An accurate Kriging-based regional ionospheric model using combined GPS/BeiDou observations

2018 ◽  
Vol 12 (1) ◽  
pp. 65-76 ◽  
Author(s):  
Mohamed Abdelazeem ◽  
Rahmi N. Çelik ◽  
Ahmed El-Rabbany
Keyword(s):  
Convergence Time ◽  
Single Frequency ◽  
Kriging Interpolation ◽  
Time Interval ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Ionospheric Model ◽  
Total Electron ◽  
Kriging Interpolation Method ◽  
Regional Ionospheric Model

AbstractIn this study, we propose a regional ionospheric model (RIM) based on both of the GPS-only and the combined GPS/BeiDou observations for single-frequency precise point positioning (SF-PPP) users in Europe. GPS/BeiDou observations from 16 reference stations are processed in the zero-difference mode. A least-squares algorithm is developed to determine the vertical total electron content (VTEC) bi-linear function parameters for a 15-minute time interval. The Kriging interpolation method is used to estimate the VTEC values at a 1 ° × 1 ° grid. The resulting RIMs are validated for PPP applications using GNSS observations from another set of stations. The SF-PPP accuracy and convergence time obtained through the proposed RIMs are computed and compared with those obtained through the international GNSS service global ionospheric maps (IGS-GIM). The results show that the RIMs speed up the convergence time and enhance the overall positioning accuracy in comparison with the IGS-GIM model, particularly the combined GPS/BeiDou-based model.

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 An Enhanced Real-Time Regional Ionospheric Model Using IGS Real-Time Service (IGS-RTS) Products

2015 ◽  
Vol 69 (3) ◽  
pp. 521-530 ◽  
Author(s):  
Mohamed Abdelazeem ◽  
Rahmi N. Çelik ◽  
Ahmed El-Rabbany
Keyword(s):  
Real Time ◽  
Convergence Time ◽  
Single Frequency ◽  
High Solar Activity ◽  
Satellite Orbits ◽  
Electron Content ◽  
Ionospheric Model ◽  
Time Service ◽  
The Real ◽  
Regional Ionospheric Model

Recently, the International Global Navigation Satellite System (GNSS) Service (IGS) has launched the Real-Time Service (IGS-RTS). The RTS products enable real-time precise positioning applications. For single-frequency Real-Time Precise Point Positioning (RT-PPP), ionospheric delay mitigation is a major challenge. To overcome this challenge, we developed a Real-Time Regional Ionospheric Model (RT-RIM) over Europe using the RTS satellite orbits and clock products. The model has spatial and temporal resolution of 1° × 1° and 15 minutes, respectively. Global Positioning System (GPS) observations from 60 IGS and EUREF reference stations are processed using the Bernese 5·2 PPP module in order to extract the Real-Time Vertical Electron Content (RT-VTEC). The PPP convergence time and positioning accuracy using the RTS products is estimated and compared with dual frequency PPP and single-frequency PPP obtained through the combined rapid IGS Global Ionospheric Maps (IGS-GIM) over three consecutive days under high solar activity and one of them under active geomagnetic activity. The results show that the proposed model improves PPP accuracy and convergence time under the mid-latitude region about 40%, 55% and 40% for the horizontal, height and three-dimensional (3D) components respectively in comparison with the IGS-GIM.

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 Smartphone Positioning and Accuracy Analysis Based on Real-Time Regional Ionospheric Correction Model

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3879
Author(s):  
Qi Liu ◽  
Chengfa Gao ◽  
Zihan Peng ◽  
Ruicheng Zhang ◽  
Rui Shang
Keyword(s):  
Real Time ◽  
Convergence Time ◽  
Electron Content ◽  
Ionospheric Model ◽  
Positioning Accuracy ◽  
Correction Model ◽  
The Real ◽  
Gnss Positioning ◽  
Klobuchar Model ◽  
Regional Ionospheric Model

As one of the main errors that affects Global Navigation Satellite System (GNSS) positioning accuracy, ionospheric delay also affects the improvement of smartphone positioning accuracy. The current ionospheric error correction model used in smartphones has a certain time delay and low accuracy, which is difficult to meet the needs of real-time positioning of smartphones. This article proposes a method to use the real-time regional ionospheric model retrieved from the regional Continuously Operating Reference Stations (CORS) observation data to correct the GNSS positioning error of the smartphone. To verify the accuracy of the model, using the posterior grid as the standard, the electron content error of the regional ionospheric model is less than 5 Total Electron Content Unit (TECU), which is about 50% higher than the Klobuchar model, and to further evaluate the impact of the regional ionosphere model on the real-time positioning accuracy of smartphones, carrier-smoothing pseudorange and single-frequency Precise Point Positioning (PPP) tests were carried out. The results show that the real-time regional ionospheric model can significantly improve the positioning accuracy of smartphones, especially in the elevation direction. Compared with the Klobuchar model, the improvement effect is more than 34%, and the real-time regional ionospheric model also shortens the convergence time of the elevation direction to 1 min. (The convergence condition is that the range of continuous 20 s is less than 0.5 m).

scholarly journals Single Point Positioning with Vertical Total Electron Content estimation based on single epoch data

2020 ◽  
Author(s):  
Artur Fischer ◽  
Sławomir Cellmer ◽  
Krzysztof Nowel
Keyword(s):  
Single Point ◽  
Error Reduction ◽  
Ionospheric Delay ◽  
Single Frequency ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Single Point Positioning ◽  
External Data ◽  
Point Positioning

Abstract. This paper proposes a new mathematical method of ionospheric delay estimation in single point positioning (SPP) using a single-frequency receiver. The proposed approach focuses on the ΔVTEC component estimation (MSPPwithdVTEC) with the assumption of an initial and constant value equal to 5 in any observed epoch. The principal purpose of the study is to examine the reliability of this approach to become independent from the external data in the ionospheric correction calculation process. To verify the MSPPwithdVTEC, the SPP with the Klobuchar algorithm was employed as a reference model, utilizing the coefficients from the navigation message. Moreover, to specify the level of precision of the MSPPwithdVTEC, the SPP with the IGS TEC map was adopted for comparison as the high-quality product in the ionospheric delay determination. To perform the computational tests, real code data was involved from three different localizations in Scandinavia using two parallel days. The criterion were the ionospheric changes depending on geodetic latitude. Referring to the Klobuchar model, the MSPPwithdVTEC obtained a significant improvement of 15–25 % in the final SPP solutions. For the SPP approach employing the IGS TEC map and for the MSPPwithdVTEC, the difference in error reduction was not significant, and it did not exceed 1.0 % for the IGS TEC map. Therefore, the MSPPwithdVTEC can be assessed as an accurate SPP method based on error reduction value, close to the SPP approach with the IGS TEC map. The main advantage of the proposed approach is that it does not need external data.

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 A Causal Long Short-Term Memory Sequence to Sequence Model for TEC Prediction Using GNSS Observations

2020 ◽  
Vol 12 (9) ◽  
pp. 1354
Author(s):  
Maria Kaselimi ◽  
Athanasios Voulodimos ◽  
Nikolaos Doulamis ◽  
Anastasios Doulamis ◽  
Demitris Delikaraoglou
Keyword(s):  
Deep Learning ◽  
Total Electron Content ◽  
Short Term Memory ◽  
Convergence Time ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Short Term ◽  
Total Electron ◽  
Term Memory ◽  
Long Short Term Memory

The necessity of predicting the spatio-temporal phenomenon of ionospheric variability is closely related to the requirement of many users to be able to obtain high accuracy positioning with low cost equipment. The Precise Point Positioning (PPP) technique is highly accepted by the scientific community as a means for providing high level of position accuracy from a single receiver. However, its main drawback is the long convergence time to achieve centimeter-level accuracy in positioning. Hereby, we propose a deep learning-based approach for ionospheric modeling. This method exploits the advantages of Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNN) for timeseries modeling and predicts the total electron content per satellite from a specific station by making use of a causal, supervised deep learning method. The scope of the proposed method is to compare and evaluate the between-satellites ionospheric delay estimation, and to aggregate the Total Electron Content (TEC) outcomes per-satellite into a single solution over the station, thus constructing regional TEC models, in an attempt to replace Global Ionospheric Maps (GIM) data. The evaluation of our proposed recurrent method for the prediction of vertical total electron content (VTEC) values is compared against the traditional Autoregressive (AR) and the Autoregressive Moving Average (ARMA) methods, per satellite. The proposed model achieves error lower than 1.5 TECU which is slightly better than the accuracy of the current GIM products which is currently about 2.0–3.0 TECU.

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