination of ionospheric biases over the estimated lengths of many baselines up to 1000 km has resulted in positive findings, which show the feasibility of the suggested assessment procedure.

Sign in / Sign up

Export Citation Format

Share Document