Ionospheric Delay Correction Research Articles

Analysis of Ionospheric Delay Correction Model Performance During Geomagnetic Storms

AbstractIonospheric delay, as one of the largest error sources in radio propagation, can only be corrected for this error using the ionospheric delay correction model for Global Navigation Satellite System (GNSS) single‐frequency users. In this paper, the 2021 geomagnetic storm event is selected, and based on the measured ionospheric data from the GNSS observatory, the perturbation of the ionosphere by the geomagnetic storm event is analyzed, and it is found that the response of the ionosphere to the geomagnetic storm has obvious differences in the response characteristics and response time in different latitude regions. The performance of the global ionospheric map (GIM), the empirical model, and the broadcast ionospheric model during the geomagnetic storm‐induced ionospheric perturbation is analyzed and the change in the accuracy of each ionospheric model during the geomagnetic storm‐induced ionospheric perturbation is investigated, using the measured electron content of the GNSS as a benchmark. The results show that there is good agreement between the GIM products and the measured electron content during the period of ionospheric calm and the period of ionospheric perturbation. It is worth noting that geomagnetic storms do not necessarily lead to a decrease in the accuracy of ionospheric delay‐correction models, and in some cases, the models that were originally under‐accurate show a tendency to improve their accuracy during the period of perturbation instead. Neither the broadcast ionospheric model nor the electron content of the empirical model output responds to geomagnetic storm‐induced ionospheric perturbations.

Investigation of the Contribution of Five Broadcast Ionospheric Models (GPSK, NTCMG, NEQG, BDGIM, and BDSK) and IRTG to GNSS Positioning During Different Solar Activities in Solar Cycle 25

AbstractAdditional ionospheric information is essential for mitigating errors in single‐frequency (SF) Global Navigation Satellite Systems (GNSS) positioning. The increasing number of low‐cost dual‐frequency (DF) receiver users faces limitations in tracking DF observables compared to traditional geodetic receivers. Consequently, ionospheric correction algorithms (ICAs) are also essential for low‐cost DF devices in hybrid‐frequency positioning. To evaluate the performance of commonly used ICAs during solar cycle 25, our study presents a global statistical investigation of the contribution of five broadcast ionospheric models (BIMs) and the International GNSS Service (IGS) combined real‐time global ionospheric maps (IRTG) to the positioning domain, covering both quiet and perturbed ionospheric conditions. The BIMs investigated include the GPS Klobuchar (GPSK), Galileo NequickG (NEQG), NTCM‐GlAzpar (NTCMG), BDS‐2 Klobuchar (BDSK), and BeiDou Global Ionospheric delay correction Model (BDGIM). Experimental results from standard point positioning indicate that IRTG demonstrates superior overall accuracy compared to all BIMs, with a mean 3D root mean squared (RMS) of 2.76 m during perturbed period. Specifically, GPSK, NTCMG, NEQG, BDGIM, and BDSK exhibit RMS values of 2.03, 1.67, 1.72, 1.62, and 2.36 m during quiet conditions, and 4.02, 3.17, 2.86, 3.14, and 4.44 m during perturbed conditions, respectively. Among the BIMs, NEQG demonstrates superior performance at middle and high latitudes but exhibits lower accuracy than NTCMG and BDGIM at low latitudes during daytime under quiet conditions. BDGIM performs slightly better than NTCMG at low latitudes but slightly worse at high latitudes. BDSK shows notable improvement for high‐ and mid‐latitude regions since 3 June 2020.

Implementation and testing of single point positioning on IRNSS/NavIC receiver data

SummaryIndia has developed its own regional navigation satellite system called the Indian Regional Navigation Satellite System (IRNSS), also known as Navigation with Indian Constellation (NavIC). IRNSS/NavIC provides standard positioning and timing services for civilians and restricted services for authorized users. In this paper, single point positioning is implemented on the NavIC receiver data. Estimation techniques of the least squares method and extended Kalman filter are implemented after applying broadcast‐based clock corrections, orbit computation, relative time correction, and ionosphere delay correction for single and dual frequency. A data extraction and storage module is developed to store computed parameters at every intermediate stage in separate files. This is followed by an error plotter module to plot the extracted parameters for each satellite and to separately analyze their performance and the obtained errors. The estimated receiver position is visualized on Google Earth. The absolute error in both estimation techniques ranges between 5 and 15 m throughout the period.

Analyzing the spatial variation characteristics of grid TEC using long-term GIM data

Global ionosphere maps (GIM), a grid model generated based on observations from global GNSS stations, is often used for ionospheric delay correction and total electron content (TEC) analysis, and is an important data for ionospheric modeling and code bias estimation, as well as related applications. Understanding the spatial variation characteristics of the grid TEC in GIM data can help the better use of GIM data. In this paper, the GIM data of CODE (Center for Orbit Determination in Europe) analysis center for a total of 15 years from 2008 to 2022 are used to analyze the variation of TEC of adjacent grid points and the difference of TEC of four grid points in each grid. The results show that the mean values of the grid TEC variations range from about 0.26–1.86 TECu in the longitude direction and 0.36–2.76 TECu in the latitude direction, and most of the differences in the TECs of neighboring grid points are within ± 2 TECu. In the low solar activity years, the STD of the TEC of the four grid points in most of the grids in the GIM data is less than 1.2 TECu, indicating that the TEC values of the four grid points in most of the grids in their GIMs are relatively close to each other and the differences are small, whereas the differences are larger in the high solar activity years. In other words, the TEC values of the areas covered by the GIM grids in the low solar activity years are close. The results of the study can provide some references and lessons for the interpolation and application of the TEC of the GIM grid, and the TEC modeling of the single-station area.

A Two-Step Regional Ionospheric Modeling Approach for PPP-RTK.

In the precise point positioning/real-time kinematic (PPP-RTK) technique, high-precision ionospheric delay correction information is an important prerequisite for rapid PPP convergence. The commonly used ionospheric modeling approaches in the PPP-RTKs only take the trend term of the ionospheric total electron content (TEC) variations into account. As a result, the residual ionospheric delay still affects the positioning solutions. In this study, we propose a two-step regional ionospheric modeling approach that involves combining a polynomial fitting model (PFM) and a Kriging interpolation (KI) model. In the first step, a polynomial fitting method is used to model the trend term of the ionospheric TEC variations. In the second step, a KI method is used to compensate for the residual term of the ionospheric TEC variations. Datasets collected from continuously operating reference stations (CORSs) in Hunan Province, China, are used to validate the PFM/KI method by comparing with a single PFM method and a combined PFM and inverse distance weighting interpolation (IDWI) method. The experimental results show that the two-step PFM/KI modeled ionospheric delay achieves an average root mean square (RMS) error of 1.8 cm, which is improved by about 48% and 23% when compared with the PFM and PFM/IDWI methods, respectively. Regarding the positioning performance, the PPP-RTK with the PFM/KI method takes an average of 1.8 min or 4.0 min to converge to a positioning accuracy of 1.3 cm or 2.5 cm in the horizontal and vertical directions, respectively. The convergence times are decreased by about 18% and 14% in the horizontal direction and 9% and 5% in the vertical direction over the PFM and the PFM/IDWI methods, respectively.

Characteristic analysis of the differences between total electron content (TEC) values in global ionosphere map (GIM) grids

Abstract. Using total electron content (TEC) from a global ionosphere map (GIM) for ionospheric delay correction is a common method of eliminating ionospheric errors in satellite navigation and positioning. On this basis, the TEC of a puncture point can be obtained by GIM grid TEC interpolation. However, in terms of grid, only few studies have analyzed the TEC value size characteristics of its four grid points, that is, the TEC difference characteristics among them. In view of this, by utilizing the GIM data from high solar-activity years (2014) and low solar-activity years (2021) provided by CODE (Center for Orbit Determination in Europe), this paper proposes the grid TEC difference as a way of analyzing TEC variation characteristics within the grid, which is conducive to exploring and analyzing the variation characteristics of the ionosphere TEC in the single-station area. The value is larger in high solar-activity years and generally small in low solar-activity years, and the value of high-latitude areas is always smaller than that of low-latitude areas. Specifically, in high solar-activity years, most of the GIM grid TEC internal differences are within 4 TECu (1 TECu = 1016 electrons m−2) in high-latitude and midlatitude regions, while only 78.17 % are in low-latitude regions. In low solar-activity years, the TEC difference values within a GIM grid are mostly less than 2 TECu, and most of them in the high and middle latitudes are within 1 TECu. The main finding of this analysis is that the grid TEC differences are small for most GIM grids, especially in the midlatitudes to high latitudes of low solar years. This means that relevant extraction methods and processes can be simplified when TEC within these GIM grids is needed.

Ionospheric Delay Phase Estimation and Correction for Multiple-aperture InSAR: Azimuth Group Phase Delay Method

Ionospheric Delay Phase Estimation and Correction for Multiple-aperture InSAR: Azimuth Group Phase Delay Method

Analysis of spatial–temporal characteristics for BDS-3 broadcast ionospheric models (BDS Klobuchar and BDGIM) in multi-GNSS real-time single-frequency precise point positioning

With the full operation of BDS-3 broadcast ionospheric models, i.e., the BeiDou global ionospheric delay correction model (BDGIM) and the BDS Klobuchar model, its impact on the multi-GNSS real-time (RT) single-frequency (SF) precise point positioning (PPP) needs to be investigated for low-cost GNSS users. The GPS Klobuchar model as a reference is also considered in this study. Two types of SF-PPP models including the ionosphere-corrected (IC) and ionosphere-weighted (IW) strategies are adopted in the positioning domain. GPS + GLONASS + Galileo + BDS-3 observations from 40 multi-GNSS experiment (MGEX) stations distributed in different latitudes are selected for conducting RT SF-PPP during the ionospheric quiet and active periods. The experiment shows that the positioning accuracy of IC RT SF-PPP can be degraded with the increase of the ionospheric activity levels or the decrease of latitudes. Except for low-latitude regions during the ionospheric active period, the 3D positioning accuracy of the northern hemisphere can be improved by at least 15.2 % compared to the southern hemisphere in the IC model with the BDS Klobuchar. The BDGIM model has the best performance among all IC RT SF-PPP solutions, but its 3D positioning accuracy can reach the sub-meter level only in mid-latitude regions. With the adoption of ionospheric constraints, the convergence of the IW model is always superior to that of the group and phase ionospheric correction (GRAPHIC) model, and the improvement of convergence in mid-latitude regions is clearly better than that in low-latitude regions. Due to the quality limitation of the BDS Klobuchar model, it has the longest convergence time among all IW models regardless of ionospheric conditions or latitude regions. Compared to the GPS Klobuchar, the significant improvement of convergence for the BDGIM-constrained RT SF-PPP is mainly presented in low-latitude regions of the northern hemisphere. The horizontal positioning accuracy of the BDGIM-constrained model is always improved in comparison with the GRAPHIC model, but there is a degradation in the vertical component, and the improvement of 3D positioning accuracy is no more than 11.7 %. In summary, the BDGIM-constrained model has the best performance among all RT SF-PPP solutions, its 3D positioning accuracy has the ability to achieve 0.25 m at present.

A Multi-Parameter Empirical Fusion Model for Ionospheric TEC in China’s Region

This article takes the measured Total Electron Content (TEC) from the GPS points of the China Regional Crust Observation Network as the starting point to establish a regional ionospheric empirical model. The model’s performance is enhanced by considering solar flux and geomagnetic activity data. The refinement function model of the ionospheric TEC diurnal variation component, seasonal variation component, and geomagnetic component is studied. Using the nonlinear least squares method to fit undetermined coefficients, MEFM-ITCR (Multi-parameter Empirical Fusion Model–Ionospheric TEC China Regional Model) is proposed to forecast the regional ionosphere TEC in China. The results show that the standard deviation of MEFM-ITCR residuals is 3.74TECU, and MEFM-ITCR fits the modeling dataset well. Analyses of geographic location variation, seasonal variation, and geomagnetic disturbance were carried out for MEFM-ITCR performance. The results indicate that in the Chinese region, MEFM-ITCR outperforms IRI2020 and NeQuick2 models in terms of forecast accuracy, linear correlation, and model precision for TEC measured using GPS points under different latitudes and longitudes, different seasons, and different geomagnetic disturbances. The empirical TEC model built for the Chinese region in this paper provides a new ionospheric delay correction method for GNSS single frequency users and is of great significance for establishing other new and improving existing ionospheric empirical models.

Investigating the contribution of BDS-3 observations to multi-GNSS single-frequency precise point positioning with different ionospheric models

Due to the advantages of low-cost and high precision, single-frequency precise point positioning (SF-PPP) plays a vital role in the booming market of the SF global navigation satellite system (GNSS) receivers. With the full completion of the BeiDou global navigation satellite system (BDS-3), its contribution to single-GNSS SF-PPP is worthy of comprehensive exploration. In this study, three SF-PPP models including ionosphere-corrected (IC), ionosphere-free (IF), and ionosphere-weighted (IW) strategies are analyzed, and four ionospheric models including the GPS Klobuchar, BDGIM (BeiDou global ionospheric delay correction model), CNES real-time VTEC (vertical total electron content) and GIM (global ionospheric maps) are used for conducting SF-PPP. As to GPS/GLONASS/Galileo-only IC SF-PPP, its 3D positioning accuracy can be improved by 6.9–11.6 % with the adoption of BDS-3 observations. Similarly, for the IF SF-PPP solution, the corresponding positioning accuracy and convergence time can be improved by at least 17.3 and 38.3 %, respectively. In IW SF-PPP, the convergence performance of the CNES-VTEC-constrained SF-PPP is much better than that of both GPS Klobuchar- and BDGIM-constrained solutions. When using the BDGIM constraints, the horizontal/vertical convergence time of GPS/Galileo + BDS-3 solutions can be shortened by at least 16.5/27.9 % in comparison with GPS/Galileo-only solutions. While for GIM-constrained SF-PPP, the convergence improvement is only shown in the vertical component. In summary, the GIM-constrained SF-PPP with quad-system observations has the best performance, compared to IF solution, its convergence time can be shortened by 82.8 % to 5.5 min in horizontal and 29.7 % to 26.0 min in vertical when converging to 0.3 m. Note that the corresponding improvements in the BDGIM-constrained solution are relatively limited with only 5 %. At present, the quad-system IW SF-PPP has the ability to achieve cm-level fast positioning, with an RMS of 0.06 m in horizontal, showing promising applications in engineering and scientific fields.

A revised BDS Klobuchar model with a non-symmetrical processing strategy and a high-latitude amplitude constraint

The BeiDou Navigation Satellite System (BDS) broadcasts the BDS Klobuchar model (BDSK) for ionospheric delay correction in both BDS-2 regional service phase and BDS-3 global service phase. Unlike the GPS Klobuchar model, the BDSK model adopts a simple “symmetrical strategy” due to the limited ionospheric input data within China, which results in inaccurate total electron content (TEC) estimation in the southern hemisphere. Besides, the “high latitude anomaly” occurs in the BDSK model due to the lack of latitude limitation strategy, which deteriorates the accuracy of the BDSK model in the southern hemisphere further. To solve this problem, we propose a revised BDS Klobuchar model (RBDK), in which the “non-symmetrical strategy” is adopted in the southern hemisphere and an amplitude constraint is introduced at high latitudes. For comparison, the fitted BDS Klobuchar model (BDFK) that is estimated using the same ionospheric input data and constraint algorithm for the RBDK model but with the “symmetrical strategy” is also included. First, we conduct a comparative analysis of the time series of the eight parameters for the BDSK, BDFK and RBDK models in 2021. The parameters of the BDFK and RBDK models are more stable, and there will be no abnormal jumping phenomenon that occurs in the BDSK model. Then, the performance of the broadcast BDSK model, the fitted BDFK model and the proposed RBDK model during the whole year of 2021 are evaluated by comparing them with the high-precision global ionospheric map (GIM) of the International GNSS Service (IGS). In the southern hemisphere, the root mean square (RMS) values of the BDSK and BDFK are 6.5 and 5.8 TEC unit (TECU), respectively, while that of the RBDK is 4.6 TECU, showing improvements of 29% and 21%, respectively. At high latitudes in the northern hemisphere, the RMS value of the BDSK is 7.6 TECU, while they are only 3.7 TECU for the RBDK and BDFK when the amplitude constraint is introduced. Final, we select 16 IGS stations to validate the performance of the BDSK, BDFK and RBDK models in the standard point positioning (SPP) domain in 2021. The average SPP accuracy of the BDSK is 8.88 m at 6 high-latitude stations, while they are 5.48 m for the RBDK and BDFK, showing significant improvement of 38%. Excluding the high-latitude stations, the SPP accuracy of the RBDK outperforms the BDFK and BDSK by 14% and 18%, respectively, at stations in the southern hemisphere. As expected, the proposed RBDK model shows significantly better performance in the southern hemisphere and at high latitudes in contrast to the broadcast BDSK model.

Time Series InSAR Ionospheric Delay Estimation, Correction, and Ground Deformation Monitoring With Reformulating Range Split-Spectrum Interferometry

Time Series InSAR Ionospheric Delay Estimation, Correction, and Ground Deformation Monitoring With Reformulating Range Split-Spectrum Interferometry

Ionospheric Phase Delay Correction for Time Series Multiple-Aperture InSAR Constrained by Polynomial Deformation Model

As a supplement to time-series interferometric synthetic aperture radar (TS-InSAR), time-series multiple-aperture InSAR (TS-MAI) can measure the spatiotemporal changes in SAR along-track surface deformation. TS-MAI is often applied with low-frequency SAR data (e.g., L-band data) due to its ability to retain high interferometric coherence. However, the low-frequency SAR signal is vulnerable to ionospheric delays, which can significantly degrade the measurement accuracy of TS-MAI. This letter presents an approach to correct the ionospheric errors in TS-MAI. A polynomial cubic model is employed to constrain the ground deformation, which is then incorporated into the observation model for effectively separating the deformation signal and the ionospheric delays. The proposed method is tested using the L-band ALOS-1 PALSAR-1 datasets covering the Tocopilla area in Chile between November 2007 and March 2011. The correction performance and accuracy of the proposed method are demonstrated by comparing the range split-spectrum interferometry (RSSI)-based method and the local GPS data, respectively. The root mean square error (RMSE) improvement rates between TS-MAI and GPS are 72.17% for the SRGD site and 84.51% for the VLZL site, and their correlation coefficients increase from 0.23 and 0.50 to 0.52 and 0.61 after the correction.

A New GNSS TEC Neural Network Prediction Algorithm With the Data Fusion of Physical Observation

This work models and predicts anomalous jumps in GNSS total electron content (TEC) caused by geomagnetic disturbance or solar radiation by introducing F10.7 and regional Dst indices, which are used to characterize solar radiation and geomagnetic disturbance status, respectively. We then introduced long-distance constraint stations to restrain ionospheric variations during high solar activity, which reduced the influence of unmodelled factors on prediction accuracy. In our experimental work, Global Ionosphere Map (GIM) TEC data from 11 stations located at different latitudes were used for comparison during maximum (2014) and minimum (2018) of solar cycle 24. Sample data for >27 days were used for learning, and then ionospheric changes for the whole year were predicted using the sliding window method. The results showed that, the standard deviation for the global ionospheric prediction products could be guaranteed to be within 2 TECU. The proximity station constraint method proposed in this paper and the Dst high-order polynomial correction method during geomagnetic disturbance control the prediction error within -4.4 TECU, while the change of adjacent days is -51.4 TECU in 2014. The new algorithm reduced the TEC jump effect in predictions, and the prediction of ionospheric products provided by this algorithm can meet the basic requirements of ionospheric delay correction in high-precision positioning.

Performance research of real-time kinematic/5G combined positioning model

The global navigation satellite system provides real-time and all-weather positioning with high accuracy. Under a good observational environment, short-baseline real-time kinematic (RTK) can provide centimeter-level positioning results. However, RTK without model correction of ionospheric delay can significantly reduce the positioning accuracy, and cannot achieve fast and high-precision positioning when the baseline is too long or heavily occluded. Therefore, we propose a combined RTK/fifth-generation (5G) mobile communication technology positioning model by combining global positioning system-RTK with 5G time-of-arrival observations to improve the positioning accuracy under medium and long baselines. Experimental validation and analysis were conducted based on the measured data of different baseline lengths. The results revealed that the combined RTK/5G positioning model markedly improved the positioning performance in both static and dynamic modes under medium- and long-distance baselines. In particular, the RTK/5G model can also achieve good positioning results in conditions where some satellites are occluded. The combined RTK/5G positioning model is important for achieving high-accuracy, real-time, and continuous positioning in complex environments.

Enhanced neural network model for regional ionospheric modeling and evaluation under different solar-geomagnetic conditions

Monitoring spatiotemporal variations of ionospheric vertical total electron content (VTEC) is crucial for space weather and satellite positioning. In the present study, an enhanced neural network (ENN) model is proposed to capture the changing characteristics of ionospheric VTEC and compared with the traditional mathematical models, i.e. the POLYnomial (POLY) model, generalized trigonometric series function and spherical harmonic function (SHF) model. The ionospheric VTEC data obtained from 31 permanent global positioning system stations in the southwest region of China on 26 August and 8 September, 2017, were used to test the performance of the mentioned models under different Solar-geomagnetic conditions. The ENN model is derived from the ensemble learning method, and the disadvantage that simple backpropagation neural network learners that are not robust enough is weakened by the ENN model. After statistical analysis and single-frequency precise point positioning (SF-PPP) experiments, it is demonstrated that the ENN model is superior to the above three mathematical models, regardless of the solar-geomagnetic conditions. In terms of mean absolute error, root mean square error, standard deviation, and mean absolute percentage error, the ENN model outperforms the SHF model, which is the best mathematical model in the analysis, by 40.7%, 30.20%, 29.88%, 38.04% under quiet solar-geomagnetic conditions, and by 37.66%, 29.93%, 30.96%, 32.01% under active solar-geomagnetic conditions. In addition, the accuracy of the SF-PPP is greatly affected by the error caused by ionosphere. In the static SF-PPP experiment of this study, the ENN model can better correct ionospheric error. Under quiet and active solar-geomagnetic conditions, the SF-PPP accuracy can be improved by 85.1% and 85.2% with the ionosphere delay correction from the ENN model.

Quasi-4-dimension ionospheric modeling and its application in PPP

Ionospheric delay modeling is not only important for Global Navigation Satellite System (GNSS) based space weather study and monitoring, but also an efficient tool to speed up the convergence time of Precise Point Positioning (PPP). In this study, a novel model, denoted as Quasi-4-Dimension Ionospheric Modeling (Q4DIM) is proposed for wide-area high precision ionospheric delay correction. In Q4DIM, the Line Of Sight (LOS) ionospheric delays from a GNSS station network are divided into different clusters according to not only the location of latitude and longitude, but also satellite elevation and azimuth. Both Global Ionosphere Map (GIM) and Slant Ionospheric Delay (SID) models that are traditionally used for wide-area and regional ionospheric delay modeling, respectively, can be regarded as the special cases of Q4DIM by defining proper grids in latitude, longitude, elevation, and azimuth. Thus, Q4DIM presents a resilient model that is capable for both wide-area coverage and high precision. Four different sets of clusters are defined to illustrate the properties of Q4DIM based on 200 EUREF Permanent Network (EPN) stations. The results indicate that Q4DIM is compatible with the GIM products. Moreover, it is proved that by inducting the elevation and azimuth angle dependent residuals, the precision of the 2-dimensional GIM-like model, i.e., Q4DIM 2-Dimensional (Q4DIM-2D), is improved from around 1.5 Total Electron Content Units (TECU) to better than 0.5 TECU. In addition, treating Q4DIM as a 4-dimensional matrix in latitude, longitude, elevation, and azimuth, whose sparsity is less than 5%, can result in its feasibility in a bandwidth-sensitive applications, e.g., satellite-based Precising Point Positioning Real-Time Kinematic (PPP-RTK) service. Finally, the advantages of Q4DIM in PPP over the 2-dimensional models are demonstrated with the one month's data from 30 EPN stations in both high solar activity year 2014 and low solar activity year 2020.

High-order ionospheric delay correction of GNSS data for precise reduced-dynamic determination of LEO satellite orbits: cases of GOCE, GRACE, and SWARM

High-order ionospheric delay correction of GNSS data for precise reduced-dynamic determination of LEO satellite orbits: cases of GOCE, GRACE, and SWARM

A BDGIM-Based Phase-Smoothed Pseudorange Algorithm for BDS-3 High-Precision Time Transfer

Single point positioning (SPP) can meet the requirements of the majority of real-time time transfer applications. Meanwhile, a single-frequency (SF) receiver is cheaper than a dual-frequency receiver. However, SPP performance can be greatly affected by large pseudorange observation noise. Phase smoothing the pseudorange is an effective approach to reduce pseudorange noise. Since the classical phase-smoothed pseudorange algorithm does not account for the effect of ionosphere delay, we propose a BDGIM-based phase-smoothed pseudorange algorithm to eliminate the ionospheric delay and apply it to BeiDou Navigation Satellite System (BDS-3) SPP time transfer. In this paper, we first evaluate the performance of the BeiDou global ionospheric delay correction model (BDGIM) and compare it with that of the BeiDou Klobuchar model to determine if it is practical to incorporate the BDGIM into our suggested method. The performance of the BDGIM is better than that of the Klobuchar model. The mean RMS value of the BDGIM is 2.6 Total Electron Content Unit (TECU). The average ionospheric correction rate of the BDGIM is 75.5%. Then, we investigate the performance of the improved SF SPP time transfer. The performance of the improved SPP time transfer is much better than that of the traditional SPP time transfer. Compared with the traditional time transfer, the average Type A uncertainty of the improved time transfer is 2.08 ns, which is reduced by about 11.1% from the time transfer without it. Regarding frequency stability, the modified Allan deviations of the improved time transfer are 1.43E-12 and 1.68E-13 at 960 s and 61,440 s, with improvements of 51.2% and 59.9%, respectively.

Evaluation of Seasonal Variability of First-Order Ionospheric Delay Correction at L5 and S1 Frequencies Using Dual-Frequency NavIC System

For the precise positioning applications it is important to determine and eliminate the positioning error introduced by various sources such as the ionosphere. To develop a standalone precise navigation system, India has launched the seven satellite constellations for NavIC (Navigation with Indian Constellation) system which can provide precision positioning over India and surrounded landmass. Since the ionospheric delay depends on the frequency of the satellite signal and NavIC systems work at different frequencies L5 and S1 than Global Positioning System (GPS) at L1 and L2, it is not possible to use the GPS data-driven study for NavIC based location calculations directly. Thus there is a need for a specialized ionospheric study for NavIC systems. In addition, the ionospheric delay is directly proportional to Slant Total Electron Content (STEC) which is dependent upon diurnal and seasonal solar activity. To achieve accurate positioning facilities, there is also a need for evaluation for seasonal variability of ionospheric delay correction for NavIC receivers. This paper deals with the STEC estimation; it's smoothing, and removal of instrumental biases from STEC. The determined true STEC has been used to determine first-order ionospheric delay correction at L5 and S1 frequencies. The delay correction at S1 has been found less (2–7 m) as compared to L5 (10–30 m). Furthermore, the seasonal variability of ionospheric delay has been analyzed using about 19 months of data (from June 2017 to December 2018) and found that the ionospheric delay follows unique seasonal characteristics which can be utilized for delay modeling. It has been also observed that the geostationary satellites of the NavIC system are more appropriate than geosynchronous satellites for ionospheric related studies.