PPP at low latitudes with ionospheric model exclusively based on single frequency GNSS measurements

1. Introduction In satellite-based navigation and positioning, the ionospheric delay is considered a crucial error source. In low latitudes, for instance, the precise point positioning (PPP) accuracy is severely affected by the high ionospheric variability (Veettil etal.,2020). Autonomous receivers that operate on two or more frequencies can eliminate up to 99.9% of the ionospheric delay by using the so-called ionospheric free combination. However, single frequency receivers are not capable to form the dual frequency combinations and are therefore dependent on the ionospheric delay derived by ionospheric models (Rovira-Garcia etal.,2020). Global Ionospheric Maps (GIMs) are products based on Global Navigation Satellite System (GNSS) data vastly used to represent the ionosphere and improve single frequency positioning. Since 1998, the GIMs are computed by the Ionosphere Associated Analysis Centers (IAACs) and provided by the International GNSS Service (IGS) (Hernández-Pajares etal.,2009). Currently, there are eight IAACs that provide GIMs: the Center for Orbit Determination in Europe (CODE), European Space Agency (ESA), Jet Propulsion Laboratory (JPL), Universitat Politecnica de Catalunya (UPC), Chinese Academy of Science, Wuhan University (WHU), Natural Resources Canada (NRCan), and Operational Tool for Ionospheric Mapping And Prediction/Deutsches Geodätisches ForschungsinstitutTechnische Universität München (OPTIMAP/DGFI-TUM) (Feltens & Schaer,1998; Goss etal.,2019; Roma-Dollase etal.,2018). Different estimation techniques have been developed by each center. CODE, ESA, NRCan, and WHU generate GIMs using spherical harmonic (SH) series expansion (Goss Abstract Single frequency users of the Global Navigation Satellite System (GNSS) should correct the ionospheric delay to obtain positioning solutions. A valuable source of ionospheric delay corrections is the global ionospheric models (GIMs) of Vertical Total Electron Content. The accuracy of GIMs is therefore important to improve the positioning accuracy. One of the main issues that affects the GIM performance, especially at low latitude regions, is the high sensitivity of the global positioning system (GPS) L2 frequency to ionospheric scintillation. As an attempt to overcome this issue, in this work, we study the capabilities of using only GPS L1 frequency to compute ionospheric corrections in form of regional ionospheric maps. The performance of the new ionospheric model is evaluated by means of single frequency precise point positioning, comparing the positioning results against the correction using dual-frequency GPS signals, as well as compared to the corrections provided by GIMs produced by the international GNSS service. As a result, the positioning performance using single frequency model presented similar accuracy to the dual frequency models and, at the same time, provided less observations affected by ionospheric scintillations. These results demonstrate the feasibility of using single frequency GNSS data to develop ionospheric models and to improve the positioning over low latitudes. Plain Language Summary Precise Point Positioning (PPP) is a technique used to determine the position of a receiver on the Earth’s surface using signals from Global Navigation Satellite Systems (GNSS), which are transmitted with a minimum of two frequencies. The ionosphere, an ionized layer in the Earth’s atmosphere, can cause errors in GNSS signals and affect the PPP accuracy. To improve accuracy, an ionospheric model can be used to correct these errors. In this study, we assess an single frequency ionospheric model. The results show that it is possible to use single frequency GNSS data to develop ionospheric models that can improve positioning accuracy over low latitudes. CHRISTOVAM ETAL. © 2023. The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. PPP at Low Latitudes With Ionospheric Model Exclusively Based on Single Frequency GNSS Measurements Ana L. Christovam1 , Fabricio S. Prol2, Gabriel O. Jerez1, Manuel Hernández-Pajares3 , and Paulo O. Camargo1 1Department of Cartography, São Paulo State University (UNESP), São Paulo, Brazil, 2Department of Navigation and Positioning, Finnish Geospatial Research Institute, National Land Survey of Finland, Espoo, Finland, 3Department of Mathematics, UPC-IonSAT and UPC-IEEC Research Groups, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain Key Points: • Single frequency ionospheric models allows to obtain similar precise point positioning accuracy than dual frequency ionospheric models • Single frequency Global Navigation Satellite System measurements provide more IPPs than dual frequency during ionospheric scintillation events Correspondence to: A. L. Christovam, [email protected] Citation: Christovam, A. L., Prol, F. S., Jerez, G. O., Hernández-Pajares, M., & Camargo, P.O. (2023). PPP at low latitudes with ionospheric model exclusively based on single frequency GNSS measurements. Space Weather, 21, e2023SW003513. https://doi.org/10.1029/2023SW003513 Received 30 MAR 2023 Accepted 4 JUL 2023 Author Contributions: Conceptualization: Fabricio S. Prol Supervision: Fabricio S. Prol, Manuel Hernández-Pajares, Paulo O. Camargo Writing – review & editing: Fabricio S. Prol, Gabriel O. Jerez, Manuel Hernández-Pajares 10.1029/2023SW003513 RESEARCH ARTICLE 1 of 13 Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 2 of 13 etal.,2020; Li etal.,2015; Roma-Dollase etal.,2018). The technique adopted by JPL is bi-cubic splines whereas UPC adopted the tomographic approach (Hernández-Pajares etal.,1999; Mannucci etal.,1998). The OPTIMAP use polynomial B-spline for the ionospheric modeling (Goss etal.,2020). Common to all products is the data distribution provided in IONosphere map EXchange (IONEX) format with a spatial resolution 5°×2.5° in longitude and latitude, respectively, and with a temporal resolution from 15min to 2hr (Hernández-Pajares etal.,2017; Schaer etal.,1998). The GIMs provide Total Electron Content (TEC) from hundreds of worldwide permanent GNSS receivers, normally computed from dual frequency measurements (Hernández-Pajares etal.,1999; Mannucci etal.,1998; Schaer etal.,1996). Carrier phase ambiguities and DCBs are essential parameters estimated by IAACs. The process for estimating DCBs and ambiguities is known as the TEC calibration method, which can be performed either network-wide, such as in the case of GIMs, or with individual GNSS stations (Ciraolo etal.,2007; Prol, Camargo, etal.,2018; Shaikh,2023). The performance of GIMs generated by IGS is consistent within the IAACs (Hernández-Pajares etal.,2009), but usually provides lower performance in low latitude regions, especially during ionospheric scintillation events. Prol, Camargo, etal.(2018), for instance, evaluate the performance of TEC calibration procedures by analyzing the improvement in single frequency PPP considering several latitudes. The authors found a worse PPP performance in low latitudes, mainly due to the ionospheric variability associated with the Equatorial Ionization Anomaly (EIA) and ionospheric scintillation. Rovira-Garcia etal.(2020) additionally assess the quality of the ionospheric models by GNSS positioning and showed larger positioning errors in receivers located at latitudes close to the geomagnetic equator. One of the main challenges in ionospheric modeling at low latitudes is the presence of ionospheric irregularities that can result in the lack of continuous GNSS operation, especially in global positioning system (GPS) L2 frequency. The influence of the ionosphere is different for each frequency since the ionosphere is a dispersive medium, where higher frequencies are less affected when compared with lower frequencies. Delay etal.(2015) show that, during the presence of ionospheric irregularities, the probability of interrupted tracking was larger on GPS L2 and L5 than on the L1 signal frequency. Similarly, Moraes etal.(2017) also present that during the ionospheric irregularities' occurrence, the GPS L1 signal is less sensitive to loss of locks than the L2 frequency. Given that GPS L1 performs better than GPS L2 frequency, it is reasonable to investigate the possibility to develop ionospheric models exclusively based on GPS L1 frequencies. In this regard, Christovam etal.(2023) present a regional ionospheric model developed for the low latitude region only using single-frequency data. The main disadvantage is that the single frequency TEC measurements is highly dependent on the code noise. Nevertheless, Christovam etal.(2023) have shown that models exclusively based on GPS L1 can be used to detect and analyze equatorial plasma bubbles, despite of the code noise and multipath, which can be strongly mitigated for single-frequency ionospheric monitoring (Hernández-Pajares etal.,2018). Built on this previous work, we intend here to verify whether models exclusively based on GPS L1 frequencies can also be used to improve the single-frequency PPP performance. The main goal is to verify if the single frequency PPP based on single frequency ionospheric model can provide comparable level to those ionospheric models obtained by dual frequency GNSS measurements. In this intend, the PPP performance obtained with the model developed by Christovam etal.(2023) is compared with the single frequency PPP results aided by other consolidated models. Section2 presents an overview of the method developed by Christovam etal.(2023) based on single frequency data and some modifications for dual frequency data. In addition, Section2 also presents the configurations used to run the single frequency PPP solutions. Section3 presents an initial validation of TEC values obtained by the single and dual frequency models. It also includes a brief discussion about the impact of ionospheric variability on GPS frequencies, as well as an assessment of single frequency PPP based on the single frequency ionospheric model. Section4 presents the conclusions. 2. Method Section2.1 presents an overview of the ionospheric model proposed by Christovam etal.(2023) exclusively based on single frequency data, as well as the adaptations required to run the same model using dual frequency data. The dual frequency model is presented here to have a base for comparison purposes. Additionally, Section2.2 shows the configuration used to run the single frequency PPP solutions. The PPP algorithm is used as main indicator to evaluate the proposed model. 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 3 of 13 2.1. Modeling Christovam etal.(2023) developed a ionospheric regional model to calibrate GNSS single frequency measurements and derive ionospheric maps showing plasma bubble in one of most challenging condition, the Brazilian region. The authors have shown, for the first time, that it is possible to detect ionospheric bubbles using single frequency GNSS data. In addition, the authors also present a comparison of the STEC values obtained with single and dual frequency. The results showed that single frequency STEC data agree with dual frequency data, with differences varying between ±2.5 TECU. This difference corresponds to the overall noise level of code measurements, since the single frequency STEC values are computed based on combination between the observables called Code-Minus-Carrier (CMC). In this section we present an overview of the ionospheric model proposed by Christovam etal.(2023) along with the necessary adaptations to utilize dual-frequency data with the same model. The mathematical formulation to extract TEC data using GNSS observations was developed in three stages. In the first step, the conversion of GNSS observations to non-calibrated TEC data was performed. The second refers to ambiguity estimation by SH modeling. The third step is carried out to estimate the absolute (i.e., calibrated) TEC values and carry out a regional interpolation. The main difference between the regional modeling using single or dual frequency is related to GNSS measurements combinations. TEC data estimated using dual-frequency GNSS measurements is performed by the geometry free combination 𝐴𝐴𝐴𝐴 1−𝐴𝐴2 . It eliminates all the terms independent on the frequencies, such as the tropospheric delay, clocks, and geometric distance. When using single frequency, the combination between the observables 𝐴𝐴𝐴𝐴 1−𝐿𝐿1 named CMC is used since it eliminates all geometry-dependent components. The combinations used to compute TEC using single ( 𝐴𝐴TECSF ) and dual frequency ( 𝐴𝐴TECDF ), respectively, can be summarize as follows: TECSF =𝑘𝑘×(𝑃𝑃1−𝐿𝐿1𝜆𝜆1+𝐵𝐵SF) (1) TECDF =𝐹𝐹×(𝜆𝜆2𝐿𝐿1−𝜆𝜆2𝐿𝐿2+𝐵𝐵DF) (2) where 𝐴𝐴𝐴𝐴 𝑖𝑖 and 𝐴𝐴𝐴𝐴 𝑖𝑖 are the GNSS pseudorange and carrier phase, respectively; 𝐴𝐴𝐴𝐴 𝑖𝑖 is the wavelength in meters; 𝐴𝐴𝐴𝐴 SF and 𝐴𝐴𝐴𝐴 DF bias term that represents the ambiguity term, and instrumental delay term affected by the multipath and thermal noise and the residual term for single and dual frequency respectively. The 𝐴𝐴𝐴𝐴 and 𝐴𝐴𝐴𝐴 terms convert meters of delay to the electrons/m 2 units, being 𝐴𝐴𝐴𝐴 = ( 𝑓𝑓𝐿𝐿 12 ∕(2 × 40.3) ) and 𝐴𝐴𝐴𝐴 = ( 𝑓𝑓2 𝐿𝐿1 𝑓𝑓2 𝐿𝐿2 ∕40.3× ( 𝑓𝑓2 𝐿𝐿1 −𝑓𝑓2 𝐿𝐿2)) , with 𝐴𝐴𝐴𝐴 𝐿𝐿1 and 𝐴𝐴𝐴𝐴 𝐿𝐿2 representing the frequencies for L1 and L2, respectively. The non-calibrated TEC represents the combination between the calibrated TEC, the ambiguity term, and instrumental delay term affected by the multipath and thermal noise. The ambiguity and instrumental delay can be solved together as a unique bias term ( 𝐴𝐴𝐴𝐴 SF ) for single frequency and 𝐴𝐴𝐴𝐴 DF for dual frequency. This term is solved in the second step using a SH expansion model. The SH model adopted was the same developed by Schaer(1999); however, 24hr of GNSS data in local time (LT) is used. The model obtains enough spatial information to accurately estimate the coefficients of spherical harmonics with a high order of harmonics. Then, gets the necessary coverage to estimate the SH coefficients with a typical harmonic order of 15°. The use of 24hr of data does not involve huge problems in the estimation, since most of the GNSS stations used in the model are defined over the Brazilian region, that is, the LT and UT are very similar among the stations, just implying a slight smoothing effect. It is relevant to mention that cycle slips and gross errors in the carrier phase observations must be eliminated before using 𝐴𝐴TECSF or 𝐴𝐴TECDF in the SH model. For this purpose, we used the non-calibrated TEC values. The non-calibrated TEC values are compared epoch-by-epoch, and the discrepancy between the epochs should not be higher than the adopted threshold (4 TEC Units (TECU), being 1 TECU= 𝐴𝐴1016 el/m 2.) The ambiguity and instrumental delay term was computed with the following equation for single and dual frequencies, respectively: MF × TEC SF = 𝑛𝑛max ∑ 𝑛𝑛=0 𝑛𝑛 ∑ 𝑚𝑚=0  𝑃𝑃𝑛𝑛𝑚𝑚(𝑠𝑠𝑠𝑠𝑛𝑛𝑠𝑠𝑖𝑖𝑖𝑖 𝑚𝑚)[𝐴𝐴𝑛𝑛𝑚𝑚𝑐𝑐𝑐𝑐𝑠𝑠(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠)+𝐵𝐵𝑛𝑛𝑚𝑚 sin(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠 )] (3) MF × TEC DF = 𝑛𝑛 max ∑ 𝑛𝑛=0 𝑛𝑛 ∑ 𝑚𝑚=0  𝑃𝑃𝑛𝑛𝑚𝑚(𝑠𝑠𝑠𝑠𝑛𝑛𝑠𝑠𝑖𝑖𝑖𝑖 𝑚𝑚)[𝐴𝐴𝑛𝑛𝑚𝑚𝑐𝑐𝑐𝑐𝑠𝑠(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠)+𝐵𝐵𝑛𝑛𝑚𝑚𝑠𝑠𝑖𝑖(𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖 𝑠𝑠 )] (4) where 𝐴𝐴𝐴𝐴 𝑖𝑖𝑖𝑖 𝑚𝑚 is the latitude of the ionospheric pierce point (IPP), 𝐴𝐴𝐴𝐴 𝑖𝑖𝑖𝑖 𝑠𝑠 is the longitude of IPP in terms of LT, 𝐴𝐴𝐴𝐴 max is the maximum degree of expansion, 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 and 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 are the ionosphere model coefficients, 𝐴𝐴 𝑃𝑃𝑛𝑛𝑛𝑛 are the normalized Legendre polynomials of degree 𝐴𝐴𝐴𝐴 and order 𝐴𝐴𝐴𝐴 , and 𝐴𝐴MF is the standard mapping function (Schaer,1999). The 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 4 of 13 number of parameters is calculated by ( 𝐴𝐴𝐴𝐴 max  +1) 2, where 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 , 𝐴𝐴𝐴𝐴 𝑛𝑛𝑛𝑛 , 𝐴𝐴𝐴𝐴 DF , and 𝐴𝐴𝐴𝐴 SF are unknown parameters to be estimated by the least square method. The third step is carried out to estimate the absolute (i.e., calibrated) TEC values, which can be directly calculated after the ambiguity and instrumental delay terms are calculated for all continuous arcs. The third step also perform a regional interpolation in the Brazilian region. The spatial interpolation of the calibrated Vertical Total Electron Content (VTEC) values is carried out based on the inverse of the distance. It is considered a grid over the Brazilian region with a horizontal resolution of 1° in latitude and 1° in longitude, with an ionospheric shell height of 450km in altitude and temporal resolution of 6min. The shell height adopted is the same as that adopted by the CODG and UQRG models, which can be considered approximately the median height of electron density for a typical daytime profile (Mannucci etal.,1998). The model is executed using data from approximately 200 ground-based receivers from the continuous operating GNSS stations throughout America, especially over the Brazilian region. The data from RBMC (Brazilian Network for Continuous GNSS Monitoring), IGS, GNSS NavAer (De Paula etal.,2022), LISN (Low latitude Ionospheric Sensor Network), and RAMSAC (Red Argentina de Monitoreo Satelital Continuo) are used. The location of the GNSS stations used in regional model are presented in Figure1a. 2.2. Positioning Settings The GNSS PPP with single frequency data is an important strategy to evaluate the ionospheric models (Rovira-Garcia etal.,2020), complementing the direct assessment in the ionospheric domain (Hernández-Pajares etal.,2017). The main point is to evaluate the quality of the ionospheric delay based on direct corrections over carrier phase and pseudorange measurements. In this work, the evaluation is performed to assess the quality of the developed regional ionospheric model when using single frequency TEC data and compare it with the results obtained by the same model, when using dual frequency GNSS data. The most usual ionospheric products for GNSS applications, that is, GIMs provided by IGS, UQRG, and CODG, are also included in the positioning analysis. The UQRG and CODG products are selected because they have shown some of the best results in terms of GNSS positioning (Jerez etal.,2023). Once the single and dual frequency TEC values are obtained by the proposed method, VTEC grids are exported in IONEX format with the previously mentioned resolution (1°×1° in latitude and longitude, updated every 6min). To analyze the performance of the ionospheric models, as applied to the GNSS positioning, the RTKLib is used (Takasu & Yasuda,2009). Single frequency PPP in kinematic positioning method is chosen to evaluate the ionospheric models, as the kinematic mode directly applies the ionospheric delay to correct the GNSS observations epoch by epoch. Table1 summarized the PPP settings. For the analysis, 37 stations from RBMC are used (Figure1b). It is important to mention that the stations used to the validation were chosen to cover several latitudes in the Brazilian region. The days chosen are DOYs 3–9, as well as 21–31 of 2014. These days are selected because they have clear evidence of plasma bubbles occurrence Figure 1. Location of GNSS stations (a) for regional model (b) for the positioning assessment. The dashed line represents the Magnetic Equator. 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 5 of 13 over the Brazilian region. The main analysis is performed to evaluate the improvement that the TEC obtained from the proposed model offers to PPP during the presence of plasma bubbles. In the following section, we show the PPP results when applying the proposed method. Three parameters were used to evaluate the three-dimensional (3-D) PPP error: mean error, standard deviation (STD), and the root mean-square error (RMS) of the estimations. The main 3-D error is computed by taking the differences between the coordinates obtained in the PPP processing and the reference coordinates. The reference coordinates were obtained from final solution of the SIstema de Referencia Géocentrico para las Americas (SIRGAS) at epoch 2014. 3. Results Section3.1 presents an initial validation of TEC values obtained by the single and dual frequency models. Section3.2 presents brief discussion about ionospheric variability impact on GPS frequencies. Section3.3 shows the single frequency PPP assessment based on single frequency ionospheric model. 3.1. VTEC Plasma Bubbles Maps With Analyzed Models In order to perform an initial validation, a visual comparison of the ionospheric models is presented in Figure2. This example shows snapshot VTEC maps obtained from ionospheric models for the Brazilian region in DOY 003 of 2014 at 02hr UT. (a) and (b) panels shows the maps available from the IGS (CODG and UQRG) whereas (c) and (d) panel present the maps obtained by the proposed methods. Due to the different spatial resolution, the maps provided by the proposed method are quite different from the maps available from IGS In the maps available from IGS, the presence of the northern and southern crest of the EIA are clearly observed, where these two regions are characterized by higher electron density values. For the maps obtained with the proposed methods, it is also possible to see the crests of EIA, however with several irregularities in the region. In addition, two well-defined VTEC depletion (plasma bubbles) can be seen aligned with the geomagnetic equator. Notice that the main difference between the ionospheric maps is the ability to detect plasma bubbles. This difference can be explained by the spatial and temporal resolution differences. CODG and UQRG produce ionospheric maps with a spatial resolution of 2.5° in latitude and 5° in longitude and a temporal resolution of 2hr and 15min, respectively. The grid size used by the IGS models are larger than the scale size of the plasma bubbles detected by ground-based observations. Indeed, the scale size of the plasma bubbles are in level of 100m to a few kms (Bhattacharyya,2022). 3.2. Ionospheric Variability on GPS Frequencies During strong ionospheric events, the GPS L1 signal is less sensitive to loss of lock than using dual frequency data (GPS L1 and L2). Therefore, in regions susceptible to strong ionospheric events, more TEC data are expected to be observed with single frequency data. In such case, single frequency data can therefore improve the imaging of ionospheric bubbles due to the provided better data coverage. One way to analyze this point is counting the number of IPPs observed by dual and single frequency data. To perform this comparison, the Brazilian region is divided into 4 sub-regions (quadrants). Figure3 shows a comparative example of VTEC maps and spatial distribution of IPPs between single and dual frequency data. In this experimental analysis, the total number of IPPs counted for single frequency data was 27,970, whereas 27,008 IPPs were observed for dual frequency data. It may be noticed that there are different IPPs densities for each quadrant. A summary of the number of IPPs for each quadrant (Q) with single and dual frequency data is listed in Table2. For the period considered, except for a few instances after the plasma bubble passage (around 02hr UT), the number of IPPs for single frequency is considerably higher than those for dual frequency, these values are highlighted (bold) in Table2. The lower number of IPPs occurs because, as previously mentioned, the L2 frequency is more susceptible to ionospheric effects, which produces GNSS loss of lock and reinitializations of the TEC estimation. The main difference of the IPP numbers between the Item PPP settings Filter type Combined solutions obtained by forward and backward filters Elevation mask Cutoff angle 10° Earth tides correction Earth tides corrections Troposphere correction Estimation of tropospheric delays during PPP Satellite ephemeris/clock Precise ephemerides (sp3) and satellite clock corrections (clk_5s) acquired from IGS products Navigation system Global Positioning System (GPS) constellation Receiver/satellite antenna Correction of the phase center variation of both transmitter and receiver antennas PhWindup Phase wind up corrections Ambiguity No strategy for ambiguity solution, because metric accuracy is expected Outage to reset ambiguity/slip threshould 5/0.05m DCB data Corrections of differential instrumental bias between the civil and precise codes (CI-P1) Table 1 PPP Settings 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 6 of 13 L1 and L1L2 is, therefore, the loss of lock of the L2 measurements. As expected, better coverage of IPPs is obtained with single frequency TEC data when compared with dual frequency. 3.3. Assessment by Single Frequency PPP In a preliminary evaluation, it is analyzed the results of a single day to show details of the PPP accuracy when applying the TEC provided by different models to account for the ionospheric delay. Figure4 shows a comparison between the 3-D positioning errors throughout the day together with a correspondent keogram for Cachoeira Paulista (CHPI) station (22.7°S, 45.0°W), and the ionospheric scintillation S4 index at the same latitudinal sector, located in the southern crest of the EIA. In order to apply the keogram technique, it is required to fix the latitude, and then stack the west-east slices of the reconstructed VTEC maps data to form one image (Prol, Hernández-Pajares, etal.,2018; Silva etal.,2019). In this case, they were generated with the developed single frequency ionospheric model. According to the daily behavior, the initial (00–04hr UT) and final (22–24hr TU) hours showed the highest 3D error values, which are caused by depletions in the ionospheric plasma density, as seen in the keograms. This behavior occurs due to ionospheric plasma instability (Rayleigh-Taylor instability), which triggers plasma depletions (bubbles) after the sunset (Takahashi etal.,2015). In the keograms, we can see the general plasma bubble motion progressing from west to east, represented by a tilted dark blue region relative to the temporal axis of the figure, well connected with the highest PPP errors in the initial and final hours of the day. At the same time, it can be seen the higher values to ionospheric scintillation index (S4). This result confirms the close relationship between the ionospheric plasma bubbles occurrences and the ionospheric scintillation, causing high errors in positioning. Under strong ionospheric scintillations caused by the ionospheric plasma bubbles, the GNSS receiver tracking loop performance is degraded, causing low positioning accuracy. It is important to point out that the increased positioning errors during the 00–04hr UT are not associated with the convergence of the single frequency kinematic PPP since we used combined solutions obtained by forward and backward filtering. Figure 2. Example of ionospheric models for the Brazilian region, for DOY 003 of 2014 at 02hr UT. (a) and (b) panels corresponds to CODG and UQRG (c) and (d) corresponds to models obtained with L1 and L1L2. 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 7 of 13 After understanding the correspondence between the plasma bubble keograms and PPP performance for one station, six representative stations were chosen to evaluate different latitudinal regions of the ionosphere. The selected stations were BRAZ (15.9°S, 47.9°W); CHPI (22.7°S, 45.0°W); BOAV (2.8°N, 60.7°W); PBJP (07.1°S, 34.9°W); POAL (30.1°S, 51.1°W) and SMAR (29.7°S, 53.7°W). Figure5 presents the 3D error calculated for each epoch, and for each model, in the representative stations. Again, larger positioning errors are noticed in the initial and final hours of the day, when the ionospheric irregularities associated to equatorial plasma bubbles impacted the GNSS observations more effectively. It is important to highlight that the magnitudes of 3D errors are considered high for PPP, reaching up to 3m. Considering the entire day of data (24hr), the mean error, STD, and RMS for each model are summarized in Table3. According to the statistics, the UQRG presented a better performance compared to the others model in terms of mean and RMS, whereas the proposed model using dual frequency presented a better performance in terms of STD. When we compare the statistics results between the models, the difference is in the decimeter level, while the error is in the meter level. Therefore, it is possible to conclude that the proposed models showed results compatible with the models available from the IGS, including the single frequency model. As the main goal of the proposed model is to provide a feasible data source to map the plasma bubbles, the next evaluation is carried out only in periods of ionospheric plasma bubbles occurrence. In this regard, Figure6 shows the 3D error obtained in PPP and calculated during the periods with plasma bubble occurrences (00–06hr UT). As a result, stations BRAZ, PBJP, CHPI, and BOAV, Figure 3. Comparative example the Vertical Total Electron Content maps and spatial distribution of IPPS over the Brazilian region in DOY 003 of 2014 at 1.2hr UT between single and dual frequency. The dashed line indicates the geomagnetic equator. The continuous line represents the division of the map into quadrants. (a) and (b) panels present maps with single frequency (L1); (c) and (d) panels presents maps with dual frequency (L1 and L2). Time (UT) Frequencies 1°Q2°Q3°Q4°Q 1.0hr L1 6,715 6,746 8,583 4,388 L1L2 6,495 6,548 8,841 4,381 1.2hr L1 7,517 7,123 8,745 4,585 L1L2 6,824 6,992 8,608 4,584 1.4hr L1 7,830 7,441 8,855 4,850 L1L2 7,129 7,035 8,843 4,789 1.6hr L1 7,673 7,649 8,727 5,206 L1L2 7,178 7,357 8,651 5,201 1.8hr L1 7,456 7,812 8,672 5,789 L1L2 7,499 7,383 8,258 5,595 2.0hr L1 7,735 7,935 8,750 5,560 L1L2 7,747 7,825 8,788 5,923 Table 2 Number of IPPs Per Quadrant During 1 hr Period Over Brazilian Region for DOY 004 of 2014 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 8 of 13 Figure 4. (a) Keogram of the Vertical Total Electron Content values for the latitudinal section of 22.7°S (CHPI station) in terms of longitude and hours; (b) 3D error for the same GNSS station and (c) S4.index at latitudinal section of (23.2°S) for DOY003 of 2014. Figure 5. 3D error in meters for DOY 003 of 2014. 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Space Weather CHRISTOVAM ETAL. 10.1029/2023SW003513 9 of 13 located in regions with high ionospheric activity, presented the 3D error around 15m whereas the error is around 5 and 10m in POAL and SMAR stations, respectively. This difference among the stations occurs because BRAZ, PBJP, CHPI, and BRAZ are in the crests of the EIA, where ionospheric scintillations are more effective, while POAL and SMAR are closer to the mid-latitude region. The corresponding mean, STD, and RMS of the 3D errors in each model are summarized in Table4. Analyzing the statistics, the model proposed with single frequency presented the best performance, followed by the proposed model with dual frequency and UQRG. In this case, CODG presented the worst performance. In addition, the proposed model was also evaluated during a day characterized by low ionospheric activity DOY 171. Figure7 presents the 3D error obtained in PPP for 24hr of data for non-disturbed day. It can be seen that for all representative stations, the 3D error did not exceed 5m. Additionally, a similar behavior between the models can be observed. Table5 summarize the corresponding mean, STD and RSM values of 3D errors for each model. According to the statistics, the proposed models using single and dual frequency presented a similar mean, STD and RMS values. The CODG presented a better performance in terms of mean and RMS, whereas, in this case, the URQG presented the worst performance. It is important to point out that the difference is negligible. Therefore, it can be inferred that the proposed models demonstrated results consistent with the models provided by IGS. To provide an overview of the model performance considering several days and stations, we also estimated the statistics using the 37 stations selected during the disturbed days. The results are shown in Figure8. Comparing the statistical results between the results obtained with 24hr of data and only the period of plasma bubble occurrences, it is noted that, in the period that bubbles are occurring, the results are more disperse, especially in terms of RMS since the largest errors occur in this period. The results using 24hr of data are smoothed out by the period when no ionospheric irregularities are present. In addition, considering the latitudinal distribution, we can note a pattern. For the stations near the latitude of 15°S, close to the Southern EIA crest, the errors among the stations tend to converge to a common value. This behavior reveals that the models presented a Model Mean (m) STD (m) RMS (m) CODG 1.56 1.91 2.47 UQRG 1.55 1.87 2.44 L1 1.76 2.06 2.72 L1L2 1.70 1.82 2.49 Table 3 Mean, Standard Deviation and Root Mean Square 3D Error During 24hr of Data, Considering Each Model for DOY003, 2014 Figure 6. 3D error in meters during plasma bubble occurrence (00–06hr UT) for DOY 003 of 2014. 15427390, 2023, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023SW003513 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [27/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License