1. In oduc ion
In sa elli e-based na iga ion and posi ioning, he ionosphe ic delay is conside ed a c ucial e o sou ce. In low
la i udes, o ins ance, he p ecise poin posi ioning (PPP) accu acy is se e ely a ec ed by he high ionosphe ic
a iabili y (Vee il e al.,2020). Au onomous ecei e s ha ope a e on wo o mo e equencies can elimina e up
o 99.9% o he ionosphe ic delay by using he so-called ionosphe ic ee combina ion. Howe e , single equency
ecei e s a e no capable o o m he dual equency combina ions and a e he e o e dependen on he ionosphe ic
delay de i ed by ionosphe ic models (Ro i a-Ga cia e al.,2020).
Global Ionosphe ic Maps (GIMs) a e p oduc s based on Global Na iga ion Sa elli e Sys em (GNSS) da a
as ly used o ep esen he ionosphe e and imp o e single equency posi ioning. Since 1998, he GIMs a e
compu ed by he Ionosphe e Associa ed Analysis Cen e s (IAACs) and p o ided by he In e na ional GNSS
Se ice (IGS) (He nández-Paja es e al.,2009). Cu en ly, he e a e eigh IAACs ha p o ide GIMs: he Cen e
o O bi De e mina ion in Eu ope (CODE), Eu opean Space Agency (ESA), Je P opulsion Labo a o y (JPL),
Uni e si a Poli ecnica de Ca alunya (UPC), Chinese Academy o Science, Wuhan Uni e si y (WHU), Na u al
Resou ces Canada (NRCan), and Ope a ional Tool o Ionosphe ic Mapping And P edic ion/Deu sches Geodä-
isches Fo schungsins i u - Technische Uni e si ä München (OPTIMAP/DGFI-TUM) (Fel ens & Schae ,1998;
Goss e al.,2019; Roma-Dollase e al.,2018). Di e en es ima ion echniques ha e been de eloped by each
cen e . CODE, ESA, NRCan, and WHU gene a e GIMs using sphe ical ha monic (SH) se ies expansion (Goss
Abs ac Single equency use s o he Global Na iga ion Sa elli e Sys em (GNSS) should co ec he
ionosphe ic delay o ob ain posi ioning solu ions. A aluable sou ce o ionosphe ic delay co ec ions is he
global ionosphe ic models (GIMs) o Ve ical To al Elec on Con en . The accu acy o GIMs is he e o e
impo an o imp o e he posi ioning accu acy. One o he main issues ha a ec s he GIM pe o mance,
especially a low la i ude egions, is he high sensi i i y o he global posi ioning sys em (GPS) L2 equency
o ionosphe ic scin illa ion. As an a emp o o e come his issue, in his wo k, we s udy he capabili ies o
using only GPS L1 equency o compu e ionosphe ic co ec ions in o m o egional ionosphe ic maps. The
pe o mance o he new ionosphe ic model is e alua ed by means o single equency p ecise poin posi ioning,
compa ing he posi ioning esul s agains he co ec ion using dual- equency GPS signals, as well as compa ed
o he co ec ions p o ided by GIMs p oduced by he in e na ional GNSS se ice. As a esul , he posi ioning
pe o mance using single equency model p esen ed simila accu acy o he dual equency models and, a
he same ime, p o ided less obse a ions a ec ed by ionosphe ic scin illa ions. These esul s demons a e he
easibili y o using single equency GNSS da a o de elop ionosphe ic models and o imp o e he posi ioning
o e low la i udes.
Plain Language Summa y P ecise Poin Posi ioning (PPP) is a echnique used o de e mine
he posi ion o a ecei e on he Ea h’s su ace using signals om Global Na iga ion Sa elli e Sys ems
(GNSS), which a e ansmi ed wi h a minimum o wo equencies. The ionosphe e, an ionized laye in he
Ea h’s a mosphe e, can cause e o s in GNSS signals and a ec he PPP accu acy. To imp o e accu acy, an
ionosphe ic model can be used o co ec hese e o s. In his s udy, we assess an single equency ionosphe ic
model. The esul s show ha i is possible o use single equency GNSS da a o de elop ionosphe ic models
ha can imp o e posi ioning accu acy o e low la i udes.
CHRISTOVAM ETAL.
© 2023. The Au ho s.
This is an open access a icle unde
he e ms o he C ea i e Commons
A ibu ion-NonComme cial-NoDe i s
License, which pe mi s use and
dis ibu ion in any medium, p o ided he
o iginal wo k is p ope ly ci ed, he use is
non-comme cial and no modi ica ions o
adap a ions a e made.
PPP a Low La i udes Wi h Ionosphe ic Model Exclusi ely
Based on Single F equency GNSS Measu emen s
Ana L. Ch is o am1 , Fab icio S. P ol2, Gab iel O. Je ez1, Manuel He nández-Paja es3 , and
Paulo O. Cama go1
1Depa men o Ca og aphy, São Paulo S a e Uni e si y (UNESP), São Paulo, B azil, 2Depa men o Na iga ion and
Posi ioning, Finnish Geospa ial Resea ch Ins i u e, Na ional Land Su ey o Finland, Espoo, Finland, 3Depa men o
Ma hema ics, UPC-IonSAT and UPC-IEEC Resea ch G oups, Uni e si a Poli ècnica de Ca alunya (UPC), Ba celona, Spain
Key Poin s:
• Single equency ionosphe ic models
allows o ob ain simila p ecise
poin posi ioning accu acy han dual
equency ionosphe ic models
• Single equency Global Na iga ion
Sa elli e Sys em measu emen s
p o ide mo e IPPs han dual
equency du ing ionosphe ic
scin illa ion e en s
Co espondence o:
A. L. Ch is o am,
[email p o ec ed]
Ci a ion:
Ch is o am, A. L., P ol, F. S., Je ez, G.
O., He nández-Paja es, M., & Cama go,
P.O. (2023). PPP a low la i udes wi h
ionosphe ic model exclusi ely based on
single equency GNSS measu emen s.
Space Wea he , 21, e2023SW003513.
h ps://doi.o g/10.1029/2023SW003513
Recei ed 30 MAR 2023
Accep ed 4 JUL 2023
Au ho Con ibu ions:
Concep ualiza ion: Fab icio S. P ol
Supe ision: Fab icio S. P ol, Manuel
He nández-Paja es, Paulo O. Cama go
W i ing – e iew & edi ing: Fab icio
S. P ol, Gab iel O. Je ez, Manuel
He nández-Paja es
10.1029/2023SW003513
RESEARCH ARTICLE
1 o 13
Space Wea he
CHRISTOVAM ETAL.
10.1029/2023SW003513
2 o 13
e al.,2020; Li e al.,2015; Roma-Dollase e al.,2018). The echnique adop ed by JPL is bi-cubic splines whe eas
UPC adop ed he omog aphic app oach (He nández-Paja es e al.,1999; Mannucci e al.,1998). The OPTI-
MAP use polynomial B-spline o he ionosphe ic modeling (Goss e al.,2020). Common o all p oduc s is he
da a dis ibu ion p o ided in IONosphe e map EXchange (IONEX) o ma wi h a spa ial esolu ion 5°×2.5°
in longi ude and la i ude, espec i ely, and wi h a empo al esolu ion om 15min o 2h (He nández-Paja es
e al.,2017; Schae e al.,1998). The GIMs p o ide To al Elec on Con en (TEC) om hund eds o wo ld-
wide pe manen GNSS ecei e s, no mally compu ed om dual equency measu emen s (He nández-Paja es
e al.,1999; Mannucci e al.,1998; Schae e al.,1996). Ca ie phase ambigui ies and DCBs a e essen ial pa am-
e e s es ima ed by IAACs. The p ocess o es ima ing DCBs and ambigui ies is known as he TEC calib a ion
me hod, which can be pe o med ei he ne wo k-wide, such as in he case o GIMs, o wi h indi idual GNSS
s a ions (Ci aolo e al.,2007; P ol, Cama go, e al.,2018; Shaikh,2023).
The pe o mance o GIMs gene a ed by IGS is consis en wi hin he IAACs (He nández-Paja es e al.,2009), bu
usually p o ides lowe pe o mance in low la i ude egions, especially du ing ionosphe ic scin illa ion e en s.
P ol, Cama go, e al.(2018), o ins ance, e alua e he pe o mance o TEC calib a ion p ocedu es by analyz-
ing he imp o emen in single equency PPP conside ing se e al la i udes. The au ho s ound a wo se PPP
pe o mance in low la i udes, mainly due o he ionosphe ic a iabili y associa ed wi h he Equa o ial Ioniza ion
Anomaly (EIA) and ionosphe ic scin illa ion. Ro i a-Ga cia e al.(2020) addi ionally assess he quali y o he
ionosphe ic models by GNSS posi ioning and showed la ge posi ioning e o s in ecei e s loca ed a la i udes
close o he geomagne ic equa o .
One o he main challenges in ionosphe ic modeling a low la i udes is he p esence o ionosphe ic i egula i-
ies ha can esul in he lack o con inuous GNSS ope a ion, especially in global posi ioning sys em (GPS) L2
equency. The in luence o he ionosphe e is di e en o each equency since he ionosphe e is a dispe si e
medium, whe e highe equencies a e less a ec ed when compa ed wi h lowe equencies. Delay e al.(2015)
show ha , du ing he p esence o ionosphe ic i egula i ies, he p obabili y o in e up ed acking was la ge
on GPS L2 and L5 han on he L1 signal equency. Simila ly, Mo aes e al.(2017) also p esen ha du ing he
ionosphe ic i egula i ies' occu ence, he GPS L1 signal is less sensi i e o loss o locks han he L2 equency.
Gi en ha GPS L1 pe o ms be e han GPS L2 equency, i is easonable o in es iga e he possibili y o
de elop ionosphe ic models exclusi ely based on GPS L1 equencies. In his ega d, Ch is o am e al.(2023)
p esen a egional ionosphe ic model de eloped o he low la i ude egion only using single- equency da a.
The main disad an age is ha he single equency TEC measu emen s is highly dependen on he code noise.
Ne e heless, Ch is o am e al.(2023) ha e shown ha models exclusi ely based on GPS L1 can be used o
de ec and analyze equa o ial plasma bubbles, despi e o he code noise and mul ipa h, which can be s ongly
mi iga ed o single- equency ionosphe ic moni o ing (He nández-Paja es e al.,2018). Buil on his p e ious
wo k, we in end he e o e i y whe he models exclusi ely based on GPS L1 equencies can also be used o
imp o e he single- equency PPP pe o mance. The main goal is o e i y i he single equency PPP based
on single equency ionosphe ic model can p o ide compa able le el o hose ionosphe ic models ob ained by
dual equency GNSS measu emen s. In his in end, he PPP pe o mance ob ained wi h he model de eloped by
Ch is o am e al.(2023) is compa ed wi h he single equency PPP esul s aided by o he consolida ed models.
Sec ion2 p esen s an o e iew o he me hod de eloped by Ch is o am e al.(2023) based on single equency
da a and some modi ica ions o dual equency da a. In addi ion, Sec ion2 also p esen s he con igu a ions used
o un he single equency PPP solu ions. Sec ion3 p esen s an ini ial alida ion o TEC alues ob ained by he
single and dual equency models. I also includes a b ie discussion abou he impac o ionosphe ic a iabili y
on GPS equencies, as well as an assessmen o single equency PPP based on he single equency ionosphe ic
model. Sec ion4 p esen s he conclusions.
2. Me hod
Sec ion2.1 p esen s an o e iew o he ionosphe ic model p oposed by Ch is o am e al.(2023) exclusi ely based
on single equency da a, as well as he adap a ions equi ed o un he same model using dual equency da a.
The dual equency model is p esen ed he e o ha e a base o compa ison pu poses. Addi ionally, Sec ion2.2
shows he con igu a ion used o un he single equency PPP solu ions. The PPP algo i hm is used as main indi-
ca o o e alua e he p oposed model.
15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
Space Wea he
CHRISTOVAM ETAL.
10.1029/2023SW003513
3 o 13
2.1. Modeling
Ch is o am e al.(2023) de eloped a ionosphe ic egional model o calib a e GNSS single equency measu emen s
and de i e ionosphe ic maps showing plasma bubble in one o mos challenging condi ion, he B azilian egion. The
au ho s ha e shown, o he i s ime, ha i is possible o de ec ionosphe ic bubbles using single equency GNSS
da a. In addi ion, he au ho s also p esen a compa ison o he STEC alues ob ained wi h single and dual equency.
The esul s showed ha single equency STEC da a ag ee wi h dual equency da a, wi h di e ences a ying be ween
±2.5 TECU. This di e ence co esponds o he o e all noise le el o code measu emen s, since he single equency
STEC alues a e compu ed based on combina ion be ween he obse ables called Code-Minus-Ca ie (CMC).
In his sec ion we p esen an o e iew o he ionosphe ic model p oposed by Ch is o am e al.(2023) along wi h
he necessa y adap a ions o u ilize dual- equency da a wi h he same model. The ma hema ical o mula ion
o ex ac TEC da a using GNSS obse a ions was de eloped in h ee s ages. In he i s s ep, he con e sion o
GNSS obse a ions o non-calib a ed TEC da a was pe o med. The second e e s o ambigui y es ima ion by
SH modeling. The hi d s ep is ca ied ou o es ima e he absolu e (i.e., calib a ed) TEC alues and ca y ou a
egional in e pola ion.
The main di e ence be ween he egional modeling using single o dual equency is ela ed o GNSS measu e-
men s combina ions. TEC da a es ima ed using dual- equency GNSS measu emen s is pe o med by he geome-
y ee combina ion
𝐴𝐴𝐴𝐴
1−𝐴𝐴2
. I elimina es all he e ms independen on he equencies, such as he oposphe ic
delay, clocks, and geome ic dis ance. When using single equency, he combina ion be ween he obse ables
𝐴𝐴𝐴𝐴
1−𝐿𝐿1
named CMC is used since i elimina es all geome y-dependen componen s. The combina ions used
o compu e TEC using single (
𝐴𝐴TECSF
) and dual equency (
𝐴𝐴TECDF
), espec i ely, can be summa ize as ollows:
TECSF =𝑘𝑘×(𝑃𝑃1−𝐿𝐿1𝜆𝜆1+𝐵𝐵SF)
(1)
TECDF =𝐹𝐹×(𝜆𝜆2𝐿𝐿1−𝜆𝜆2𝐿𝐿2+𝐵𝐵DF)
(2)
whe e
𝐴𝐴𝐴𝐴
𝑖𝑖
and
𝐴𝐴𝐴𝐴
𝑖𝑖
a e he GNSS pseudo ange and ca ie phase, espec i ely;
𝐴𝐴𝐴𝐴
𝑖𝑖
is he wa eleng h in me e s;
𝐴𝐴𝐴𝐴
SF
and
𝐴𝐴𝐴𝐴
DF
bias e m ha ep esen s he ambigui y e m, and ins umen al delay e m a ec ed by he mul ipa h and
he mal noise and he esidual e m o single and dual equency espec i ely. The
𝐴𝐴𝐴𝐴
and
𝐴𝐴𝐴𝐴
e ms con e me e s
o delay o he elec ons/m
2 uni s, being
𝐴𝐴𝐴𝐴
=
(
𝑓𝑓𝐿𝐿
12
∕(2 × 40.3)
)
and
𝐴𝐴𝐴𝐴
=
(
𝑓𝑓2
𝐿𝐿1
𝑓𝑓2
𝐿𝐿2
∕40.3×
(
𝑓𝑓2
𝐿𝐿1
−𝑓𝑓2
𝐿𝐿2))
, wi h
𝐴𝐴𝐴𝐴
𝐿𝐿1
and
𝐴𝐴𝐴𝐴
𝐿𝐿2
ep esen ing he equencies o L1 and L2, espec i ely.
The non-calib a ed TEC ep esen s he combina ion be ween he calib a ed TEC, he ambigui y e m, and ins u-
men al delay e m a ec ed by he mul ipa h and he mal noise. The ambigui y and ins umen al delay can be
sol ed oge he as a unique bias e m (
𝐴𝐴𝐴𝐴
SF
) o single equency and
𝐴𝐴𝐴𝐴
DF
o dual equency. This e m is sol ed in
he second s ep using a SH expansion model. The SH model adop ed was he same de eloped by Schae (1999);
howe e , 24h o GNSS da a in local ime (LT) is used. The model ob ains enough spa ial in o ma ion o accu-
a ely es ima e he coe icien s o sphe ical ha monics wi h a high o de o ha monics. Then, ge s he necessa y
co e age o es ima e he SH coe icien s wi h a ypical ha monic o de o 15°. The use o 24h o da a does no
in ol e huge p oblems in he es ima ion, since mos o he GNSS s a ions used in he model a e de ined o e he
B azilian egion, ha is, he LT and UT a e e y simila among he s a ions, jus implying a sligh smoo hing
e ec . I is ele an o men ion ha cycle slips and g oss e o s in he ca ie phase obse a ions mus be elimi-
na ed be o e using
𝐴𝐴TECSF
o
𝐴𝐴TECDF
in he SH model. Fo his pu pose, we used he non-calib a ed TEC alues.
The non-calib a ed TEC alues a e compa ed epoch-by-epoch, and he disc epancy be ween he epochs should
no be highe han he adop ed h eshold (4 TEC Uni s (TECU), being 1 TECU=
𝐴𝐴1016
el/m 2.) The ambigui y and
ins umen al delay e m was compu ed wi h he ollowing equa ion o single and dual equencies, espec i ely:
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)
whe e
𝐴𝐴𝐴𝐴
𝑖𝑖𝑖𝑖
𝑚𝑚
is he la i ude o he ionosphe ic pie ce poin (IPP),
𝐴𝐴𝐴𝐴
𝑖𝑖𝑖𝑖
𝑠𝑠
is he longi ude o IPP in e ms o LT,
𝐴𝐴𝐴𝐴
max
is
he maximum deg ee o expansion,
𝐴𝐴𝐴𝐴
𝑛𝑛𝑛𝑛
and
𝐴𝐴𝐴𝐴
𝑛𝑛𝑛𝑛
a e he ionosphe e model coe icien s,
𝐴𝐴
𝑃𝑃𝑛𝑛𝑛𝑛
a e he no malized
Legend e polynomials o deg ee
𝐴𝐴𝐴𝐴
and o de
𝐴𝐴𝐴𝐴
, and
𝐴𝐴MF
is he s anda d mapping unc ion (Schae ,1999). The
15427390, 2023, 8, Downloaded om h ps://agupubs.onlinelib a y.wiley.com/doi/10.1029/2023SW003513 by Csic O ganización Cen al Om (O icialia Mayo ) (U ici), Wiley Online Lib a y on [27/02/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
Space Wea he
CHRISTOVAM ETAL.
10.1029/2023SW003513
4 o 13
numbe o pa ame e s is calcula ed by (
𝐴𝐴𝐴𝐴
max
 +1) 2, whe e
𝐴𝐴𝐴𝐴
𝑛𝑛𝑛𝑛
,
𝐴𝐴𝐴𝐴
𝑛𝑛𝑛𝑛
,
𝐴𝐴𝐴𝐴
DF
, and
𝐴𝐴𝐴𝐴
SF
a e unknown pa ame e s o be
es ima ed by he leas squa e me hod.
The hi d s ep is ca ied ou o es ima e he absolu e (i.e., calib a ed) TEC alues, which can be di ec ly calcu-
la ed a e he ambigui y and ins umen al delay e ms a e calcula ed o all con inuous a cs. The hi d s ep also
pe o m a egional in e pola ion in he B azilian egion. The spa ial in e pola ion o he calib a ed Ve ical To al
Elec on Con en (VTEC) alues is ca ied ou based on he in e se o he dis ance. I is conside ed a g id o e he
B azilian egion wi h a ho izon al esolu ion o 1° in la i ude and 1° in longi ude, wi h an ionosphe ic shell heigh
o 450km in al i ude and empo al esolu ion o 6min. The shell heigh adop ed is he same as ha adop ed by
he CODG and UQRG models, which can be conside ed app oxima ely he median heigh o elec on densi y o
a ypical day ime p o ile (Mannucci e al.,1998).
The model is execu ed using da a om app oxima ely 200 g ound-based ecei e s om he con inuous ope a -
ing GNSS s a ions h oughou Ame ica, especially o e he B azilian egion. The da a om RBMC (B azilian
Ne wo k o Con inuous GNSS Moni o ing), IGS, GNSS Na Ae (De Paula e al.,2022), LISN (Low la i ude
Ionosphe ic Senso Ne wo k), and RAMSAC (Red A gen ina de Moni o eo Sa eli al Con inuo) a e used. The
loca ion o he GNSS s a ions used in egional model a e p esen ed in Figu e1a.
2.2. Posi ioning Se ings
The GNSS PPP wi h single equency da a is an impo an s a egy o e alua e he ionosphe ic models (Ro i a-Ga cia
e al.,2020), complemen ing he di ec assessmen in he ionosphe ic domain (He nández-Paja es e al.,2017). The
main poin is o e alua e he quali y o he ionosphe ic delay based on di ec co ec ions o e ca ie phase and pseu-
do ange measu emen s. In his wo k, he e alua ion is pe o med o assess he quali y o he de eloped egional iono-
sphe ic model when using single equency TEC da a and compa e i wi h he esul s ob ained by he same model,
when using dual equency GNSS da a. The mos usual ionosphe ic p oduc s o GNSS applica ions, ha is, GIMs
p o ided by IGS, UQRG, and CODG, a e also included in he posi ioning analysis. The UQRG and CODG p oduc s
a e selec ed because hey ha e shown some o he bes esul s in e ms o GNSS posi ioning (Je ez e al.,2023).
Once he single and dual equency TEC alues a e ob ained by he p oposed me hod, VTEC g ids a e expo ed
in IONEX o ma wi h he p e iously men ioned esolu ion (1°×1° in la i ude and longi ude, upda ed e e y
6min). To analyze he pe o mance o he ionosphe ic models, as applied o he GNSS posi ioning, he RTKLib
is used (Takasu & Yasuda,2009). Single equency PPP in kinema ic posi ioning me hod is chosen o e alua e
he ionosphe ic models, as he kinema ic mode di ec ly applies he ionosphe ic delay o co ec he GNSS obse -
a ions epoch by epoch. Table1 summa ized he PPP se ings.
Fo he analysis, 37 s a ions om RBMC a e used (Figu e1b). I is impo an o men ion ha he s a ions used o
he alida ion we e chosen o co e se e al la i udes in he B azilian egion. The days chosen a e DOYs 3–9, as
well as 21–31 o 2014. These days a e selec ed because hey ha e clea e idence o plasma bubbles occu ence
Figu e 1. Loca ion o GNSS s a ions (a) o egional model (b) o he posi ioning assessmen . The dashed line ep esen s he
Magne ic Equa o .
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o e he B azilian egion. The main analysis is pe o med o e alua e he imp o emen ha
he TEC ob ained om he p oposed model o e s o PPP du ing he p esence o plasma
bubbles. In he ollowing sec ion, we show he PPP esul s when applying he p oposed
me hod. Th ee pa ame e s we e used o e alua e he h ee-dimensional (3-D) PPP e o :
mean e o , s anda d de ia ion (STD), and he oo mean-squa e e o (RMS) o he es i-
ma ions. The main 3-D e o is compu ed by aking he di e ences be ween he coo dina es
ob ained in he PPP p ocessing and he e e ence coo dina es. The e e ence coo dina es
we e ob ained om inal solu ion o he SIs ema de Re e encia Géocen ico pa a las Ame -
icas (SIRGAS) a epoch 2014.
3. Resul s
Sec ion3.1 p esen s an ini ial alida ion o TEC alues ob ained by he single and dual
equency models. Sec ion3.2 p esen s b ie discussion abou ionosphe ic a iabili y impac
on GPS equencies. Sec ion3.3 shows he single equency PPP assessmen based on single
equency ionosphe ic model.
3.1. VTEC Plasma Bubbles Maps Wi h Analyzed Models
In o de o pe o m an ini ial alida ion, a isual compa ison o he ionosphe ic models is
p esen ed in Figu e2. This example shows snapsho VTEC maps ob ained om ionosphe ic
models o he B azilian egion in DOY 003 o 2014 a 02h UT. (a) and (b) panels shows he
maps a ailable om he IGS (CODG and UQRG) whe eas (c) and (d) panel p esen he maps
ob ained by he p oposed me hods. Due o he di e en spa ial esolu ion, he maps p o ided
by he p oposed me hod a e qui e di e en om he maps a ailable om IGS In he maps
a ailable om IGS, he p esence o he no he n and sou he n c es o he EIA a e clea ly
obse ed, whe e hese wo egions a e cha ac e ized by highe elec on densi y alues. Fo he
maps ob ained wi h he p oposed me hods, i is also possible o see he c es s o EIA, howe e
wi h se e al i egula i ies in he egion. In addi ion, wo well-de ined VTEC deple ion (plasma
bubbles) can be seen aligned wi h he geomagne ic equa o . No ice ha he main di e ence
be ween he ionosphe ic maps is he abili y o de ec plasma bubbles. This di e ence can be
explained by he spa ial and empo al esolu ion di e ences. CODG and UQRG p oduce iono-
sphe ic maps wi h a spa ial esolu ion o 2.5° in la i ude and 5° in longi ude and a empo al
esolu ion o 2h and 15min, espec i ely. The g id size used by he IGS models a e la ge han
he scale size o he plasma bubbles de ec ed by g ound-based obse a ions. Indeed, he scale
size o he plasma bubbles a e in le el o 100m o a ew kms (Bha acha yya,2022).
3.2. Ionosphe ic Va iabili y on GPS F equencies
Du ing s ong ionosphe ic e en s, he GPS L1 signal is less sensi i e o loss o lock han using
dual equency da a (GPS L1 and L2). The e o e, in egions suscep ible o s ong ionosphe ic
e en s, mo e TEC da a a e expec ed o be obse ed wi h single equency da a. In such case,
single equency da a can he e o e imp o e he imaging o ionosphe ic bubbles due o he
p o ided be e da a co e age. One way o analyze his poin is coun ing he numbe o IPPs
obse ed by dual and single equency da a. To pe o m his compa ison, he B azilian egion is
di ided in o 4 sub- egions (quad an s). Figu e3 shows a compa a i e example o VTEC maps
and spa ial dis ibu ion o IPPs be ween single and dual equency da a. In his expe imen al
analysis, he o al numbe o IPPs coun ed o single equency da a was 27,970, whe eas
27,008 IPPs we e obse ed o dual equency da a. I may be no iced ha he e a e di e en
IPPs densi ies o each quad an . A summa y o he numbe o IPPs o each quad an (Q) wi h
single and dual equency da a is lis ed in Table2. Fo he pe iod conside ed, excep o a ew
ins ances a e he plasma bubble passage (a ound 02h UT), he numbe o IPPs o single
equency is conside ably highe han hose o dual equency, hese alues a e highligh ed
(bold) in Table2. The lowe numbe o IPPs occu s because, as p e iously men ioned, he L2
equency is mo e suscep ible o ionosphe ic e ec s, which p oduces GNSS loss o lock and
eini ializa ions o he TEC es ima ion. The main di e ence o he IPP numbe s be ween he
I em PPP se ings
Fil e ype Combined solu ions ob ained by o wa d and backwa d il e s
Ele a ion mask Cu o angle 10°
Ea h ides co ec ion Ea h ides co ec ions
T oposphe e co ec ion Es ima ion o oposphe ic delays du ing PPP
Sa elli e epheme is/clock P ecise epheme ides (sp3) and sa elli e clock co ec ions (clk_5s) acqui ed om IGS p oduc s
Na iga ion sys em Global Posi ioning Sys em (GPS) cons ella ion
Recei e /sa elli e an enna Co ec ion o he phase cen e a ia ion o bo h ansmi e and ecei e an ennas
PhWindup Phase wind up co ec ions
Ambigui y No s a egy o ambigui y solu ion, because me ic accu acy is expec ed
Ou age o ese ambigui y/slip h eshould 5/0.05m
DCB da a Co ec ions o di e en ial ins umen al bias be ween he ci il and p ecise codes (CI-P1)
Table 1
PPP Se ings
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L1 and L1L2 is, he e o e, he loss o lock o he L2 measu emen s. As expec ed, be e co e age o IPPs is ob ained
wi h single equency TEC da a when compa ed wi h dual equency.
3.3. Assessmen by Single F equency PPP
In a p elimina y e alua ion, i is analyzed he esul s o a single day o show de ails o he PPP accu acy when
applying he TEC p o ided by di e en models o accoun o he ionosphe ic delay. Figu e4 shows a compa -
ison be ween he 3-D posi ioning e o s h oughou he day oge he wi h a co esponden keog am o Cachoe-
i a Paulis a (CHPI) s a ion (22.7°S, 45.0°W), and he ionosphe ic scin illa ion S4 index a he same la i udinal
sec o , loca ed in he sou he n c es o he EIA. In o de o apply he keog am echnique, i is equi ed o ix
he la i ude, and hen s ack he wes -eas slices o he econs uc ed VTEC maps da a o o m one image (P ol,
He nández-Paja es, e al.,2018; Sil a e al.,2019). In his case, hey we e gene a ed wi h he de eloped single
equency ionosphe ic model. Acco ding o he daily beha io , he ini ial (00–04h UT) and inal (22–24h TU)
hou s showed he highes 3D e o alues, which a e caused by deple ions in he ionosphe ic plasma densi y, as
seen in he keog ams. This beha io occu s due o ionosphe ic plasma ins abili y (Rayleigh-Taylo ins abili y),
which igge s plasma deple ions (bubbles) a e he sunse (Takahashi e al.,2015). In he keog ams, we can see
he gene al plasma bubble mo ion p og essing om wes o eas , ep esen ed by a il ed da k blue egion ela i e o
he empo al axis o he igu e, well connec ed wi h he highes PPP e o s in he ini ial and inal hou s o he day.
A he same ime, i can be seen he highe alues o ionosphe ic scin illa ion index (S4). This esul con i ms he
close ela ionship be ween he ionosphe ic plasma bubbles occu ences and he ionosphe ic scin illa ion, causing
high e o s in posi ioning. Unde s ong ionosphe ic scin illa ions caused by he ionosphe ic plasma bubbles, he
GNSS ecei e acking loop pe o mance is deg aded, causing low posi ioning accu acy. I is impo an o poin
ou ha he inc eased posi ioning e o s du ing he 00–04h UT a e no associa ed wi h he con e gence o he
single equency kinema ic PPP since we used combined solu ions ob ained by o wa d and backwa d il e ing.
Figu e 2. Example o ionosphe ic models o he B azilian egion, o DOY 003 o 2014 a 02h UT. (a) and (b) panels
co esponds o CODG and UQRG (c) and (d) co esponds o models ob ained wi h L1 and L1L2.
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A e unde s anding he co espondence be ween he plasma bubble keog ams and PPP pe o mance o one
s a ion, six ep esen a i e s a ions we e chosen o e alua e di e en la i udinal egions o he ionosphe e. The
selec ed s a ions we e 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). Figu e5 p esen s he 3D e o calcula ed o
each epoch, and o each model, in he ep esen a i e s a ions. Again, la ge
posi ioning e o s a e no iced in he ini ial and inal hou s o he day, when he
ionosphe ic i egula i ies associa ed o equa o ial plasma bubbles impac ed
he GNSS obse a ions mo e e ec i ely. I is impo an o highligh ha he
magni udes o 3D e o s a e conside ed high o PPP, eaching up o 3m.
Conside ing he en i e day o da a (24h ), he mean e o , STD, and RMS o
each model a e summa ized in Table3. Acco ding o he s a is ics, he UQRG
p esen ed a be e pe o mance compa ed o he o he s model in e ms o
mean and RMS, whe eas he p oposed model using dual equency p esen ed
a be e pe o mance in e ms o STD. When we compa e he s a is ics esul s
be ween he models, he di e ence is in he decime e le el, while he e o
is in he me e le el. The e o e, i is possible o conclude ha he p oposed
models showed esul s compa ible wi h he models a ailable om he IGS,
including he single equency model.
As he main goal o he p oposed model is o p o ide a easible da a sou ce o
map he plasma bubbles, he nex e alua ion is ca ied ou only in pe iods o
ionosphe ic plasma bubbles occu ence. In his ega d, Figu e6 shows he 3D
e o ob ained in PPP and calcula ed du ing he pe iods wi h plasma bubble
occu ences (00–06h UT). As a esul , s a ions BRAZ, PBJP, CHPI, and BOAV,
Figu e 3. Compa a i e example he Ve ical To al Elec on Con en maps and spa ial dis ibu ion o IPPS o e he B azilian
egion in DOY 003 o 2014 a 1.2h UT be ween single and dual equency. The dashed line indica es he geomagne ic
equa o . The con inuous line ep esen s he di ision o he map in o quad an s. (a) and (b) panels p esen maps wi h single
equency (L1); (c) and (d) panels p esen s maps wi h dual equency (L1 and L2).
Time (UT) F equencies 1°Q2°Q3°Q4°Q
1.0h L1 6,715 6,746 8,583 4,388
L1L2 6,495 6,548 8,841 4,381
1.2h L1 7,517 7,123 8,745 4,585
L1L2 6,824 6,992 8,608 4,584
1.4h L1 7,830 7,441 8,855 4,850
L1L2 7,129 7,035 8,843 4,789
1.6h L1 7,673 7,649 8,727 5,206
L1L2 7,178 7,357 8,651 5,201
1.8h L1 7,456 7,812 8,672 5,789
L1L2 7,499 7,383 8,258 5,595
2.0h L1 7,735 7,935 8,750 5,560
L1L2 7,747 7,825 8,788 5,923
Table 2
Numbe o IPPs Pe Quad an Du ing 1 h Pe iod O e B azilian Region
o DOY 004 o 2014
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Figu e 4. (a) Keog am o he Ve ical To al Elec on Con en alues o he la i udinal sec ion o 22.7°S (CHPI s a ion) in
e ms o longi ude and hou s; (b) 3D e o o he same GNSS s a ion and (c) S4.index a la i udinal sec ion o (23.2°S) o
DOY003 o 2014.
Figu e 5. 3D e o in me e s o DOY 003 o 2014.
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loca ed in egions wi h high ionosphe ic ac i i y, p esen ed he 3D e o a ound
15m whe eas he e o is a ound 5 and 10m in POAL and SMAR s a ions,
espec i ely. This di e ence among he s a ions occu s because BRAZ, PBJP,
CHPI, and BRAZ a e in he c es s o he EIA, whe e ionosphe ic scin illa ions
a e mo e e ec i e, while POAL and SMAR a e close o he mid-la i ude egion.
The co esponding mean, STD, and RMS o he 3D e o s in each model a e
summa ized in Table4. Analyzing he s a is ics, he model p oposed wi h single
equency p esen ed he bes pe o mance, ollowed by he p oposed model wi h
dual equency and UQRG. In his case, CODG p esen ed he wo s pe o mance.
In addi ion, he p oposed model was also e alua ed du ing a day cha ac e -
ized by low ionosphe ic ac i i y DOY 171. Figu e7 p esen s he 3D e o
ob ained in PPP o 24h o da a o non-dis u bed day. I can be seen ha o all ep esen a i e s a ions, he 3D
e o did no exceed 5m. Addi ionally, a simila beha io be ween he models can be obse ed. Table5 summa-
ize he co esponding mean, STD and RSM alues o 3D e o s o each model. Acco ding o he s a is ics, he
p oposed models using single and dual equency p esen ed a simila mean, STD and RMS alues. The CODG
p esen ed a be e pe o mance in e ms o mean and RMS, whe eas, in his case, he URQG p esen ed he wo s
pe o mance. I is impo an o poin ou ha he di e ence is negligible. The e o e, i can be in e ed ha he
p oposed models demons a ed esul s consis en wi h he models p o ided by IGS.
To p o ide an o e iew o he model pe o mance conside ing se e al days and s a ions, we also es ima ed he
s a is ics using he 37 s a ions selec ed du ing he dis u bed days. The esul s a e shown in Figu e8. Compa -
ing he s a is ical esul s be ween he esul s ob ained wi h 24h o da a and only he pe iod o plasma bubble
occu ences, i is no ed ha , in he pe iod ha bubbles a e occu ing, he esul s a e mo e dispe se, especially
in e ms o RMS since he la ges e o s occu in his pe iod. The esul s using 24h o da a a e smoo hed ou
by he pe iod when no ionosphe ic i egula i ies a e p esen . In addi ion, conside ing he la i udinal dis ibu-
ion, we can no e a pa e n. Fo he s a ions nea he la i ude o 15°S, close o he Sou he n EIA c es , he e o s
among he s a ions end o con e ge o a common alue. This beha io e eals ha he models p esen ed 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, S anda d De ia ion and Roo Mean Squa e 3D E o Du ing 24h o
Da a, Conside ing Each Model o DOY003, 2014
Figu e 6. 3D e o in me e s du ing plasma bubble occu ence (00–06h UT) o DOY 003 o 2014.
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