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Correlation between ionospheric scintillation effects and GNSS positioning over Brazil during the last solar maximum (2012–2014)
Journal of Atmospheric and Solar-Terrestrial Physics xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Journal of Atmospheric and Solar-Terrestrial Physics journal homepage: www.elsevier.com/locate/jastp
Correlation between ionospheric scintillation effects and GNSS positioning over Brazil during the last solar maximum (2012–2014) Daniele Barroca Marra Alvesa,∗, Eniuce Menezes de Souzab, Tayná Aparecida Ferreira Gouveiaa,∗∗ a b
UNESP - São Paulo State University, School of Technology and Sciences, Roberto Simonsen, 305, Presidente Prudente, São Paulo State, 19060-900, Brazil Maringa State University - UEM – Brazil, Colombo Av., 5790, Parana State, 87020 – 900, Brazil
ARTICLE INFO
ABSTRACT
Keywords: Ionosphere Scintillation Time series GNSS positioning Spearman correlation Odds ratio
GNSS (Global Navigation Satellite Systems) can provide high accuracy positioning at low cost. But, depending on the sources of error, e.g. the atmospheric effects, this accuracy can be degraded. The ionosphere is one of the most important error sources in GNSS positioning. Among several effects caused by the ionosphere, irregularities such as ionospheric scintillations are very relevant. They can cause cycle slips, degrade the positioning accuracy and, when severe enough, can even lead to a complete loss of signal lock. Brazil, in particular, is located in one of the regions most affected by ionospheric scintillations and these effects were intensified during the last solar maximum. The main goal of this paper is to evaluate the impact of scintillation effects on the degradation of positioning during the last solar maximum. Data from 2012 to 2014 of three reference stations located in different regions of Brazil was used. Statistically significant correlations were identified from Spearman's correlation coefficient. Using Odds Ratio, an effect-size statistic, it was possible to see that the chance of large discrepancies in 3D positioning coordinates could be three times greater under strong scintillation effects (S4 ≥ 1) than under moderate ones (0.5 < S4 < 1).
1. Introduction
complex, presenting electron density irregularities (Spogli et al., 2013; Cesaroni et al., 2015a; Marques et al., 2016). One important phenomenon is ionospheric scintillation, which can degrade the positioning or cause a complete loss of lock (Skone et al., 2001; Conker et al., 2003; Cesaroni et al., 2015b). The aim of this paper is to evaluate the impact of ionospheric scintillation effects on GNSS positioning during the last period of solar maximum (2012–2014) from 3 stations located in Brazilian regions with different ionospheric conditions. We used the S4 index as a measure of the intensity of scintillation effects. For each day of available data, different percentiles of S4 data were correlated with 2D and 3D daily discrepancies of point-positioning coordinates using Spearman's correlation. The size-effect of the association between scintillation and coordinate discrepancies was estimated by the odds ratio, as well as its confidence interval. The methodology, results and analyses are presented in the following sections.
Global Navigation Satellite Systems (GNSS) positioning has been widely used by the geodetic community. Depending on the applied positioning technique, it can provide centimeter level accuracy. However, there are some sources of error that degrade the GNSS positioning. Among them, one of the most important effects is caused by the ionosphere. The main ionospheric parameter derived from GNSS measurements is the Total Electron Content (TEC) of the atmosphere, the free electrons concentrated in the ionosphere. TEC is strongly affected by solar activity, but during low phases of the solar cycle, at middle latitudes, it can be modeled reasonably. However, solar disturbances may cause rapid ionospheric perturbations at various spatial and temporal scales. The Brazilian ionosphere is characterized by the presence of the Equatorial Ionospheric Anomaly that results in two crests of electron density located at ± 15° off the magnetic equator. The South Atlantic Magnetic Anomaly is also present in this region (Abdu et al., 2005). Such characterization implies a complex configuration of the local ionospheric plasma even when the heliogeophysical conditions are quiet. When perturbations occur, the ionosphere becomes even more
∗
2. Ionospheric scintillation GNSS scintillations are rapid and random variations of the amplitude and phase of radio waves passing through small-scale plasma
Corresponding author. Corresponding author. E-mail addresses: [email protected] (D.B.M. Alves), [email protected] (E.M. de Souza), [email protected] (T.A.F. Gouveia).
∗∗
https://doi.org/10.1016/j.jastp.2019.03.013 Received 23 March 2017; Received in revised form 15 February 2019; Accepted 26 March 2019 1364-6826/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Daniele Barroca Marra Alves, Eniuce Menezes de Souza and Tayná Aparecida Ferreira Gouveia, Journal of Atmospheric and Solar-Terrestrial Physics, https://doi.org/10.1016/j.jastp.2019.03.013
Journal of Atmospheric and Solar-Terrestrial Physics xxx (xxxx) xxxx
D.B.M. Alves, et al.
density irregularities in the ionosphere. Scintillation activities are more intense near the crests of the ionosphere anomaly and solar maximum. As stated before, scintillation reduces the accuracy of both carrier-phase and pseudorange measurements, consequently the positioning accuracy, and can even result in a loss of lock on a satellite (Conker et al., 2003). There are several indexes to quantify the ionospheric scintillation in GNSS signals; one of the most used is the S4 index. This index can be computed from satellite signal power or signal intensity (I) tracked by the receiver and can be interpreted as normalized standard deviation around the intensity average (Streets, 1969):
S4 =
I2
I2 I2
,
Table 1 2 × 2 table representing n pairs of observations at each station. Coordinate Discrepancies
(1)
OR =
di2 1)
,
OR =
=
0.6325 , n 1
n 1
2 , rs2
a /b ad = . c/d bc
log(OR)
(5)
(6)
=
1 1 1 1 + + + . a b c d
(7)
When the OR confidence interval includes the value 1, it means that the estimated odds ratio is not statistically significant. When this happens, it does not indicate that strong S4 values increase the chance of coordinates being less accurate. 4. Data and experiment
(2)
In this section, we discuss the material and methods applied in the experiment. First of all, GNSS and S4 data are presented, considering a temporal series of 3 years. The software and statistical analysis methods are also detailed. 4.1. GNSS and S4 data
(3)
Data from three stations of the CIGALA/CALIBRA network, PALM, PRU2, and POAL, during the period from January 2012 to December 2014, 24 h per day, were used for the experiments. These stations and days of data were selected taking account of the data availability, their strategic position in relation to the magnetic equator, the Equatorial Ionospheric Anomaly crest and the last solar maximum. The magnetic latitude of these stations is approximately 0.9°, 12.6° and 20.6° south for PALM, PRU2, and POAL, respectively. The CIGALA/CALIBRA stations are equipped with PolaRxS receivers. These receivers have been installed under the GSA/FP7 funded projects CIGALA and CALIBRA (http://is-cigala-calibra.fct.unesp.br/is/ ), and are maintained by UNESP for ionospheric monitoring. Due to a very stable internal oscillator and a high sampling rate (50 Hz), these receivers are usually capable of maintaining signal lock even under strong scintillation conditions (Romano et al., 2011; Bougard et al., 2011). The data collected are stored in RINEX (Receiver Independent Exchange Format) files that can be used to carry out GNSS positioning.
and for Spearman's test, with t approximation (for large n), the statistic is
t = rs
P (StrongDicrepancies/ StrongS4 )) P (StrongDicrepancies/ ModerateS4 ))
To obtain the confidence interval for the odds ratio, one quite simple way is to estimate the standard error for the natural logarithm of the odds ratio:
where di is the difference between the ranks of each of the n values of S4 and coordinate discrepancies. If there are no repeated data values, a perfect Spearman's correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other. The standard error can be expressed as rs
b d
The odds ratio (OR) is a useful effect-size statistic. It gives clear and direct information about the odds of an event or result occurring to the odds of the event not happening. Table 1 represents an example of a 2 × 2 table built to estimate the OR. Considering the 2 × 2 table presented in Table 1, the OR can be estimated as
To investigate the association between the ionospheric scintillation and the coordinate degradation, data were considered as both quantitative (continuous variable) and qualitative (nominal variable). For quantitative values, the correlation can be measured by Spearman's coefficient, which is a robust statistic and assesses monotonic relationships, whether linear or not (Daniel, 1990). Spearman's coefficient can be computed by n i=1 2 n (n
a c
P (StrongDicrepancies / StrongS4 )/(1 P (StrongDicrepancies / ModerateS4 )/(1 .
3. Association between ionospheric scintillation and coordinate degradation
6
Moderate
related to the classification of 2D and 3D coordinate discrepancies was arbitrary; other classifications or categories could have been chosen. Thus, 2 × 2 tables were built and Fisher's exact test was applied to test for association between S4 and coordinate discrepancies. In order to estimate the chance of obtaining strong discrepancies (larger than a specific value) when S4 is strong in relation to the same chance when S4 is moderate, the odds ratio was estimated as
where is an average operator over some interval, say 60 s for a sample rate of 50 Hz (Rezende et al., 2007). Based on the S4 index, the ionospheric scintillation can be classified as weak (S4 0.5), moderate (0.5 < S4 < 1) or strong S4 1 (Tiwari et al., 2011). In Brazil, the CIGALA/CALIBRA (Concept for Ionospheric Scintillation Mitigation for Professional GNSS in Latin America/ Countering GNSS high Accuracy applications Limitations due to Ionospheric disturbances in BRAzil) network is equipped with ionospheric scintillation monitor receivers capable of collecting GNSS data at a sample rate of 50 Hz. Among the several available quantities is the S4 index. These data were used for accomplishing the experiments discussed in section 4.
rs = 1
Strong Moderate
S4
Strong
(4)
which is distributed approximately as a Student's t distribution with n 2 degrees of freedom under the null hypothesis. The critical correlation can also be calculated for some confidence levels from equation (4). In order to analyze the data as qualitative variables, the data need to be classified into categories. The usual moderate (0.5 < S4 < 1) and strong (S4 1) S4 categories were considered. The 2D coordinate discrepancies obtained by point positioning were classified into moderate (< 1 m) and strong (≥1 m) while the 3D coordinate discrepancies were considered as moderate when less than 2 m and strong when they reached 2 m or more. The choice of values and names for the categories 2
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Fig. 1. CIGALA/CALIBRA stations used in the experiments (red circles). The green line represents the magnetic equator. Source: http://is-cigala-calibra.fct.unesp.br/is/stations/fixed.php
Fig. 2. Histogram of S4 index for one day and satellite selected randomly.
The collected data are also used to compute several ionospheric scintillation indices, for example, the S4 index, available on http://iscigala-calibra.fct.unesp.br/is/ismrtool/index.php (Vani et al., 2016). In order to estimate the correlation between GNSS positioning and ionospheric scintillation we used values of moderate (0.5 < S4 < 1) and strong (S4 1) S4 index, whose values are available for each minute and satellite. But, concerning the positioning results, one value per day is obtained. Considering these differences, it was necessary to obtain a daily S4 statistical value. More details can be found in section 4.3.
software applied the following configurations: IGS precise ephemerides and clocks, P1-C1 and P2-C2 bias, Davis model for troposphere hydrostatic delay and Hopfield model for troposphere wet delay, and IONEX (IONosphere map EXchange format) from IGS for ionospheric refraction. In order to generate the 2D and 3D coordinate discrepancy series, the estimated coordinates were compared to ground-truth coordinates. The PALM, POAL, and PRU2 station coordinates are known because they belong to the CIGALA/CALIBRA network (Fig. 1).
4.2. GNSS data processing
4.3. Statistical analysis
Experiments were carried out in the static PP (Point Positioning) mode using the NRCan (Natural Resources Canada) software which is available online (https://webapp.geod.nrcan.gc.ca/geod/tools-outils/ ppp.php). Single frequency code GPS data were used and the NRCan
To obtain a statistic that represents the daily scintillation effect, it is important to remember that its daily distribution is asymmetric, as already shown in the literature (Moraes et al., 2013) and illustrated in Fig. 2, for example, considering the station PRU2, PRN 32 and day of 3
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Fig. 3. Time series of all S4 indexes computed each minute for all satellites (each color represents one PRN) from 2012 to 2014 for the PRU2 (a), PALM (b), and POAL (c) stations.
year 32, selected randomly. Bearing in mind that the S4 is asymmetric, the average is not a satisfactory measure to represent it. The median could be used as an indicator of daily ionospheric scintillation for each satellite. From one side, the median is a robust statistic, but on the other hand, the discrepant values (outliers) indicate when the scintillation was very strong and may be important to identify associations with daily coordinate degradation. Hence, median (50th percentile) and other percentiles (60th, 70th 75th, 80th, 90th, and 95th) were evaluated considering only observations of S4 > 0.5. The percentage of non-available pairs of observations (daily S4 and coordinates) were 15%, 28.5%, and 6% for the PRU2, PALM, and POAL stations respectively. Thus, excluding the non-available pairs of values, the remaining pairs of data were considered independent and classified into two categories, as presented
before. Remembering that the focus of the analysis is mainly on moderate (0.5 < S4 < 1) and strong S4 ( 1) index values, the daily maximum S4 categorized into these two nominal classifications were used for Fisher's exact test and OR analysis. The confidence intervals and hypothesis test were estimated considering significance levels of 5% and using the standard errors presented in section 3. The analyses were implemented and performed in R language (R Core Team, 2016). 5. Results and analyses Fig. 3 presents the 3-year-time series of the S4 index computed each minute for all the satellites tracked by the PRU2, PALM, and POAL 4
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Fig. 4. Spearman's correlation coefficient computed between the 2D and 3D coordinate discrepancies and S4-daily percentiles (50, 60, 70, 75, 80, 90, 95, and maximum) for PRU2 station.
Fig. 5. Spearman's correlation coefficient computed between the 2D and 3D coordinate discrepancies and S4-daily percentiles (50, 60, 70, 75, 80, 90, 95, and maximum) for PALM station.
Fig. 6. Spearman's correlation coefficient computed between the 2D and 3D coordinate discrepancies and S4-daily percentiles (50, 60, 70, 75, 80, 90, 95, and maximum) for POAL station.
stations. The black vertical lines represent the days March 31st and October 1st of each year. It is possible to verify larger values between October and March, where the ionospheric effects are more relevant in Brazil. Another important aspect is that the S4 index is more expressive for the PRU2 station, as expected. To evaluate the impact of ionospheric scintillation in GNSS positioning, Figs. 4–6 present the correlation between the 2D (horizontal) and 3D (horizontal and vertical) coordinate discrepancies and S4 percentiles for the PRU2, PALM, and POAL stations respectively. The critical correlation calculated from equation (4), considering a significance level of 5%, can be visualized in the blue dotted line. Analyzing Figs. 4 and 5, a higher correlation can be seen for the PRU2 than for the PALM station. Although the PALM correlations are weaker, they were significant for almost all percentiles. Considering the POAL station (Fig. 6), almost all correlations were not significant, except for the correlation between the maximum S4 and 2D coordinate
discrepancies. In the evaluation of the 2D and 3D coordinate discrepancies and their correlation with S4, it was noted that they were quite similar for all stations. In general, as expected, the 3D discrepancies are larger than the 2D ones, but that does not conduce necessarily to a strong correlation, because the Spearman's coefficient measures a monotonic association, indicating whether both variables are consistently increasing or decreasing. The scintillation effect seems to harm both 2D and 3D coordinates for the evaluated data, although the altitude is, in general, the most impaired. In Fig. 4 it can also observed that the correlations are similar for the different evaluated percentiles. Because of that, one of them was chosen to plot together with the coordinate discrepancies. Thus, in Fig. 7, the time series of S4 percentile 75th (third quartile), 2D and 3D discrepancy coordinates are shown for the PRU2, PALM, and POAL stations. It can be noted in Fig. 7 that the correlation between S4 percentile 75th and 2D and 3D coordinate discrepancies is more evident for the 5
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Fig. 7. Time series of S4 percentile 75th, 2D and 3D coordinate discrepancies (m) for PRU2, PALM, and POAL stations. Coordinate discrepancies larger than 4 m in the coordinates were omitted to make the visualization easier.
Fig. 8. Percentage of S4
0.5 values considering the PRU2, PALM, and POAL stations.
Fig. 9. Percentage of 0.5 < S4 < 1 values considering the PRU2, PALM, and POAL stations.
PRU2 and PALM stations than for the POAL station. In the POAL station, although the S4 index reached high values during all the evaluated years, only during 2014, did the 2D and 3D coordinates get large discrepancies. These results are in agreement with Spearman's results presented in Fig. 6. Although the POAL station is located in a region with low ionospheric activity, the uncorrelated results must be investigated. Figs. 8–10 present the percentage of S4 index values for the PRU2, PALM, and POAL stations considering S4 0.5, 0.5 < S4 < 1, and
1, respectively. Fig. 8 shows that the majority of S4 index values is weak (S4 0.5) , and the POAL station obtained the greatest number of values in this category, as expected. Considering 0.5 < S4 < 1 (Fig. 9) PRU2 has the largest values and POAL the lowest ones. Finally, evaluating S4 1 (Fig. 10), PRU2 again has the most expressive number of strong values. But, POAL presents a bigger dataset than the PALM station. As stated, POAL presented a large number of S4 1 values, which can degrade the positioning results, and a low number of 0.5 < S4 < 1. This probably S4
6
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Fig. 10. Percentage of S4
1 values considering the PRU2, PALM, and POAL stations.
Spearman's correlation coefficient, mainly for stations located in strategic positions in relation to the magnetic equator. From qualitative investigation, estimating an effect-size statistic, Odds Ratio, it could be seen that the chance of large discrepancies in 3D positioning coordinates could be three times greater under strong scintillation effects (S4 ≥ 1) than under moderate ones (0.5 < S4 < 1). The statistical significance of the results from the categorical analysis was also confirmed from Fisher's exact tests.
Table 2 Fisher's exact test p-value and odds ratio (OR) and its 95% confidence interval (CI) for daily-maximum S4. Stations
PRU2 PALM POAL
S4 x 2D Coord
S4 x 3D Coord
p-value
OR (CI)
p-value
OR (CI)
< 0.001 0.01 0.11
2.1 (1.6; 2.8) 2.1 (1.2; 3.6) 2.2 (0.9; 6.0)
< 0.001 < 0.001 0.62
3.1 (1.8; 5.3) 2.2 (1.6; 3.2) 0.7 (0.2; 1.9)
Acknowledgements
caused the non-correlation of POAL positioning coordinates and the S4 index series. The p-values for Fisher's exact tests and OR estimates are presented in Table 2. From Table 2, the statistically significant association between S4 index values and 2D and 3D coordinate discrepancies was confirmed from Fisher's exact test (p-value < 0.05) and from the CI of OR which does not contain the value 1 for the PRU2 and PALM stations. From OR, it could be seen that the chance of large (≥2 m) discrepancies in 3D coordinates was 3 times greater under strong scintillation effects (S4 ≥ 1) than under moderate ones (0.5 < S4 < 1) for the PRU2 station. For 2D coordinate discrepancies in PRU2, the chance of large (≥1 m) discrepancies in coordinates was about 2 times greater under strong scintillation effects. For PALM, this chance was also about 2 times greater under strong scintillation effects, considering both 2D and 3D coordinate discrepancies. For POAL, the OR was not statistically significant, i.e., the value 1 is in the CI, indicating that strong S4 values do not increase the chance of the coordinates be less accurate in this station. Another important evaluation is the high correlation between solar activity and the S4 index. Although sunspots themselves produce only minor effects on solar emissions, the magnetic activity that accompanies sunspots can produce important changes in the ultraviolet and soft x-ray emission levels. These changes over the solar cycle can have important consequences for the Earth's upper atmosphere. Analyzing S4 index values, it is possible to verify the impact of solar activity during the last solar maximum in the S4 index. The sunspot number peak occurred in 2014 (http://solarscience.msfc.nasa.gov/SunspotCycle. shtml), exactly when the largest S4 values were found.
The authors would like to thank FAPESP (Foundation for Research Support of São Paulo) and CNPq (National Council of Research and Development) for the financial support provided for this research (FAPESP research project – process number 2012/19906-7; CNPq research scholarships – process numbers 303079/2011-8, 304247/20120, and 473973/2012). Thanks to the CIGALA/CALIBRA project, both funded by the European Commission (EC) in the framework of the FP7GALILEO-2009-GSA and FP7–GALILEO–2011–GSA–1a, respectively, and FAPESP Project Number 06/04008-2. References Abdu, M.A., Batista, I.S., Carrasco, A.J., Brum, C.G.M., 2005. South Atlantic magnetic anomaly ionization: a review and a new focus on electrodynamic effects in the equatorial ionosphere. J. Atmos. Sol. Terr. Phys. 67, 1643–1657. https://doi.org/10. 1016/j.jastp.2005.01.014. Bougard, B., Sleewaegen, J.M., Spogli, L., Sreeja, V., Monico, J.F.G., 2011. CIGALA: challenging the solar maximum in Brazil with PolaRxS. In: Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, pp. 2572–2579. Cesaroni, C., Alfonsi, L., Romero, R., Linty, N., Veettil, S.V., Park, J., Alves, D.B.M., Ortega, M.C., Perez, R.O., 2015a. Monitoring ionosphere over south America: the MImOSA and MImOSA2 projects. In: International Association of Institutes of Navigation World Congress, pp. 1–7. https://doi.org/10.1109/IAIN.2015.7352226. Cesaroni, C., Spogli, L., Alfonsi, L., Franceschi, G., Ciraolo, L., Monico, J.F.G., Scotto, C., Vincenzo, R., Aquino, Ma, Bougard, B., 2015b. L-band scintillations and calibrated total electron content gradients over Brazil during the last solar maximum. J. Space Weather Space Clim. 5, A36. https://doi.org/10.1051/swsc/2015038. Conker, R.S., El-Arini, M.B., Hegarty, C.J., Hsiao, T., 2003. Modeling the effects of ionospheric scintillation on GPS/satellite-based augmentation system availability. Radio Sci. 38, 1–23. https://doi.org/10.1029/2000RS002604. Daniel, W.W., 1990. Spearman Rank Correlation Coefficient. Applied Nonparametric Statistics. PWS-Kent. Marques, H.A.S., Monico, J.F., Marques, H.A., 2016. Performance of the L2C civil GPS signal under various ionospheric scintillation effects. GPS Solut. 20, 139–149. https://doi.org/10.1007/s10291-015-0472-2. Moraes, A.O., Paula, E.R., Perrella, W.J., Rodrigues, F.S., 2013. On the distribution of GPS signal amplitudes during low-latitude ionospheric scintillation. GPS Solut. 17, 499–510. https://doi.org/10.1007/s10291-012-0295-3. R Core Team, 2016. R: A Language and Environment for Statistical Computing. R Foundation for Statistical. Computing, Vienna, Austria URL. https://www.R-project. org/. Rezende, L.F.C., Paula, E.R., Batista, I.S., Kantor, I.J., Muella, M.T.A., 2007. Study of ionospheric irregularities during intense magnetic storms. Rev. Bras. Geofís. 25, 151–158. Romano, V., Bougard, B., Aquino, M., Monico, J.F.G., Willems, T., Solé, M., 2011. Investigation of low latitude scintillations in Brazil within the cigala project. In: 3rd Int. Colloq. Sci. Fundam. Asp. Galileo Program. Skone, S., Knudsen, K., de Jong, M., 2001. Limitations in GPS receiver tracking performance under ionospheric scintillation conditions. Phys. Chem. Earth Part A 26, 613–621. https://doi.org/10.1016/S1464-1895(01)00110-7.
6. Conclusions We discussed the impact of scintillation effects on positioning degradation during the last solar maximum (2012–2014). Data from three stations located in Brazil, one of the regions most affected by ionospheric scintillations, were evaluated by some statistical tools that have not previously been used in such applications. An index of ionospheric scintillation S4 was used as (continuous variable) and qualitative (nominal or categorical variable) measures. For quantitative analysis, the asymmetric distribution of this index was considered, evaluating different percentiles to build a daily index. In this analysis, statistically significant correlations were identified from 7
Journal of Atmospheric and Solar-Terrestrial Physics xxx (xxxx) xxxx
D.B.M. Alves, et al. Spogli, L., Alfonsi, L., Romano, V., Franceschi, G., Monico, J.F.G., Shimabukuro, M.H., Bougard, B., Aquino, M., 2013. Assessing the GNSS scintillation climate over Brazil under increasing solar activity. J. Atmos. Sol. Terr. Phys. 105, 199–206. Streets Jr., R.B., 1969. Variation of radio star and satellite scintillations with sunspot number and geomagnetic latitude. Can. J. Explor. Geophys. 5, 35–52. Tiwari, R., Skone, S., Tiwari, S., Strangeways, H.J., 2011. WBMod Assisted PLL GPS
software receiver for mitigating scintillation affect in high latitude region. In: General Assembly and Scientific Symposium, XXXth. URSI, pp. 1–4. Vani, B.C., Shimabukuro, M.H., Monico, J.F.G., 2016. Visual exploration and analysis of ionospheric scintillation monitoring data: the ISMR Query Tool. Comput. Geosci (in press). https://doi.org/10.1016/j.cageo.2016.08.022.
8
Contents lists available at ScienceDirect
Journal of Atmospheric and Solar-Terrestrial Physics journal homepage: www.elsevier.com/locate/jastp
Correlation between ionospheric scintillation effects and GNSS positioning over Brazil during the last solar maximum (2012–2014) Daniele Barroca Marra Alvesa,∗, Eniuce Menezes de Souzab, Tayná Aparecida Ferreira Gouveiaa,∗∗ a b
UNESP - São Paulo State University, School of Technology and Sciences, Roberto Simonsen, 305, Presidente Prudente, São Paulo State, 19060-900, Brazil Maringa State University - UEM – Brazil, Colombo Av., 5790, Parana State, 87020 – 900, Brazil
ARTICLE INFO
ABSTRACT
Keywords: Ionosphere Scintillation Time series GNSS positioning Spearman correlation Odds ratio
GNSS (Global Navigation Satellite Systems) can provide high accuracy positioning at low cost. But, depending on the sources of error, e.g. the atmospheric effects, this accuracy can be degraded. The ionosphere is one of the most important error sources in GNSS positioning. Among several effects caused by the ionosphere, irregularities such as ionospheric scintillations are very relevant. They can cause cycle slips, degrade the positioning accuracy and, when severe enough, can even lead to a complete loss of signal lock. Brazil, in particular, is located in one of the regions most affected by ionospheric scintillations and these effects were intensified during the last solar maximum. The main goal of this paper is to evaluate the impact of scintillation effects on the degradation of positioning during the last solar maximum. Data from 2012 to 2014 of three reference stations located in different regions of Brazil was used. Statistically significant correlations were identified from Spearman's correlation coefficient. Using Odds Ratio, an effect-size statistic, it was possible to see that the chance of large discrepancies in 3D positioning coordinates could be three times greater under strong scintillation effects (S4 ≥ 1) than under moderate ones (0.5 < S4 < 1).
1. Introduction
complex, presenting electron density irregularities (Spogli et al., 2013; Cesaroni et al., 2015a; Marques et al., 2016). One important phenomenon is ionospheric scintillation, which can degrade the positioning or cause a complete loss of lock (Skone et al., 2001; Conker et al., 2003; Cesaroni et al., 2015b). The aim of this paper is to evaluate the impact of ionospheric scintillation effects on GNSS positioning during the last period of solar maximum (2012–2014) from 3 stations located in Brazilian regions with different ionospheric conditions. We used the S4 index as a measure of the intensity of scintillation effects. For each day of available data, different percentiles of S4 data were correlated with 2D and 3D daily discrepancies of point-positioning coordinates using Spearman's correlation. The size-effect of the association between scintillation and coordinate discrepancies was estimated by the odds ratio, as well as its confidence interval. The methodology, results and analyses are presented in the following sections.
Global Navigation Satellite Systems (GNSS) positioning has been widely used by the geodetic community. Depending on the applied positioning technique, it can provide centimeter level accuracy. However, there are some sources of error that degrade the GNSS positioning. Among them, one of the most important effects is caused by the ionosphere. The main ionospheric parameter derived from GNSS measurements is the Total Electron Content (TEC) of the atmosphere, the free electrons concentrated in the ionosphere. TEC is strongly affected by solar activity, but during low phases of the solar cycle, at middle latitudes, it can be modeled reasonably. However, solar disturbances may cause rapid ionospheric perturbations at various spatial and temporal scales. The Brazilian ionosphere is characterized by the presence of the Equatorial Ionospheric Anomaly that results in two crests of electron density located at ± 15° off the magnetic equator. The South Atlantic Magnetic Anomaly is also present in this region (Abdu et al., 2005). Such characterization implies a complex configuration of the local ionospheric plasma even when the heliogeophysical conditions are quiet. When perturbations occur, the ionosphere becomes even more
∗
2. Ionospheric scintillation GNSS scintillations are rapid and random variations of the amplitude and phase of radio waves passing through small-scale plasma
Corresponding author. Corresponding author. E-mail addresses: [email protected] (D.B.M. Alves), [email protected] (E.M. de Souza), [email protected] (T.A.F. Gouveia).
∗∗
https://doi.org/10.1016/j.jastp.2019.03.013 Received 23 March 2017; Received in revised form 15 February 2019; Accepted 26 March 2019 1364-6826/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Daniele Barroca Marra Alves, Eniuce Menezes de Souza and Tayná Aparecida Ferreira Gouveia, Journal of Atmospheric and Solar-Terrestrial Physics, https://doi.org/10.1016/j.jastp.2019.03.013
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density irregularities in the ionosphere. Scintillation activities are more intense near the crests of the ionosphere anomaly and solar maximum. As stated before, scintillation reduces the accuracy of both carrier-phase and pseudorange measurements, consequently the positioning accuracy, and can even result in a loss of lock on a satellite (Conker et al., 2003). There are several indexes to quantify the ionospheric scintillation in GNSS signals; one of the most used is the S4 index. This index can be computed from satellite signal power or signal intensity (I) tracked by the receiver and can be interpreted as normalized standard deviation around the intensity average (Streets, 1969):
S4 =
I2
I2 I2
,
Table 1 2 × 2 table representing n pairs of observations at each station. Coordinate Discrepancies
(1)
OR =
di2 1)
,
OR =
=
0.6325 , n 1
n 1
2 , rs2
a /b ad = . c/d bc
log(OR)
(5)
(6)
=
1 1 1 1 + + + . a b c d
(7)
When the OR confidence interval includes the value 1, it means that the estimated odds ratio is not statistically significant. When this happens, it does not indicate that strong S4 values increase the chance of coordinates being less accurate. 4. Data and experiment
(2)
In this section, we discuss the material and methods applied in the experiment. First of all, GNSS and S4 data are presented, considering a temporal series of 3 years. The software and statistical analysis methods are also detailed. 4.1. GNSS and S4 data
(3)
Data from three stations of the CIGALA/CALIBRA network, PALM, PRU2, and POAL, during the period from January 2012 to December 2014, 24 h per day, were used for the experiments. These stations and days of data were selected taking account of the data availability, their strategic position in relation to the magnetic equator, the Equatorial Ionospheric Anomaly crest and the last solar maximum. The magnetic latitude of these stations is approximately 0.9°, 12.6° and 20.6° south for PALM, PRU2, and POAL, respectively. The CIGALA/CALIBRA stations are equipped with PolaRxS receivers. These receivers have been installed under the GSA/FP7 funded projects CIGALA and CALIBRA (http://is-cigala-calibra.fct.unesp.br/is/ ), and are maintained by UNESP for ionospheric monitoring. Due to a very stable internal oscillator and a high sampling rate (50 Hz), these receivers are usually capable of maintaining signal lock even under strong scintillation conditions (Romano et al., 2011; Bougard et al., 2011). The data collected are stored in RINEX (Receiver Independent Exchange Format) files that can be used to carry out GNSS positioning.
and for Spearman's test, with t approximation (for large n), the statistic is
t = rs
P (StrongDicrepancies/ StrongS4 )) P (StrongDicrepancies/ ModerateS4 ))
To obtain the confidence interval for the odds ratio, one quite simple way is to estimate the standard error for the natural logarithm of the odds ratio:
where di is the difference between the ranks of each of the n values of S4 and coordinate discrepancies. If there are no repeated data values, a perfect Spearman's correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other. The standard error can be expressed as rs
b d
The odds ratio (OR) is a useful effect-size statistic. It gives clear and direct information about the odds of an event or result occurring to the odds of the event not happening. Table 1 represents an example of a 2 × 2 table built to estimate the OR. Considering the 2 × 2 table presented in Table 1, the OR can be estimated as
To investigate the association between the ionospheric scintillation and the coordinate degradation, data were considered as both quantitative (continuous variable) and qualitative (nominal variable). For quantitative values, the correlation can be measured by Spearman's coefficient, which is a robust statistic and assesses monotonic relationships, whether linear or not (Daniel, 1990). Spearman's coefficient can be computed by n i=1 2 n (n
a c
P (StrongDicrepancies / StrongS4 )/(1 P (StrongDicrepancies / ModerateS4 )/(1 .
3. Association between ionospheric scintillation and coordinate degradation
6
Moderate
related to the classification of 2D and 3D coordinate discrepancies was arbitrary; other classifications or categories could have been chosen. Thus, 2 × 2 tables were built and Fisher's exact test was applied to test for association between S4 and coordinate discrepancies. In order to estimate the chance of obtaining strong discrepancies (larger than a specific value) when S4 is strong in relation to the same chance when S4 is moderate, the odds ratio was estimated as
where is an average operator over some interval, say 60 s for a sample rate of 50 Hz (Rezende et al., 2007). Based on the S4 index, the ionospheric scintillation can be classified as weak (S4 0.5), moderate (0.5 < S4 < 1) or strong S4 1 (Tiwari et al., 2011). In Brazil, the CIGALA/CALIBRA (Concept for Ionospheric Scintillation Mitigation for Professional GNSS in Latin America/ Countering GNSS high Accuracy applications Limitations due to Ionospheric disturbances in BRAzil) network is equipped with ionospheric scintillation monitor receivers capable of collecting GNSS data at a sample rate of 50 Hz. Among the several available quantities is the S4 index. These data were used for accomplishing the experiments discussed in section 4.
rs = 1
Strong Moderate
S4
Strong
(4)
which is distributed approximately as a Student's t distribution with n 2 degrees of freedom under the null hypothesis. The critical correlation can also be calculated for some confidence levels from equation (4). In order to analyze the data as qualitative variables, the data need to be classified into categories. The usual moderate (0.5 < S4 < 1) and strong (S4 1) S4 categories were considered. The 2D coordinate discrepancies obtained by point positioning were classified into moderate (< 1 m) and strong (≥1 m) while the 3D coordinate discrepancies were considered as moderate when less than 2 m and strong when they reached 2 m or more. The choice of values and names for the categories 2
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Fig. 1. CIGALA/CALIBRA stations used in the experiments (red circles). The green line represents the magnetic equator. Source: http://is-cigala-calibra.fct.unesp.br/is/stations/fixed.php
Fig. 2. Histogram of S4 index for one day and satellite selected randomly.
The collected data are also used to compute several ionospheric scintillation indices, for example, the S4 index, available on http://iscigala-calibra.fct.unesp.br/is/ismrtool/index.php (Vani et al., 2016). In order to estimate the correlation between GNSS positioning and ionospheric scintillation we used values of moderate (0.5 < S4 < 1) and strong (S4 1) S4 index, whose values are available for each minute and satellite. But, concerning the positioning results, one value per day is obtained. Considering these differences, it was necessary to obtain a daily S4 statistical value. More details can be found in section 4.3.
software applied the following configurations: IGS precise ephemerides and clocks, P1-C1 and P2-C2 bias, Davis model for troposphere hydrostatic delay and Hopfield model for troposphere wet delay, and IONEX (IONosphere map EXchange format) from IGS for ionospheric refraction. In order to generate the 2D and 3D coordinate discrepancy series, the estimated coordinates were compared to ground-truth coordinates. The PALM, POAL, and PRU2 station coordinates are known because they belong to the CIGALA/CALIBRA network (Fig. 1).
4.2. GNSS data processing
4.3. Statistical analysis
Experiments were carried out in the static PP (Point Positioning) mode using the NRCan (Natural Resources Canada) software which is available online (https://webapp.geod.nrcan.gc.ca/geod/tools-outils/ ppp.php). Single frequency code GPS data were used and the NRCan
To obtain a statistic that represents the daily scintillation effect, it is important to remember that its daily distribution is asymmetric, as already shown in the literature (Moraes et al., 2013) and illustrated in Fig. 2, for example, considering the station PRU2, PRN 32 and day of 3
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Fig. 3. Time series of all S4 indexes computed each minute for all satellites (each color represents one PRN) from 2012 to 2014 for the PRU2 (a), PALM (b), and POAL (c) stations.
year 32, selected randomly. Bearing in mind that the S4 is asymmetric, the average is not a satisfactory measure to represent it. The median could be used as an indicator of daily ionospheric scintillation for each satellite. From one side, the median is a robust statistic, but on the other hand, the discrepant values (outliers) indicate when the scintillation was very strong and may be important to identify associations with daily coordinate degradation. Hence, median (50th percentile) and other percentiles (60th, 70th 75th, 80th, 90th, and 95th) were evaluated considering only observations of S4 > 0.5. The percentage of non-available pairs of observations (daily S4 and coordinates) were 15%, 28.5%, and 6% for the PRU2, PALM, and POAL stations respectively. Thus, excluding the non-available pairs of values, the remaining pairs of data were considered independent and classified into two categories, as presented
before. Remembering that the focus of the analysis is mainly on moderate (0.5 < S4 < 1) and strong S4 ( 1) index values, the daily maximum S4 categorized into these two nominal classifications were used for Fisher's exact test and OR analysis. The confidence intervals and hypothesis test were estimated considering significance levels of 5% and using the standard errors presented in section 3. The analyses were implemented and performed in R language (R Core Team, 2016). 5. Results and analyses Fig. 3 presents the 3-year-time series of the S4 index computed each minute for all the satellites tracked by the PRU2, PALM, and POAL 4
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Fig. 4. Spearman's correlation coefficient computed between the 2D and 3D coordinate discrepancies and S4-daily percentiles (50, 60, 70, 75, 80, 90, 95, and maximum) for PRU2 station.
Fig. 5. Spearman's correlation coefficient computed between the 2D and 3D coordinate discrepancies and S4-daily percentiles (50, 60, 70, 75, 80, 90, 95, and maximum) for PALM station.
Fig. 6. Spearman's correlation coefficient computed between the 2D and 3D coordinate discrepancies and S4-daily percentiles (50, 60, 70, 75, 80, 90, 95, and maximum) for POAL station.
stations. The black vertical lines represent the days March 31st and October 1st of each year. It is possible to verify larger values between October and March, where the ionospheric effects are more relevant in Brazil. Another important aspect is that the S4 index is more expressive for the PRU2 station, as expected. To evaluate the impact of ionospheric scintillation in GNSS positioning, Figs. 4–6 present the correlation between the 2D (horizontal) and 3D (horizontal and vertical) coordinate discrepancies and S4 percentiles for the PRU2, PALM, and POAL stations respectively. The critical correlation calculated from equation (4), considering a significance level of 5%, can be visualized in the blue dotted line. Analyzing Figs. 4 and 5, a higher correlation can be seen for the PRU2 than for the PALM station. Although the PALM correlations are weaker, they were significant for almost all percentiles. Considering the POAL station (Fig. 6), almost all correlations were not significant, except for the correlation between the maximum S4 and 2D coordinate
discrepancies. In the evaluation of the 2D and 3D coordinate discrepancies and their correlation with S4, it was noted that they were quite similar for all stations. In general, as expected, the 3D discrepancies are larger than the 2D ones, but that does not conduce necessarily to a strong correlation, because the Spearman's coefficient measures a monotonic association, indicating whether both variables are consistently increasing or decreasing. The scintillation effect seems to harm both 2D and 3D coordinates for the evaluated data, although the altitude is, in general, the most impaired. In Fig. 4 it can also observed that the correlations are similar for the different evaluated percentiles. Because of that, one of them was chosen to plot together with the coordinate discrepancies. Thus, in Fig. 7, the time series of S4 percentile 75th (third quartile), 2D and 3D discrepancy coordinates are shown for the PRU2, PALM, and POAL stations. It can be noted in Fig. 7 that the correlation between S4 percentile 75th and 2D and 3D coordinate discrepancies is more evident for the 5
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Fig. 7. Time series of S4 percentile 75th, 2D and 3D coordinate discrepancies (m) for PRU2, PALM, and POAL stations. Coordinate discrepancies larger than 4 m in the coordinates were omitted to make the visualization easier.
Fig. 8. Percentage of S4
0.5 values considering the PRU2, PALM, and POAL stations.
Fig. 9. Percentage of 0.5 < S4 < 1 values considering the PRU2, PALM, and POAL stations.
PRU2 and PALM stations than for the POAL station. In the POAL station, although the S4 index reached high values during all the evaluated years, only during 2014, did the 2D and 3D coordinates get large discrepancies. These results are in agreement with Spearman's results presented in Fig. 6. Although the POAL station is located in a region with low ionospheric activity, the uncorrelated results must be investigated. Figs. 8–10 present the percentage of S4 index values for the PRU2, PALM, and POAL stations considering S4 0.5, 0.5 < S4 < 1, and
1, respectively. Fig. 8 shows that the majority of S4 index values is weak (S4 0.5) , and the POAL station obtained the greatest number of values in this category, as expected. Considering 0.5 < S4 < 1 (Fig. 9) PRU2 has the largest values and POAL the lowest ones. Finally, evaluating S4 1 (Fig. 10), PRU2 again has the most expressive number of strong values. But, POAL presents a bigger dataset than the PALM station. As stated, POAL presented a large number of S4 1 values, which can degrade the positioning results, and a low number of 0.5 < S4 < 1. This probably S4
6
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Fig. 10. Percentage of S4
1 values considering the PRU2, PALM, and POAL stations.
Spearman's correlation coefficient, mainly for stations located in strategic positions in relation to the magnetic equator. From qualitative investigation, estimating an effect-size statistic, Odds Ratio, it could be seen that the chance of large discrepancies in 3D positioning coordinates could be three times greater under strong scintillation effects (S4 ≥ 1) than under moderate ones (0.5 < S4 < 1). The statistical significance of the results from the categorical analysis was also confirmed from Fisher's exact tests.
Table 2 Fisher's exact test p-value and odds ratio (OR) and its 95% confidence interval (CI) for daily-maximum S4. Stations
PRU2 PALM POAL
S4 x 2D Coord
S4 x 3D Coord
p-value
OR (CI)
p-value
OR (CI)
< 0.001 0.01 0.11
2.1 (1.6; 2.8) 2.1 (1.2; 3.6) 2.2 (0.9; 6.0)
< 0.001 < 0.001 0.62
3.1 (1.8; 5.3) 2.2 (1.6; 3.2) 0.7 (0.2; 1.9)
Acknowledgements
caused the non-correlation of POAL positioning coordinates and the S4 index series. The p-values for Fisher's exact tests and OR estimates are presented in Table 2. From Table 2, the statistically significant association between S4 index values and 2D and 3D coordinate discrepancies was confirmed from Fisher's exact test (p-value < 0.05) and from the CI of OR which does not contain the value 1 for the PRU2 and PALM stations. From OR, it could be seen that the chance of large (≥2 m) discrepancies in 3D coordinates was 3 times greater under strong scintillation effects (S4 ≥ 1) than under moderate ones (0.5 < S4 < 1) for the PRU2 station. For 2D coordinate discrepancies in PRU2, the chance of large (≥1 m) discrepancies in coordinates was about 2 times greater under strong scintillation effects. For PALM, this chance was also about 2 times greater under strong scintillation effects, considering both 2D and 3D coordinate discrepancies. For POAL, the OR was not statistically significant, i.e., the value 1 is in the CI, indicating that strong S4 values do not increase the chance of the coordinates be less accurate in this station. Another important evaluation is the high correlation between solar activity and the S4 index. Although sunspots themselves produce only minor effects on solar emissions, the magnetic activity that accompanies sunspots can produce important changes in the ultraviolet and soft x-ray emission levels. These changes over the solar cycle can have important consequences for the Earth's upper atmosphere. Analyzing S4 index values, it is possible to verify the impact of solar activity during the last solar maximum in the S4 index. The sunspot number peak occurred in 2014 (http://solarscience.msfc.nasa.gov/SunspotCycle. shtml), exactly when the largest S4 values were found.
The authors would like to thank FAPESP (Foundation for Research Support of São Paulo) and CNPq (National Council of Research and Development) for the financial support provided for this research (FAPESP research project – process number 2012/19906-7; CNPq research scholarships – process numbers 303079/2011-8, 304247/20120, and 473973/2012). Thanks to the CIGALA/CALIBRA project, both funded by the European Commission (EC) in the framework of the FP7GALILEO-2009-GSA and FP7–GALILEO–2011–GSA–1a, respectively, and FAPESP Project Number 06/04008-2. References Abdu, M.A., Batista, I.S., Carrasco, A.J., Brum, C.G.M., 2005. South Atlantic magnetic anomaly ionization: a review and a new focus on electrodynamic effects in the equatorial ionosphere. J. Atmos. Sol. Terr. Phys. 67, 1643–1657. https://doi.org/10. 1016/j.jastp.2005.01.014. Bougard, B., Sleewaegen, J.M., Spogli, L., Sreeja, V., Monico, J.F.G., 2011. CIGALA: challenging the solar maximum in Brazil with PolaRxS. In: Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, pp. 2572–2579. Cesaroni, C., Alfonsi, L., Romero, R., Linty, N., Veettil, S.V., Park, J., Alves, D.B.M., Ortega, M.C., Perez, R.O., 2015a. Monitoring ionosphere over south America: the MImOSA and MImOSA2 projects. In: International Association of Institutes of Navigation World Congress, pp. 1–7. https://doi.org/10.1109/IAIN.2015.7352226. Cesaroni, C., Spogli, L., Alfonsi, L., Franceschi, G., Ciraolo, L., Monico, J.F.G., Scotto, C., Vincenzo, R., Aquino, Ma, Bougard, B., 2015b. L-band scintillations and calibrated total electron content gradients over Brazil during the last solar maximum. J. Space Weather Space Clim. 5, A36. https://doi.org/10.1051/swsc/2015038. Conker, R.S., El-Arini, M.B., Hegarty, C.J., Hsiao, T., 2003. Modeling the effects of ionospheric scintillation on GPS/satellite-based augmentation system availability. Radio Sci. 38, 1–23. https://doi.org/10.1029/2000RS002604. Daniel, W.W., 1990. Spearman Rank Correlation Coefficient. Applied Nonparametric Statistics. PWS-Kent. Marques, H.A.S., Monico, J.F., Marques, H.A., 2016. Performance of the L2C civil GPS signal under various ionospheric scintillation effects. GPS Solut. 20, 139–149. https://doi.org/10.1007/s10291-015-0472-2. Moraes, A.O., Paula, E.R., Perrella, W.J., Rodrigues, F.S., 2013. On the distribution of GPS signal amplitudes during low-latitude ionospheric scintillation. GPS Solut. 17, 499–510. https://doi.org/10.1007/s10291-012-0295-3. R Core Team, 2016. R: A Language and Environment for Statistical Computing. R Foundation for Statistical. Computing, Vienna, Austria URL. https://www.R-project. org/. Rezende, L.F.C., Paula, E.R., Batista, I.S., Kantor, I.J., Muella, M.T.A., 2007. Study of ionospheric irregularities during intense magnetic storms. Rev. Bras. Geofís. 25, 151–158. Romano, V., Bougard, B., Aquino, M., Monico, J.F.G., Willems, T., Solé, M., 2011. Investigation of low latitude scintillations in Brazil within the cigala project. In: 3rd Int. Colloq. Sci. Fundam. Asp. Galileo Program. Skone, S., Knudsen, K., de Jong, M., 2001. Limitations in GPS receiver tracking performance under ionospheric scintillation conditions. Phys. Chem. Earth Part A 26, 613–621. https://doi.org/10.1016/S1464-1895(01)00110-7.
6. Conclusions We discussed the impact of scintillation effects on positioning degradation during the last solar maximum (2012–2014). Data from three stations located in Brazil, one of the regions most affected by ionospheric scintillations, were evaluated by some statistical tools that have not previously been used in such applications. An index of ionospheric scintillation S4 was used as (continuous variable) and qualitative (nominal or categorical variable) measures. For quantitative analysis, the asymmetric distribution of this index was considered, evaluating different percentiles to build a daily index. In this analysis, statistically significant correlations were identified from 7
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D.B.M. Alves, et al. Spogli, L., Alfonsi, L., Romano, V., Franceschi, G., Monico, J.F.G., Shimabukuro, M.H., Bougard, B., Aquino, M., 2013. Assessing the GNSS scintillation climate over Brazil under increasing solar activity. J. Atmos. Sol. Terr. Phys. 105, 199–206. Streets Jr., R.B., 1969. Variation of radio star and satellite scintillations with sunspot number and geomagnetic latitude. Can. J. Explor. Geophys. 5, 35–52. Tiwari, R., Skone, S., Tiwari, S., Strangeways, H.J., 2011. WBMod Assisted PLL GPS
software receiver for mitigating scintillation affect in high latitude region. In: General Assembly and Scientific Symposium, XXXth. URSI, pp. 1–4. Vani, B.C., Shimabukuro, M.H., Monico, J.F.G., 2016. Visual exploration and analysis of ionospheric scintillation monitoring data: the ISMR Query Tool. Comput. Geosci (in press). https://doi.org/10.1016/j.cageo.2016.08.022.
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