Vertical Total Electron Content Estimates Research Articles

Ionospheric VTEC and satellite DCB estimated from single-frequency BDS observations with multi-layer mapping function

The ionospheric delays and satellite differential code biases (DCBs) act as the significant error sources in the global navigation satellite system (GNSS) positioning, navigation and timing (PNT) services, and are still challenging to estimate correctly. In this study, the ionospheric vertical total electron content (VTEC) and satellite DCBs are estimated by a refining single-frequency precise point positioning (SFPPP) method based on the multi-layer ionosphere mapping function (MF), as well as the dual-frequency methods, including the carrier-to-code leveling (CCL) and dual-frequency PPP (DFPPP). The solutions isolate the ionospheric VTEC values from the slant ionospheric delay with the generalized trigonometric series function (GTSF) and precisely estimate the satellite DCB with a zero-mean condition. The SFPPP-derived VTEC estimates are validated and evaluated by comparing with the International GNSS Service (IGS) products and using ionosphere-corrected (IC) SFPPP in both static and kinematic scenarios. Using the 74 experimental stations collected from the multi-GNSS experiment (MGEX) network from January to March 2020, the results show that the VTEC estimation precision by applying the multi-layer MF is improved for the SFPPP approach. The positioning performances of the static and kinematic BDS IC SFPPP with the ionospheric correction derived from the multi-layer MF SFPPP are better when compared to the single-layer MF. The estimated BDS DCB with the SFPPP is stable and of high accuracy. The SFPPP approach with multi-layer MF is demonstrated as a promising and reliable method to retrieve the VTEC and satellite DCB with the low-cost property for the GNSS users.

A Least Squares Solution to Regionalize VTEC Estimates for Positioning Applications

A new approach is presented to improve the spatial and temporal resolution of the Vertical Total Electron Content (VTEC) estimates for regional positioning applications. The proposed technique utilises a priori information from the Global Ionosphere Maps (GIMs) of the Center for Orbit Determination in Europe (CODE), provided in terms of Spherical Harmonic (SH) coefficients of up to degree and order 15. Then, it updates the VTEC estimates using a new set of base-functions (with better resolution than SHs) while using the measurements of a regional GNSS network. To achieve the highest accuracy possible, our implementation is based on a transformation of the GIM/CODE VTECs to their equivalent coefficients in terms of (spherical) Slepian functions. These functions are band-limited and reflect the majority of signal energy inside an arbitrarily defined region, yet their orthogonal property is remained. Then, new dual-frequency GNSS measurements are introduced to a Least Squares (LS) updating step that modifies the Slepian VTEC coefficients within the region of interest. Numerical application of this study is demonstrated using a synthetic example and ground-based GPS data in South America. The results are also validated against the VTEC estimations derived from independent GPS stations (that are not used in the modelling), and the VTEC products of international centres. Our results indicate that, by using 62 GPS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the new VTEC estimates in a Precise Point Positioning (PPP) 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 ∼23% and 25% for a day with moderate solar activity while 26% and ∼35% for a day with high solar activity, respectively.

FY-3D and FY-3C onboard observations for differential code biases estimation

With the development of Low Earth Orbit satellites, differential code biases (DCBs) estimation based on onboard observations has been widely studied. In this study, onboard observations of BDS and GPS satellites by the Chinese Fengyun-3D (FY-3D) and Fengyun-3C (FY-3C) satellites are applied to estimate BDS and GPS DCBs. Since only the code observations of C1C and C2W for GPS, and C2I and C7I for BDS are tracked by FY-3D and FY-3C, the DCB types of GPS C1C-C2W and BDS C2I-C7I are estimated with code multipath considered. First, the DCB estimates based on FY-3D onboard observations are analyzed. When jointly processing BDS + GPS onboard observations, the stability of satellite and receiver DCBs for both BDS and GPS has better consistency with the DCB products of the German Aerospace Center (DLR) and the Chinese Academy of Science than that for the single-system solutions (BDS-only solution and GPS-only solution). This is reasonable because more onboard observations are used in BDS + GPS solution, which can improve the strength of the DCB estimation. The variations of receiver DCB are analyzed as a function of geomagnetism and solar activity, but little relationship between them has been found. Compared with the FY-3C solution, the FY-3D solution can achieve a more stable satellite DCB with a stability improvement of 33%, 48%, 62% and 56% for GPS, BDS GEO, IGSO, and MEO satellites, respectively. Meanwhile, the receiver DCB of FY-3D is more stable than that of FY-3C as well. These improvements of satellite and receiver DCBs can be due to the enhancement of FY-3D GNSS Occultation Sounder (GNOS) instrument, which provides more observations with higher quality. Furthermore, both FY-3D and FY-3C onboard observations are processed together to estimate BDS and GPS DCBs. Compared with the FY-3D solution, the stability of satellite DCB can be improved by 16%, 9% and 7% for GPS, BDS GEO and IGSO satellites DCB, respectively, when both FY-3D and FY-3C onboard observations are jointly processed. The impact of DCB estimation on estimating the vertical total electron content (VTEC) is also investigated. Compared with FY-3D GPS-only and BDS + GPS solutions, the VTEC estimates along the FY-3D orbit can achieve more realistic results for FY-3D + FY-3C solution.

Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers

Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary approach to estimate VTEC along with SDCBs from dual-frequency GNSS data, hereinafter referred to as DF approach, consists of two sequential steps. The first step seeks to retrieve ionospheric observables through the carrier-to-code leveling technique. This observable, related to the slant total electron content (STEC) along the satellite–receiver line-of-sight, is biased also by the SDCBs and the receiver differential code biases (RDCBs). By means of thin-layer ionospheric model, in the second step one is able to isolate the VTEC, the SDCBs and the RDCBs from the ionospheric observables. In this work, we present a single-frequency (SF) approach, enabling the joint estimation of VTEC and SDCBs using low-cost receivers; this approach is also based on two steps and it differs from the DF approach only in the first step, where we turn to the precise point positioning technique to retrieve from the single-frequency GNSS data the ionospheric observables, interpreted as the combination of the STEC, the SDCBs and the biased receiver clocks at the pivot epoch. Our numerical analyses clarify how SF approach performs when being applied to GPS L1 data collected by a single receiver under both calm and disturbed ionospheric conditions. The daily time series of zenith VTEC estimates has an accuracy ranging from a few tenths of a TEC unit (TECU) to approximately 2 TECU. For 73–96% of GPS satellites in view, the daily estimates of SDCBs do not deviate, in absolute value, more than 1 ns from their ground truth values published by the Centre for Orbit Determination in Europe.

Sodankylä ionospheric tomography data set 2003–2014

Abstract. Sodankylä Geophysical Observatory has been operating a receiver network for ionospheric tomography and collecting the produced data since 2003. The collected data set consists of phase difference curves measured from COSMOS navigation satellites from the Russian Parus network (Wood and Perry, 1980) and tomographic electron density reconstructions obtained from these measurements. In this study vertical total electron content (VTEC) values are integrated from the reconstructed electron densities to make a qualitative and quantitative analysis to validate the long-term performance of the tomographic system. During the observation period, 2003–2014, there were three to five operational stations at the Fennoscandia sector. Altogether the analysis consists of around 66 000 overflights, but to ensure the quality of the reconstructions, the examination is limited to cases with descending (north to south) overflights and maximum elevation over 60°. These constraints limit the number of overflights to around 10 000. Based on this data set, one solar cycle of ionospheric VTEC estimates is constructed. The measurements are compared against the International Reference Ionosphere (IRI)-2012 model, F10.7 solar flux index and sunspot number data. Qualitatively the tomographic VTEC estimate corresponds to reference data very well, but the IRI-2012 model results are on average 40 % higher than that of the tomographic results.

Correlation analysis of vertical total electron content

It is necessary to model and analyze the ionospheric effects due to a direct relationship between Global Positioning System (GPS) applications and changes in the ionosphere. In order to monitor these changes, the ionosphere can be represented by the vertical total electron content (VTEC) which can be used to analyze ionospheric conditions from a variety of stations. In this study, 21 stations were used to carry out analysis and estimation of VTEC. Three days during a geomagnetic storm, namely, 7, 8, and 9 January 2005, are chosen for investigation. In addition, the de-correlation time of the VTEC was estimated to define ionospheric variations in time using autocorrelation analysis. The de-correlation time of the ionosphere is based on correlation times estimated by using autocorrelation functions. From the high-latitude stations, the mean of the correlation times decreased from 8 to 6 epochs during a storm. In this time period, it was found from the station results that the ionosphere was more affected at the high-latitude than at the mid-latitude region.

Epochwise prediction of GPS single differenced ionospheric delays of formation flying spacecraft

Both single and dual frequency GPS relative navigation filters may benefit from proper predictions of single differenced ionospheric delays. In this article, the single differenced ionospheric delays of GPS observations are predicted for the GRACE formation during the switch manoeuvre. Two prediction methods are considered. The first is based on a Taylor expansion to first order of a mapping function that maps slant total electron content measurements to vertical total electron content estimates. The second method fits a shape profile through undifferenced ionospheric data available. It then raytraces through this profile to estimate the difference in total electron content along the path of the GPS signals. Continuously changing ionospheric conditions hamper the assessment of the quality of the predictions. Comparison of both methods shows that the raytracing method performs better. The difference of predictions and measurements generally shows a smaller RMS than the measurements alone. However, both methods suffer from a number of systematically unpredicted observations, which arise from small unaccounted differential variations in electron densities along the path of the GPS signals. These prediction methods perform better when spacecraft separation is small. Baselines considered here range from tens of kilometres down to several hundred metres. When smallest spacecraft separation occurs (0.4 km), the single differenced ionospheric delays exhibit RMS values of 0.0089 m. The first method shows a difference between measurements and predictions with an RMS of 0.0081 m. For the second method the difference RMS is found to be 0.0067 m.

Regularized estimation of vertical total electron content from GPS data for a desired time period

In this paper a new algorithm for short‐term regularized estimation of vertical total electron content (VTEC) from Global Positioning System (GPS) data is developed. The regularization technique can combine signals, from all GPS satellites for a given instant and a given receiver, for a desired time duration within the 24 hour period without missing any important features in the temporal domain. The algorithm is based on the minimization of a cost function which includes a high pass penalty filter and detrend processing. With an optional weighting function the multipath effects are reduced. A final sliding window median filter is added to enrich the processing and smoothing of the data. The developed regularized estimation algorithm is applied to GPS data for various locations for the solar maximum week of 23–28 April 2001. The parameter set that is required by the estimation algorithm is chosen optimally using appropriate error functions. For this data set the chosen robust and optimum parameters can be used for all latitudes and for both quiet and disturbed days for a minimum of one hour time period. It is observed that the estimated TEC values are in very accordance with the TEC estimates for the 24 hour period. Owing to its 30 s time resolution, the regularized VTEC estimates from the developed algorithm are very successful in representation and tracking of sudden temporal variations of the ionosphere, especially for high latitudes and during ionospheric disturbances.

Regularized estimation of vertical total electron content from Global Positioning System data

A novel regularization technique which can combine signals from all Global Positioning System (GPS) satellites for a given instant and a given receiver is developed to estimate the vertical total electron content (VTEC) values for the 24‐hour period without missing any important features in the temporal domain. The algorithm is based on the minimization of a cost function which also includes a high pass penalty filter. Optional weighting function and sliding window median filter are added to enrich the processing and smoothing of the data. The developed regularized estimation algorithm is applied to GPS data for various locations for the solar maximum week of 23–28 April 2001. The parameter set that is required by the estimation algorithm is chosen optimally using appropriate error functions. This robust and optimum parameter set can be used for all latitudes and for both quiet and disturbed days. It is observed that the estimated TEC values are in general accordance with the TEC estimates from other global ionospheric maps, especially for quiet days and midlatitudes. Owing to its 30 s time resolution, the regularized VTEC estimates from the developed algorithm are very successful in representation and tracking of sudden temporal variations of the ionosphere, especially for high latitudes and during ionospheric disturbances.