ORIGINAL ARTICLE

Ionospheric tomography using GNSS: multiplicative algebraic
reconstruction technique applied to the area of Brazil

Fabricio dos Santos Prol1 • Paulo de Oliveira Camargo1

Received: 25 March 2015 / Accepted: 8 September 2015 / Published online: 22 September 2015

� Springer-Verlag Berlin Heidelberg 2015

Abstract Experimental analysis was performed using

multiplicative algebraic reconstruction technique (MART)

to map the ionosphere over Brazil. Code and phase

observations from the global navigation satellite system

(GNSS) together with the international reference iono-

sphere (IRI) enabled the estimation of ionospheric profiles

and total electron content (TEC) over the entire region.

Twenty-four days of data collected from existing ground-

based GNSS receivers during the recent solar maximum

period were used to analyze the performance of the MART

algorithm. The results were compared with four ionoson-

des. It was demonstrated that MART estimated the electron

density peak with the same degree of accuracy as the IRI

model in regions with appropriate geometrical coverage by

GNSS receivers for tomographic reconstruction. In addi-

tion, the slant TEC, as estimated with MART, presented

lower root-mean-square error than the TEC calculated by

ionospheric maps available from the International GNSS

Service (IGS). Furthermore, the daily variations of the

ionosphere were better represented with the algebraic

techniques, compared to the IRI model and IGS maps,

enabling a correlation of the elevation of the ionosphere at

higher altitudes with the equatorial ionization anomaly

intensification. The tomographic representations also

enabled the detection of high vertical gradients at the same

instants in which ionospheric irregularities were evident.

Keywords Total electron content � Slant TEC � Grid-
based tomography � MART � Ionospheric imaging �
Ionospheric profiles

Introduction

The spatial and temporal variation of electron density in

the upper atmosphere makes the ionosphere difficult to

model. A major difficulty arises in the equatorial region

due to the lack of data in the southern hemisphere for use in

models such as the international reference ionosphere (IRI)

(Bilitza et al. 2011). The global navigation satellite system

(GNSS), however, has become an important ally in equa-

torial ionospheric imaging, since it ensures global cover-

age. Therefore, the continued availability of new GNSS

satellites and denser GNSS networks inspires many inter-

national efforts to apply tomographic techniques to

reconstruct three-dimensional representations of the iono-

sphere in the equatorial region (Chartier et al. 2014; Muella

et al. 2011; Mridula et al. 2011; Thampi et al. 2004; Franke

et al. 2003; Andreeva et al. 2000). In addition, satellite-to-

satellite radio occultation (RO) data, such as ionospheric

information derived from CHAMP (Wickert et al. 2001)

and FORMOSAT-3/COSMIC (Fong et al. 2008) missions,

have been found to be a relevant data source in ionospheric

tomography for improving the peak height and critical

electron density estimation of the ionosphere (Yin and

Mitchell 2005) and also for enhancing the vertical resolu-

tion of the ionospheric reconstruction (Wen et al. 2007).

A peculiarity of the Brazilian sector is that some iono-

spheric dynamics over the region are not completely

understood. It is affected by plasma bubbles (Ely et al.

2012; Haase et al. 2011), by the equatorial ionization

anomaly (EIA) (Nogueira et al. 2013; Tulasi Ram et al.

& Fabricio dos Santos Prol

fabricioprol@hotmail.com

Paulo de Oliveira Camargo

paulo@fct.unsep.br

1 São Paulo State University – UNESP, Roberto Simonsen,

305, São Paulo, SP 19060-900, Brazil

123

GPS Solut (2016) 20:807–814

DOI 10.1007/s10291-015-0490-0

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2009; Materassi and Mitchell 2005), by being close to the

center of the South America Magnetic Anomaly (SAMA)

(Abdu et al. 2005) and by layered structures, such as the

sporadic E-layer, in the equatorial region (Zhao et al. 2011;

Batista et al. 2008; Rishbeth 2000). One of the major topics

of investigation is the study of the ionospheric irregularities

that occurs at the evening pre-reversal drift, which is

believed to be driven by the gravitational Rayleigh–Taylor

mechanism, characterized by high vertical gradients of

electron density (Abdu 2005). Therefore, tomographic

techniques applied to reconstruct a three-dimensional

ionosphere might contribute to many studies of ionospheric

dynamics over this region.

In general, tomographic algorithms of the ionosphere

may be classified into two categories: grid based and

function based. The first group uses algebraic techniques

for the estimation of the electron density into a grid com-

posed by three-dimensional cells (latitude, longitude, and

height) called voxels (Shukla et al. 2010), or two-dimen-

sional cells (pixels) (Yao et al. 2013). Otherwise, function-

based algorithms reduce the ionospheric variations into a

set of coefficients (Van de Kamp 2013).

Muella et al. (2011) conducted a pioneer analysis on

applying function-based tomographic algorithms in Brazil.

However, since this analysis, the Brazilian Network for

Continuous GNSS Monitoring (RBMC) has actually grown

from 50 to about 100 receivers. This impulse, coupled with

the fact that no grid-based techniques had been used to

study ionospheric dynamics in Brazil, inspired the use of

multiplicative algebraic reconstruction technique (MART)

and the existing ground-based GNSS receivers for the

recent solar maximum. MART was analyzed for the esti-

mation of critical frequencies of the F2-layer, slant TEC,

and ionospheric profiles. The performance of MART was

also investigated to reconstruct horizontal representations

of EIA and vertical gradients. The main concepts of the

tomographic formulation are presented in the next sec-

tion. In the following section, we summarize our experi-

mental results and then present the conclusions about

MART as applied to Brazil.

Tomographic formulation

The basic quantity required to obtain ionospheric infor-

mation from GNSS is the total electron content (TEC),

which is expressed as the integral of the electron density ne
along the path between the GNSS satellite s and the

receiving antenna r, in a column whose cross-sectional area

is equivalent to 1 m2. It can be written as:

TEC ¼
Zs

r

neds ð1Þ

where, in computerized ionospheric tomography (CIT), the

electron density is the parameter to be reconstructed and

the TEC corresponds to the line integral of electron density

that slice the ionosphere. For this reconstruction, the

ionosphere is broken down into a grid of cells (pixels or

voxels) and the TEC may be approximated by a finite sum.

Assuming nej is the electron density for a cell j and dij the

path length of the GNSS signal i inside the boundaries that

intersect the cell j, Eq. (1) can be formulated as:

TECi ¼
XJ
j¼1

nejdij ð2Þ

where j ranges from 1 to J (number of voxels in the grid)

and dij = 0 if the signal does not intercept the corre-

sponding cell.

The path length covered by the GNSS signal in each cell

may be calculated from the projection of an ionospheric

pierce point (IPP) in each point where the GNSS signal

transverses a grid cell (Shukla et al. 2010). Therefore, a

reasonable algorithm can be selected to solve this inverse

problem and estimate the electron density in each cell

using TEC observations.

Due to the incomplete geometrical coverage of the

GNSS signals for tomographic applications, an initial

estimate for the ionosphere is required, known as a back-

ground ionosphere (Bust and Mitchell 2008). The back-

ground is usually obtained from empirical models of the

ionosphere, such as the IRI, to fill in each cell of the CIT

grid. The grid-based algorithm then uses algebraic tech-

niques to distribute the difference between the calculated

TEC from the background and the TEC measured by

GNSS into the resulting grid.

Algebraic reconstruction technique (ART) was the first

algorithm used in computerized tomography (CT). After

Austen et al. (1988), different versions of ART were

developed for ionospheric imaging, such as the simulta-

neous algebraic reconstruction technique (SART) (Ander-

son and Kak 1984) and the MART. While ART and SART

are based on a linear formulation to calculate differences

between the TEC measured by GNSS and the TEC from

the background, MART is based on the following nonlinear

iteration (Pryse et al. 1998):

nKþ1
ej ¼ nKej

TECiPJ
j¼1 dijn

K
ej

 !wdij=dmax

ð3Þ

where nKþ1
ej is the electron density value obtained from

iteration K ? 1 and w is a weighting parameter. ThePJ
j¼1 dijn

K
ej term is equivalent to a scan through each cell of

the ionospheric grid that calculates the TEC value from the

background, and dmax is the largest path length of the

respective signal i. Even when
PJ

j¼1 dijn
K
ej [TECi, MART

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123



produces nonnegative values, so an advantage of using

MART, instead of ART or SART, is the guarantee of

nonnegative values for electron density. Many new itera-

tive algorithms are being developed to improve algebraic

techniques; however, most of them are based on the prin-

ciples of ART, SART, or MART (Hobiger et al. 2008; Wen

and Liu 2010; Wen et al. 2012).

Experiments, results, and discussion

A total of 24 days were selected during the solar maximum

period in 2013 and 2014. The analysis days were dis-

tributed over the four seasons (spring, summer, autumn,

winter), covering 3 days for each season in 2013 and

another 3 days for each season in 2014. Both years were

used to consider behavior of the ionosphere on the differ-

ential code bias (DCB) estimation. Table 1 summarizes

the days used in the analysis, where the criteria for the

selected days is based on the amount of data available from

the ionosondes installed in Brazil. A total of four

ionosondes were used, located at São Luı́s (2.3�S, 44�W;

magnetic lat. 0.8�S), Fortaleza (3.8�S, 38.0�W; magnetic

lat. 5.5�S), Boa Vista (2.8�N, 60.7�W; magnetic lat.

12.9�N), and São José dos Campos (23.21�S, 45.86�W;

magnetic lat. 17.26�S), which enabled a reduction in the

critical frequency of the ionospheric F2-layer (foF2) from

the ionograms.

All available data from the Brazilian network (RBMC)

were used to obtain GNSS observations. GNSS data from

the International GNSS Service (IGS) network and from

the Low-latitude Ionospheric Sensor Network (LISN) were

also included to improve the geometrical coverage of the

GNSS signals. The locations of the GNSS receivers and the

ionosondes are presented in Fig. 1.

All the experiments were executed with the following

processing settings: (1) GNSS observations of code (C1,

P2) and phase from L1 and L2 bands were made; (2) TEC

was estimated using the leveled carrier phase ionospheric

observable (Ciraolo et al. 2007); (3) the DCB was previ-

ously estimated for each day by using VTEC maps

available from IGS (Prol and Camargo 2014); (4) cycle

slips were detected by using a recursive method, based on

widelane ambiguity (Blewitt 1990); (5) IGS precise ephe-

merides described the satellite positions from GPS and

GLONASS constellations for an elevation mask of 20�; (6)
the MART algorithm was applied on a voxel-based grid

with a resolution of 4� 9 4� 9 10 km in latitude, longi-

tude, and height; and (7) the background ionosphere and

the plasmasphere correction was calculated by the IRI

routines.

The first analysis was performed to detect the accuracy

of the MART algorithm on the estimation of the foF2. The

second was done to check the agreement of the TEC esti-

mated by tomography with the TEC retrieved from the

GNSS observations. Therefore, a comparison between

ionospheric profiles obtained from the MART algorithm,

IRI model, and ionosondes is presented. Finally, iono-

sphere representations generated by MART are analyzed.

Critical frequency

In the experiment to estimate the critical frequency, ref-

erence values were obtained through the ionosondes.

MART and the IRI model provided an estimated critical

frequency for every fifteen minutes, and at instants when it

was not possible to obtain the foF2 from the ionograms, a

linear interpolation was performed to make the 15-min

intervals consistent. Figure 2 shows the average critical

frequency estimated by MART and observed from the

ionosondes located at Boa Vista (BV), São José dos

Campos (SJC), Fortaleza (Fort), and São Luı́s (SL).

Fig. 1 Location of the GNSS receivers and ionosondes used

Table 1 Days selected for analysis

Year Summer Autumn Winter Spring

2013 Jan 25 May 15 Aug 15 Nov 5

Feb 2 May 18 Aug 21 Nov 6

Feb 3 May 19 Aug 22 Nov 25

2014 Jan 5 May 14 Jul 25 Oct 3

Feb 15 May 19 Jul 26 Oct 16

Feb 20 May 22 Jul 28 Nov 1

GPS Solut (2016) 20:807–814 809

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Figure 3 shows the root-mean-square error (RMSE) results

for MART and IRI.

At theBoaVista location, a total RMSE equal to 1.09 MHz

was calculated for MART and 1.43 MHz for IRI. At SJC, the

critical frequency estimation showed a total RMSE equal to

1.69 MHz for MART and 1.48 MHz for IRI. On the other

hand, a superior total RMSE for MART was calculated at

Fortaleza and São Luis, corresponding to 1.77 and 1.89 MHz,

respectively, forMARTand1.57 and1.28 MHz, respectively,

for IRI. Since the IRImodelwas used as background, the foF2

estimation and error were similar for MART and IRI, but

significant discrepancies and errors were checked.

We found that the lowest RMSE values for MART were

obtained at Boa Vista and SJC; however, higher discrep-

ancies between MART and IRI were calculated at For-

taleza and São Luı́s. These discrepancies were more

evident during spring and summer in the daytime, between

12 and 20 hours universal time (UT), corresponding to 09

and 17 hours local time (LT), where MART showed higher

values of RMSE. Thus, MART had a worse performance

during periods with high values of foF2 at Fortaleza and

São Luı́s. This mainly happened due to the distribution of

the GNSS stations near to these ionosondes. Fortaleza and

São Luı́s are located close to the edge of the reconstructed

area, and the electron density estimation was affected due

to incomplete geometrical coverage by the GNSS recei-

vers. In those cases, GNSS signals from the Atlantic Ocean

were not used, degrading the geometry at the edge of the

reconstructed area because no GNSS stations were located

offshore, close to the Brazilian sector.

Furthermore, greater RMSE values in SJC, Fortaleza,

and São Luis were obtained in the nighttime between 00

and 09 hours UT for winter and autumn. It is possible to

see, at the same instants in Fig. 2, larger discrepancies

between MART and the ionosondes, where MART over-

estimated the critical frequency. This overestimation

occurred mainly due to the TEC estimation, which con-

sidered both ionosphere and plasmasphere electron densi-

ties. Despite the plasmasphere correction using IRI, the IRI

model was not completely successful in the TEC plasma-

sphere estimation, mainly because the contribution of the

plasmasphere to TEC is greater in winter and autumn, as is

shown in Balan et al. (2002) and Jin et al. (2007). Due to

the geometry limitation on the CIT, the electron density

was then overestimated mostly in the peak height of the

ionosphere. Even more, some of these high RMSE values

for winter and autumn corresponded to the local sunrise,

when the sunlight first reaches the upper atmosphere. So

the TEC increased before the critical frequency has

increases and then the tomographic reconstruction overes-

timates the foF2.

Total electron content

Here the GNSS station BRAZ (15.93�S, 47.86�W) was

used to provide reference values for TEC, since it is located

Fig. 2 Mean values of the critical frequency with MART (black line)

and ionosondes Fig. 3 RMSE values of the critical frequency with MART (black

line) and IRI

810 GPS Solut (2016) 20:807–814

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in the center of Brazil and is affected by the southern crest

of EIA. The DCB having been previously estimated, it was

possible to extract the Slant TEC (STEC) from GNSS

observations and hence compare the STEC estimated by

MART with the STEC calculated using the IONosphere

map EXchange format (IONEX) files provided from Centre

for Orbit Determination in Europe (CODE). The conver-

sion of the VTEC obtained from CODE maps to STEC was

done using the standard geometric mapping function.

Figure 4 shows the RMSE calculated for all the 24 days

analyzed, where the GNSS observations from BRAZ were

used on the tomographic reconstruction and also on the

IONEX production. The STEC values were estimated

every 15 min, and the MART RMSE was lower than the

IONEX RMSE for almost all instants. The total RMSE was

6.5 TEC Units (TECU) and 8.9 TECU for MART and

CODE, respectively, showing a better tomographic per-

formance. Besides that, the STEC with IRI routines was

also calculated, but due to the high values of the RMSE,

with a total RMSE equal to 17.2 TECU, this result is not

shown in Fig. 4. A similar agreement in the RMSE is

noticed for MART and CODE maps, but with a principal

RMSE difference for 20 hours UT (17 hours LT) and

04 hours UT (01 hours LT), where the MART algorithm

showed lower RMSE. These instants correspond to the

evening pre-reverse period, when the ionospheric irregu-

larities are more effective to impact the GNSS

observations.

An example of the STEC estimated with MART and

calculated with the CODE maps at instants with iono-

spheric irregularities is presented in Fig. 5. This figure

presents results for the satellite with the pseudorandom

number (PRN) one from GPS on the day Feb 20, 2014,

where the MART algorithm was better at representing the

hourly variations than the CODE maps.

Ionospheric profiles

Profiles from the ionosonde located at Boa Vista were con-

structed using the following parameters reduced from iono-

grams: critical frequency and peak height of F2-layer (foF2,

hmF2), F1-layer (foF1, hmF1), and E-layer (foE, hmE), bot-

tomside thickness (B0) and shape (B1), and propagation factor

M(3000)F2. These parameters in conjunction with IRI func-

tions were used to construct the ionosonde profiles. It was

possible this way to calculate values of the ionospheric

reflection frequency in altitudes above the peak height. Mean

profileswere then constructed at each hour for all the days and

are presented in Fig. 6. When the ionosonde data were not

available, a linear interpolation was carried out.

In general, the MART algorithm showed the daily

variation of the electron density. When MART estimated

higher frequency values than IRI, the ionosonde also

indicated higher values than IRI. The inverse was also

verified; when MART showed lower electron densities than

IRI, ionosonde profiles also showed lower values than IRI.

However, when both ionosonde and MART presented

higher frequencies than IRI, the MART algorithm overes-

timated the frequency values, mainly in the peak height of

the profiles. This occurred mostly because the ionosonde

does not make measurements at higher altitudes than the

peak height, while TEC considers the electron density for

the entire GNSS signal path. Increased electron density at

the higher altitudes of the ionosphere coupled with

incomplete geometric coverage of GNSS for tomographic

applications provided an overestimation of the ionospheric

electron density in the peak heights.

Furthermore, higher discrepancies between the profiles

were calculated between 21 and 01 hours UT (18 and

22 hours LT). These principal discrepancies occurred due

to vertical drift during the dusk period, elevating the

ionosphere to higher altitudes. The IRI model did not

provide a sufficiently accurate estimation for the peak

altitude of the ionosphere in the pre-reverse period, and theFig. 4 RMSE estimation with MART (black lines) and calculated

with CODE IONEX maps at station BRAZ

Fig. 5 STEC estimation at instants with ionospheric irregularities

GPS Solut (2016) 20:807–814 811

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IRI peak height was used as background in the tomo-

graphic reconstruction. However, due to the limitations of

the CIT system, the peak height was estimated by MART

with similar accuracy as the IRI model.

Ionospheric representations in Brazil

Figure 7 presents average VTEC maps constructed with

MART in order to view the horizontal behavior of the

ionosphere for the different seasons of the years. In addition,

Fig. 8 shows average representations of the ionospheric

profiles, aiming to visualize the vertical variations of the

ionosphere over Brazil. The longitudinal sector of 50�Wwas

used, since it has one of the highest numbers of GNSS

receivers for different latitudes, and because it enables

analysis of EIA. Both figures show average maps for all the

days used in the experiments and for 3 hours: The first (00

UT) shows instants with the intensification of EIA due to

vertical drift in the evening pre-reverse period; the second

(12 UT) shows instants at dawn; and the last hour (18 UT)

shows instants during the maximum daily values of VTEC.

In Figs. 7 and 8, it is possible to see the EIA intensification

due to the vertical drift of the ionosphere to higher altitudes.

The peak height at 00 UT in the spring and summer is higher

than in winter and autumn, and actually the EIA presented

higher values ofVTEC for spring and summer. In addition, at

00 UT the E-layer and F1-layer are not represented on the

profiles, increasing the vertical gradients of electron density

with the altitudes. Although 18 UT marks the maximum in

VTEC values, the profiles showed smaller electron density

vertical gradients, in comparison with 00 UT, mainly due to

the absence of the E-layer and F1-layer. Thus, these average

ionospheric profiles show the pre-conditions favorable to the

development of instability in the plasma for the spring and

Fig. 6 Mean ionospheric profiles for the ionosonde, MART, and IRI

(Boa Vista). The top, middle, and bottom panels show the ionospheric

profiles obtained from ionosonde, MART, and IRI, respectively. The

unit of the color bar is 1012 el/m3

Fig. 7 Mean VTEC ionospheric maps. The top, middle, and bottom

panels show the ionospheric VTEC maps obtained at 00, 12, and

18 hours UT, respectively. The unit of the color bar is 1016 el/m2

Fig. 8 Mean ionospheric profiles for the 50�W sector. The top,

middle, and bottom panels show the ionospheric profiles obtained at

00, 12, and 18 hours UT, respectively. The unit of the color bar is

1012 el/m3

812 GPS Solut (2016) 20:807–814

123



summer at 00 UT, where a heavy fluid is supported by a light

fluid, indicating similar characteristics to the Rayleigh–

Taylor instability. These instants are also correlated with the

hours when ionospheric irregularities were checked for the

STEC estimative.

Also, the higher values ofVTECwere estimated during the

spring. The springmarks the passage of the sun to the southern

hemisphere and, in comparison with summer, showed higher

solar activity (the largest sunspot of the solar cycle 24 was

detected during October, 2014). In this way, EIA during the

spring was more intense. It is also possible to check asym-

metry on the EIAcrest due to the seasonal variations in Figs. 7

and 8. When the sun is above the southern hemisphere, the

southern crest is located at higher altitudes and with higher

VTEC values. On the other hand, when the sun is above the

northern hemisphere, the northern crest is represented at

higher altitudes and with greater VTEC values.

Summary and conclusions

GNSS receivers from RBMC, IGS, and LISN, coupled with

four ionosondes installed in Brazil were used to evaluate the

MART algorithm during the recent solar maximum period.

The RMSE of fof2 for MART showed similar agreement to

the RMSE obtained from IRI for two ionosondes (Boa Vista

and São José dos Campos). In the other ionosondes (For-

taleza and São Luı́s), the tomographic reconstruction was

affected by the inadequate distribution of the GNSS recei-

vers on the vicinity of ionosondes. In these locations, the

geometrical coverage of the GNSS signals was not com-

pletely suitable for tomographic application because they are

located close to the edge of the reconstructed area, and there

were no GNSS receivers for IGS, RBMC, or LINS, over the

Atlantic Ocean near the Brazilian sector.

We presented a comparison between ionospheric profiles

constructed with MART, IRI, and ionosonde. The daily

variations were better represented using MART, in com-

parison with the IRI model, but with overestimated values

of electron density. This occurred because the ionosonde

does not observe the ionosphere in altitudes above the peak

height, while TEC considers the electron density over the

entire GNSS signal path from the satellite to the receiving

antenna. In addition, the peak height of the ionospheric

profiles from MART was similar to those estimated by IRI,

used as background ionosphere for the tomography, and this

contributed to the overestimated values at the peak height.

Moreover, the results presented an overestimation of the

electron density due to the plasmasphere. The plasmasphere

correction was calculated using the IRI model, but this was

not completely accurate for the tomographic application.

An overestimation in the electron density then occurred at

nighttime in winter and autumn.

The MART algorithm presented a better performance on

the STEC estimation in comparisonwith the STEC calculated

with IONEXmaps fromCODE.The total RMSE calculated at

stationBRAZwas 6.5TECUforMARTand8.9TECUfor the

IONEX maps. Furthermore, average ionospheric profiles

obtained from the MART algorithm showed high vertical

gradients of electron density during the current solar maxi-

mumperiod for the spring and summer. These conditionswere

favorable for the development of instability in the plasma at

the evening pre-reverse period and irregularities on the STEC

estimation were checked at the same instants.

Therefore, the analyses suggest that MART can be used

to combine GNSS-TEC observations with the IRI model to

construct three-dimensional ionospheric representations

and then study the ionospheric dynamics in Brazil. MART

enabled constructing ionospheric VTEC maps and vertical

profiles to show daily variations of the ionosphere, making

it possible to analyze the intensification of the EIA and

correlate this information with the vertical drift that occurs

over the equatorial ionosphere during the pre-reverse per-

iod. But it should be taken into account that representation

of the vertical drift altitude is inherent to the ionospheric

background used to perform algebraic techniques.

Acknowledgments This work was undertaken on grants of the

master degree scholarship from CAPES (Coordenação de Aper-

feiçoamento de Pessoal de Nı́vel Superior) and scholarship research

productivity of CNPq (Conselho Nacional de Pesquisa). The authors

are grateful to Instituto Brasileiro de Geografia e Estatı́stica (IBGE),

International GNSS service (IGS) and Low-latitude Ionospheric

Sensor Network (LISN) project for providing dual-frequency GNSS

receivers. We are also grateful to the Instituto Nacional de Pesquisas

Espaciais (INPE) and Universidade do Vale do Paraı́ba (UNIVAP) for

providing ionosondes installed in Brazil.

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Fabricio dos Santos Prol re-

ceived his BE degree in Carto-

graphic Engineering in 2011

and MSc degree in Cartographic

Sciences in 2015 from Univer-

sidade Estadual Paulista

(UNESP) at Presidente Pru-

dente, SP, Brazil. He is a PhD

candidate at UNESP, and the

focus of his current research lies

in ionospheric modeling using

data assimilation.

Paulo de Oliveira Camargo
received his BE degree in Car-

tographic Engineering in 1985

from Universidade Estadual

Paulista (UNESP), his MSc

degree in 1992 and PhD degree

in 1999 in Geodetic Sciences

from the Universidade Federal

do Paraná (UFPR), Brazil. He is

professor of the graduate and

postgraduate program at

UNESP focusing on the fol-

lowing topics: GNSS, iono-

sphere, quality control, and

least-squares adjustment.

814 GPS Solut (2016) 20:807–814

123


	Ionospheric tomography using GNSS: multiplicative algebraic reconstruction technique applied to the area of Brazil
	Abstract
	Introduction
	Tomographic formulation
	Experiments, results, and discussion
	Critical frequency
	Total electron content
	Ionospheric profiles
	Ionospheric representations in Brazil

	Summary and conclusions
	Acknowledgments
	References