Ionosphere Model for European Region Based on Multi-GNSS Data and TPS Interpolation

Krypiak-Gregorczyk, Anna; Wielgosz, Paweł; Borkowski, Andrzej

doi:10.3390/rs9121221

Cited by 40 publications

(30 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The time span of pre-recorded SSR corrections is 100-280 min. The geocentric corrections were calculated according to Equations (1)- (6). In the next step, geocentric corrections, δP, were predicted for the two above-mentioned scenarios.…”

Section: Methodsmentioning

confidence: 99%

“…PPP can be an effective option for precise real-time positioning, but it requires more information than GNSS observations alone. Reliable satellite orbit and clock corrections [1][2][3][4][5], ionosphere [6] and troposphere model parameters [7], and antenna phase center offsets and variations must be provided in order to obtain precise results [8]. In PPP, orbit and clock errors are of major importance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Prediction of Geocentric Corrections during Communication Link Outages in PPP

Janicka

Tomaszewski

Rapiński

et al. 2020

Sensors

View full text Add to dashboard Cite

The International GNSS Service (IGS) real-time service (RTS) provides access to real-time precise products. State-Space Representation (SSR) products are disseminated through the Internet using the Networked Transport of the RTCM (Radio Technical Commission for Maritime Services) via the Internet Protocol (NTRIP). However, communication outages caused by a loss of the communication link during ephemeris changes can occur. Unfortunately, any break in providing orbit and clock corrections affects the possibility to perform precise point positioning. To eliminate this problem, various methods have been developed and presented in the literature. The solution proposed by the authors is to directly predict geocentric corrections. This manuscript presents the results and analysis of geocentric correction predictions under two scenarios: the first between the IODE (issue of data ephemeris) value change and the second where prediction must be done for epochs containing a change in IODE ephemeris. In this case, the prediction uses data from a previous message. The Root Mean Square (RMS) values calculated based on the differences between the true correction values and the predicted geocentric corrections using a linear function, a second-degree polynomial and a constant value do not differ significantly. The numerical results show that, in most cases, maintaining the constant value of the last registered SSR correction is the best option.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Prediction of Geocentric Corrections during Communication Link Outages in PPP

Janicka

Tomaszewski

Rapiński

et al. 2020

Sensors

View full text Add to dashboard Cite

show abstract

“…In this case the transition matrix is defined as identity matrix, i.e., F s = I. Hence, the predicted state vector reads β − s = β s−1 , according to Equation (17). Detailed information about the GSM coordinate system can be found, for instance, in [29,30].…”

Section: Coordinate Systemmentioning

confidence: 99%

“…The Royal Observatory of Belgium (ROB) [13], for instance, provides Regional Ionospheric Maps (RIM) for the European region. Besides this, there are several approaches for the regional representation of VTEC, e.g., regional B-spline expansions [10,[14][15][16], the thin plate spline (TPS) interpolation [17], the Taylor series [18] and the SH expansion using a spherical cap coordinate system [19].…”

Section: Introductionmentioning

confidence: 99%

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

Goss¹,

Schmidt²,

Erdogan³

et al. 2020

Remote Sensing

View full text Add to dashboard Cite

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.

show abstract

“…The vertical TEC is modeled in a solar-geomagnetic reference frame using bi-cubic splines on a spherical grid. A Kalman filter is used to solve simultaneously for instrumental biases and VTEC on the grid (as stochastic parameters) [37,38]. The data is open-access in this file transfer protocol (FTP) server ftp://cddis.gsfc.nasa.gov/gnss/products/ionex [39].…”

Section: Data Set Descriptionmentioning

confidence: 99%

Modeling and Prediction of Regular Ionospheric Variations and Deterministic Anomalies

et al. 2020

View full text Add to dashboard Cite

Knowledge on the ionospheric total electron content (TEC) and its prediction are of great practical importance and engineering relevance in many scientific disciplines. We investigate regular ionospheric anomalies and TEC prediction by applying the least squares harmonic estimation (LS-HE) technique to a 15 year time series of the vertical TEC (VTEC) from 1998 to 2014. We first detected a few new regular and modulated signals in the TEC time series. The multivariate analysis of the time series indicates that there are diurnal, annual, 11 year, and 27 day periodic signals, as well as their higher harmonics. We also found periods matching with the global positioning system (GPS) draconitic year in the TEC time series. The results from the modulated harmonic analysis indicate that there exists a set of peaks with periods of 1 ± 0.0027 j ( j = 1 , … , 5 ) and 1 ± 0.00025 j ( j = 1 , 2 , 3 ) days. The same situation holds also true for the harmonics higher than the diurnal signal. A model is then adopted based on the discovered periods. This model, which consists of pure and modulated harmonic functions, is shown to be appropriate for assessing the regular variations and ionospheric anomalies. There is a clear maximum TEC at around 22:00 h, which we called the “evening anomaly”. The evening anomaly occurs in the winter and autumn, and is dependent on the solar activities. Also, the Semiannual, Winter, and Equatorial anomalies were investigated. Finally, to investigate the performance of the derived model, the TEC values have been predicted monthly, and the results show that the modulated signals can significantly contribute to obtaining superior prediction results. Compared with the pure signals, the modulated signals can improve a yearly average root mean squared error (RMSE) value in the lower and higher solar activities by 20% and 15%, respectively.

show abstract

Ionosphere Model for European Region Based on Multi-GNSS Data and TPS Interpolation

Cited by 40 publications

References 29 publications

The Prediction of Geocentric Corrections during Communication Link Outages in PPP

The Prediction of Geocentric Corrections during Communication Link Outages in PPP

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

Modeling and Prediction of Regular Ionospheric Variations and Deterministic Anomalies

Contact Info

Product

Resources

About