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 Comparison of spherical harmonic and B spline models for the vertical total electron content

Radio Science ◽  
2011 ◽  
Vol 46 (6) ◽  
Author(s):  
Michael Schmidt ◽  
Denise Dettmering ◽  
Matthias Mößmer ◽  
Yuanyuan Wang ◽  
Jiantong Zhang
Keyword(s):  
Total Electron Content ◽  
Spherical Harmonic ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
B Spline ◽  
Spline Models

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>

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 Comparison of simultaneous variations of the ionospheric total electron content and geomagnetic field associated with strong earthquakes

2001 ◽  
Vol 1 (1/2) ◽  
pp. 53-59 ◽  
Author(s):  
Sh. Naaman ◽  
L. S. Alperovich ◽  
Sh. Wdowinski ◽  
M. Hayakawa ◽  
E. Calais
Keyword(s):  
Total Electron Content ◽  
Vertical Displacement ◽  
Temporal Variations ◽  
Electron Content ◽  
Geomagnetic Disturbances ◽  
Total Electron ◽  
Strong Earthquakes ◽  
Ionospheric Total Electron Content ◽  
Geomagnetic Observations ◽  
Gps Observations

Abstract. In this paper, perturbations of the ionospheric Total Electron Content (TEC) are compared with geomagnetic oscillations. Comparison is made for a few selected periods, some during earthquakes in California and Japan and others at quiet periods in Israel and California. Anomalies in TEC were extracted using Global Positioning System (GPS) observations collected by GIL (GPS in Israel) and the California permanent GPS networks. Geomagnetic data were collected in some regions where geomagnetic observatories and the GPS network overlaps. Sensitivity of the GPS method and basic wave characteristics of the ionospheric TEC perturbations are discussed. We study temporal variations of ionospheric TEC structures with highest reasonable spatial resolution around 50 km. Our results show no detectable TEC disturbances caused by right-lateral strike-slip earthquakes with minor vertical displacement. However, geomagnetic observations obtained at two observatories located in the epicenter zone of a strong dip-slip earthquake (Kyuchu, M = 6.2, 26 March 1997) revealed geomagnetic disturbances occurred 6–7 h before the earthquake.

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.

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