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>

An Efficient Bayesian Integration Technique to Densify Global Ionospheric Maps using Observations of Local GNSS Networks 

2021 ◽  
Author(s):  
Saeed Farzaneh ◽  
Ehsan forootan
Keyword(s):  
Solar Activity ◽  
South America ◽  
Spherical Harmonics ◽  
Region Of Interest ◽  
High Solar Activity ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Numerical Application ◽  
Local Networks ◽  
Total Electron

<p><strong>Abstract:</strong></p><p>Global ionosphere maps (GIM) are generated on daily basis at the Center for Orbit Determination in Europe (CODE) using data from about 200 GNSS sites of the International GNSS Service (IGS) and other institutions. These measurement are used to numerically model the vertical total electron content (VTEC) in a solar-geomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. In this study, an efficient method is developed and applied to densify the GIM model in a region of interest using the TEC measurements of  local networks. Our approach follows a Bayesian updating scheme, where the GIM data are utilized as a prior information in the form of Slepian-coefficients in the region of interest. These coefficients are then updated by the GNSS measurements in a Bayesian framework that considers both the uncertainty of a priori information and the new measurements. Numerical application is demonstrated using a GNSS network in South America. Our results indicate that by using 62 GNSS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the Bayesian-derived VTEC estimates in a Standard Point Positioning (SPP) 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 found to be ∼23% and 25% for a day with moderate solar activity while 26% and ∼35% for a day with high solar activity, respectively.</p><p><strong>Key words:</strong> Bayesian densification, Slepian Functions, Spherical Harmonics, Ionospheric modelling, VTEC, SPPs</p>

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 Adaptive Modeling of the Global Ionosphere Vertical Total Electron Content

2020 ◽  
Vol 12 (11) ◽  
pp. 1822
Author(s):  
Eren Erdogan ◽  
Michael Schmidt ◽  
Andreas Goss ◽  
Barbara Görres ◽  
Florian Seitz
Keyword(s):  
Total Electron Content ◽  
Temporal Variations ◽  
Model Parameters ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Model Uncertainties ◽  
Data Set ◽  
Total Electron ◽  
B Spline ◽  
Run Time

The Kalman filter (KF) is widely applied in (ultra) rapid and (near) real-time ionosphere modeling to meet the demand on ionosphere products required in many applications extending from navigation and positioning to monitoring space weather events and naturals disasters. The requirement of a prior definition of the stochastic models attached to the measurements and the dynamic models of the KF is a drawback associated with its standard implementation since model uncertainties can exhibit temporal variations or the time span of a given test data set would not be large enough. Adaptive methods can mitigate these problems by tuning the stochastic model parameters during the filter run-time. Accordingly, one of the primary objectives of our study is to apply an adaptive KF based on variance component estimation to compute the global Vertical Total Electron Content (VTEC) of the ionosphere by assimilating different ionospheric GNSS measurements. Secondly, the derived VTEC representation is based on a series expansion in terms of compactly supported B-spline functions. We highlight the morphological similarity of the spatial distributions and the magnitudes between VTEC values and the corresponding estimated B-spline coefficients. This similarity allows for deducing physical interpretations from the coefficients. In this context, an empirical adaptive model to account for the dynamic model uncertainties, representing the temporal variations of VTEC errors, is developed in this work according to the structure of B-spline coefficients. For the validation, the differential slant total electron content (dSTEC) analysis and a comparison with Jason-2/3 altimetry data are performed. Assessments show that the quality of the VTEC products derived by the presented algorithm is in good agreement, or even more accurate, with the products provided by IGS ionosphere analysis centers within the selected periods in 2015 and 2017. Furthermore, we show that the presented approach can be applied to different ionosphere conditions ranging from very high to low solar activity without concerning time-variable model uncertainties, including measurement error and process noise of the KF because the associated covariance matrices are computed in a self-adaptive manner during run-time.

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.

scholarly journals Ionospheric response to total solar eclipse of 22 July 2009 in different Indian regions

2013 ◽  
Vol 31 (9) ◽  
pp. 1549-1558 ◽  
Author(s):  
S. Kumar ◽  
A. K. Singh ◽  
R. P. Singh
Keyword(s):  
Total Electron Content ◽  
Solar Eclipse ◽  
Total Solar Eclipse ◽  
Lower Atmosphere ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Ionospheric Response ◽  
Total Electron Content Data ◽  
Photoionization Process

Abstract. The variability of ionospheric response to the total solar eclipse of 22 July 2009 has been studied analyzing the GPS data recorded at the four Indian low-latitude stations Varanasi (100% obscuration), Kanpur (95% obscuration), Hyderabad (84% obscuration) and Bangalore (72% obscuration). The retrieved ionospheric vertical total electron content (VTEC) shows a significant reduction (reflected by all PRNs (satellites) at all stations) with a maximum of 48% at Varanasi (PRN 14), which decreases to 30% at Bangalore (PRN 14). Data from PRN 31 show a maximum of 54% at Kanpur and 26% at Hyderabad. The maximum decrement in VTEC occurs some time (2–15 min) after the maximum obscuration. The reduction in VTEC compared to the quiet mean VTEC depends on latitude as well as longitude, which also depends on the location of the satellite with respect to the solar eclipse path. The amount of reduction in VTEC decreases as the present obscuration decreases, which is directly related to the electron production by the photoionization process. The analysis of electron density height profile derived from the COSMIC (Constellation Observing System for Meteorology, Ionosphere & Climate) satellite over the Indian region shows significant reduction from 100 km altitude up to 800 km altitude with a maximum of 48% at 360 km altitude. The oscillatory nature in total electron content data at all stations is observed with different wave periods lying between 40 and 120 min, which are attributed to gravity wave effects generated in the lower atmosphere during the total solar eclipse.

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