Page 1
GPS/TEC Estimation with TONOLAB Method
H. Nayirl, F. Arikan2, 0. Arikan3, C.B. Erol4
'Aselsan Inc.,hnayirgmst.aselsan.com.tr
M. AkifErsoy Mah., 16. Str. No: 16, Yenimahalle, Ankara, 06370, TURKEY
2Hacettepe University
Department ofElectrical and Electronics Engineering,arikanghacettepe.edu.tr
Beytepe, Ankara, Turkey
3Bilkent University
Department ofElectrical and Electronics Engineering, oarikangee.bilkent.edu.tr
Bilkent, Ankara, Turkey
4TUBITAK, UEKAE
Kavaklidere, Ankara, Turkey, cemil.erolgiltaren.tubitak.gov.tr
Abstract Total Electron Content (TEC) is a key variable to
measure the ionospheric characteristics and disturbances. The
Global Positioning System (GPS) can be used for TEC estimation
making use of the recorded signals at the GPS receiver. RegEst
method that is developed by F.Arikan, C.B. Erol and 0. Arikan
can be used to estimate high resolution, robust TEC values
combining GPS measurements of 30 s resolution obtained from
the satellites which are above the 10° elevation limit. Using this
method, it is possible to estimate TEC values for a whole day or a
desired time period both for quiet and disturbed days of the
ionosphere. RegEst provides robust TEC estimates for high
latitude, midlatitude and equatorial stations. In this study, some
important parameters of RegEst such as ionospheric thin shell
height,weighting
function and
investigated. By incorporating the results of the investigation,
RegEst algorithm is developed into IONOLAB method. Thin
shell model height is an important parameter for Single Layer
Ionosphere Model (SLIM).
In this study,
IONOLABprovides
independent of the choice of the maximum ionization height
indpenentofhe
Signals from the low elevation satellites are prone to multipath Arinisnewalterti
effects. In order to reduce the distortion due to multipath signals,
the optimum weighting function is implemented in IONOLAB,
minimizing the nonionospheric noise
record both pseudorange and phase data of signals. IONOLAB
can
input
absolute TEC computed from the pseudorange
measurements or phasecorrected
lownoise TEC. The TEC
estimates for both of these inputs are in good accordance with
each other. Thus, taking either pseoudorange or phasecorrected
measurement data as input, high resolution, robust TEC estimates
can be obtained from IONOLAB. Another important parameter
for TEC estimation is satellitereceiver instrumental biases. The
biases are the frequency dependent delays due to satellite and
receiver hardware. In order to compute TEC, satellite and
receiver biases should be removed from GPS measurements
correctly. However, the properprocedure of howtoincludethem
in the TEC computation is generally vaguely defined. IONOLAB
suggests a technique for inclusion of the hardware biases obtained
from the web for TEC estimates that are consistent with the
results from the IGS analysis centers.
I. INTRODUCTION
Ionosphere forms the most important atmospheric layer for
HF and satellite communication systems. Ionosphere varies
with time, frequency, and location. Total Electron Content
(TEC) provides a convenient measure
variability of the ionosphere and
distortion on radio signals. TEC is defined as the total number
for observing the
characterization
of the
of free electrons along a ray path of 1 m2 cross section. TEC is
closely related to solar and geomagnetic activities. TEC is
measured in TECU units (1 TECU =1016 el/2 ). The Global
Positioning System (GPS), due to its availability for civilian
use in the last 10 years, provides a costeffective alternative for
estimating TEC through recorded signals at the GPS receiver.
Although the ionospheric group delay or phase advance on the
recorded GPS signals is a major source ofpositioning errors,
receiversatellitebiases
are
it
is shown that
TEC
estimates
ioizaionheiht.Arikan iS new alternative for estimation of robust TEC by
combining GPS measurements of 30 s resolution obtained from
the satellites which are above the 10° elevation limit [1], [2],
effects. GPS receivers
measurements in least squares sense. An optional weighting
function and median filter is also applied. The method is
capable of deriving TEC estimates for a whole day or for a
limited period within a day.
T
The ionosper 'thell
use of web based satellitereceiver instrumental biases in Reg
Est are the parameters that are investigated in this study. The
reliable
hoie o
androbust
these parameters canbeusedto compute TEC efficiently.
RegEst method developed by F.Arikan, C.B. Erol and0.
for
thmaimu
stima
tionobt TEob
"in press"
[3]. The methodis based on combining GPS
i
t
s
height wightr ng fion an
teg
choice of ionospheric thin shell height, appropriate weighting
function that minimizes the nonionospheric irregularities and
different methods for incorporation of instrumental biases are
studied in detail. The method for phasecorrected TEC
developed and used as an alternative for absolute TEC in Reg
Est. The proper choice of alternative are incorporated into Reg
Etadtenwmto
scle
is
sJNLB
1424410576/07/$25.00 ©)2007 IEEE.
29
Page 2
II. REGEST PARAMETERS
Bias inclusion method 1:
In previous studies, RegEst algorithm is tried for various
days and stations. It is shown that the method produces robust
TEC estimates for various stations for both quiet and disturbed
days in studies [1],[2] and "in press" [3]. The results are also
compared with IRI2001 and IGS analysis centers results. It is
shown that RegEst TEC estimates are in good accordance with
various analysis centers. Using RegEst method, estimates are
obtained at higher time resolution compared to IRI2001 and
IGS
Therefore,
RegEst
alternative for tracking the sudden ionospheric irregularities
and disturbances.
In this paper, RegEst is appliedto alarger rangeof GPS
stations from midlatitude, highlatitude and equatorial regions
asgiven in TABLE
disturbed days of October 2003. The list of quiet and disturbed
days are available at Ionospheric Dispatch Center (IDCE) [8].
As provided in [8], 10 October is quiet, 272829 October are
positively disturbed, 3031 October are negatively disturbed
days. In the last days of October 2003, a major geomagnetic
and solar storm caused severe ionospheric disturbances. Kp
index rose up to 9 and Dst index fell as low as 400 nT. In this
section,
of ionospheric
ionospheric thin shell height, weighting function and satellite
receiver instrumental biases are studied.
TABLE 1
List ofGPS recevier stations
Reeiver Station
Country
Ankara
Turkey
Braiksel
Graz
1
2
212
STECUm (n) = A
[p4 tm(n) +c(DCBm + DCBU)]
(1)
f1 
VTEC
(n) STEC,(n)IM(,c7 (n))
(
(2)
U
where
211/2
M(E
(n))
I
(3)
results.
provides an
important
L
R + h
J
In the above equations, P4
combination of pseudorange values (P4=P2P1). A is constant
which
f
. ~~~~frequency
biases, respectively. m denotes satellite, u denotes receiver
and n is the time sample. In Eq. (2), STEC is converted to
VTEC usingamapping function that is giveninEq. (3). Mis
TE uasin
the mapping functionand£
M
Method 2 includes satellite and receiver biases in VTEC
computation. The biases are added in TECU units [1],[2] as
such as
shown below in Eq. (5).
Bias inclusion method 2:
f2
STECm (n)
12 2[P4,u (n)]
A1 f2
Longitude
VTEC m(n)
STEC m(n)/M(em (n)) + bm + b,
32,45 E
C
u
4,21E
15,29 E
ofSTEC and VTEC in preprocessing of input data for RegEst
method for stations given TABLEi.The instrumantal biases are
58,33 E
20,58 E
example, results for Petropavlovsk 12.10.2003 is given in Fig.
24,41 E
158,36 E
estimates with bias
E
respectively.TEC estimates ofvarious IGS analysis centers are
146,59 E
also provided in Fig. 1. These TEC maps are obtained from
121,04 E
JPL, CODE, ESA/ESOC, UPC estimates are
103,40 E
displayed with diamond, square, circle and triangle symbols,
respectively. As can be observed from Fig.
estimates from Method 1 is very close to the results of CODE
and estimates from both methods are in very good accordance.
Instrumental satellite and receiver biases are important
parameters for TEC estimation. GPS measurements include
both ionospheric
delay andinstrumental
biases.
In
orderestimate
ionospheric
TEC,
these
instrumental biases should be removed from measurements in
an appropriate way. In the literature, there is no standard
procedure for inclusion of satellite and receiver bias parameters
in TEC estimation. In this study, two satellite and receiver bias
inclusion methods are tried for RegEst. These methods are
given in the following equations. In Method 1, the satellite and
receiver instrumental biases are used in STEC computation as
in Eq. (1) [6],[7],[14].
is the geometry free linear
is equal to40,3 m3/s2. DCBm and DCB, are the
dependent
and
' . ..
satellite
receiver
instrumental
i. Thedaysare selected from quiet and
g f
iune is thatei
isthe satellite elevationangle. In
elevatIn
angle. In
theeffect
parameters
2
(4)
Latitude
39,53 N
50,47 N
47,04 N
5)
Belgium
Austria
Bias inclusion Method1and 2 are used in the computation
Zelenchukskaya
Arti
Kiruna
Metsahovi
Petropavlosk
Petrop
Russia
Russia
Sweden
Finland
Russia
PapuaNew
Guinea
Philippines
Singapore
43,17 N
56,25 N
67,51 N
60,13 N
53,04 N
04
06
14,38 N
01,20 N
41,33 E
available in IONEXfiles of IGS analysiscenters [12]. As an
1. In Fig. 1, solid line and dashed line display the RegEst TEC
inclusion method
1
and method
2,
k
R
N
1
Lae
5
Manila
Nanyang
[12]. In Fig. 1,
1 that the TEC
RegEst estimates using both bias inclusion methods are
compared with results of other analysis centers in by using D1,
D2, and D3 defined below. Xbl, and Xb2 are TEC estimation
results of RegEst using method 1 and method 2 respectively.
XCODE represents the results of CODE analysis center. N is the
total number of GPS recordings for 24 hour period. In TABLE 2
computed TEC differences are listed for various days and
stations. In general, D2 results are smaller when compared to
D3. Thus, including instrumental biases as in Method 1 gives
TEC estimation results closer to CODE analysis center.
satellitereceiver
to
30
Page 3
402PTOALVKPseudorange measurements are morenoisy compared to carrier
computation is difficult because of initial phase ambiguity and
cycle slips. Third method is to use both pseudorange and phase
2,~  I ImeasurementstoovercomeIphase easambiguityveromeande
problems. These methods are discussed in various studies such
~~~~~~~~~~~~~~as
used as an input to RegEst. For IONOLAB, the measurement
.~~~~~~~~J
input
range
*, .
I  Ipseudorange measurementstoeliminatengemesuphase t eambiguity.
levelling process is based on computing a baseline (B) for each
2~~~~~~~~~T,, H.1,U~connectedarc of phase measurements. Then, the computed
RegEst TEC estimates obtained by applying method 1 and
baseline is used in STECcomputation as inEq. (10).
method2 bias inclusion methods for Petropavlovsk 12.10.2003 (quiet
day).
acycleyandslip
s
%
[5],[7],[9],[IO],[I4]. Previously, only the absolute TEC was
1~~
*. .
is
enlarged
to
includethe
phasecorrected
~~~~~measurements. Carrier phase measurements are levelled using
am
igut
Theh
2
Fig. 1.
1
n
Btm = N
N
ZP~~~~~~~~,4,u mfme L,mfme)
n(n
L,,i(
(9)
N
2
~~~~~~~~~~~~1f12f2
(6)
NAjf
D
___n=1
1
_
STE
f()=2
2 [1L4m(nl)+Bm+c(DCBm+DCB)]
(10)
2
n=1
~~~~~~~~~~~Fig.
2estimates obtainedusing pseudorange and carrier phase data. In
Fig. 2.a., solid line and dotted line denote estimates obtained
using carrier phase data and pseudorange data in RegEst,
respectively. In Fig. 2.b., RegEst estimates are compared with
~~~~~~~~~~the
TEC estimates of IGS analysis centers. JPL, CODE,
ESA/ESOC, UPC estimates
Z Xb2XCOEsquare, circle and triangle symbols, respectively. As can be
(8)
observed from Fig. 2.b. that, using either pseudorange or
Z ~Xb2 ~2carrierphase data as input, RegEst produces consistent TEC
estimation results with IGS analysis centers especially with
JPL and CODE. Therefore, IONOLAB can use both absolute
TEC andphasecorrected TEC as input.
2 provides an example of the comparison of RegEst
N
>
XiXCODE
N~~~~~
Y,~b
___n=1
___
(7)
2
n=1
N
CD
2
are displayed with diamond,
n=1
n=1
TABLE 2
RegEst TEC estimation differences obtainedusing different bias inclusion
methods.
40AT
Receiver Station
Zclcnchukskaya Oct 12, 2003 1.17x1~~~~~~~~~~~~~ ~~~~~02
Day
D___ D_
D3___
14x02
8.71x10
El
2x03
31, 2003
4.21x104
Graz Oct
1.73xl0 2.03xl0
I
L
L9I 80xLI'
Arti
Oct 10, 2003 6.72xl0
Oct 29, 2003
Oct 12, 2003 11.27xl0
a 10
212
22
Petropavlovsk
Nanyang
1.81X102 5.98x103 4.17x102
5.12xl0
ct
5.27xl0
8,2 003
ART
18
53 l743 l2x0
2
Although using both bias inclusion methods in RegEst gives
reasonable TEC estimates, bias inclusion Method 1 results are
closer to IGS analysis centers' estimates compared to Method
2. Sine usiginstumentl biass in
more suitable for the model for GPS observation equations,
Method
instrumental biases.
24
Gii2 i4
0 22
TEC coputaton is
Fig. 2.
Comparison ofRegEst TEC estimates using pseudorange and
carephsdt,Ati1.0203(utdy)
1
will be used
in IONOLAB
forinclusion of
Detailed comparison ofpseudorange andphase derivedReg
Est
estimates withother
analysis
computing normalized TEC differences as in equations (11)
through
(13),where
Xpr and Xph
centers
is done by
B. Computation ofCarrier Phase Corrected VTEC
are RegEst
estimates~~,1
/A
"
Page 4
given in TABLE 3 for various days and stations.
N
2
ZXprXph
measure for
following differences are defined.
the difference between TEC estimates, the
3
n=1
ART~~~~~~~~~~~~~~~~~~~~~~~~
300 1

42
8,3k~
T
 I
Z
r2
~~~~~~~~~~~~~~~~~~~~~~~~2
II

2
wi
2
7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~X P h N~~~~~~~~
 
Ankara
Gra
Oct 31, 2003
Oc 1,00Xph010
1.75x104
1,30x103
3.2x10J3.1x1
1.93x103Xh], Xh2, and Xh3 are the RegEst TEC estimation results for 14 1
Fin.3
es
epciey
30020
21~
E stmtsfr30k,
428.8 km and 450kin
stettlnmbe
Kirna=p18 039.81434x0
4.3)112
cnlddta
h hieo h
ionospheric shell height,
ri3.020,ngtvl
itre
does
TABLE3
TEC estimation differences
D8
x
h2~~~~~~~~
TBLE
ITAL3,DissalfraldyansttosthtmnsRegEst
usoing eiatheisoduagasy inut ReEst
aevrclstoecote.CmaiowihJLrslsAnkara
gienas D
ct0
and3
Zestmaenuskareai gOodareet
oJPetoalovkOt31 03Ze7l04le7l0
Arti Oct10,20032.2xI0'4.53l02
C.iEffecofI
03908I
Mania
usngeq(1.VriaTol ElcrnCnet(TC
cmueasiEq(2anusnathnselapoiainNanyang Oct 30, 2003
withinerespectsetoorionosphericer
height
"
adhaete
An
288karan
rchokskaya
sonhokskariuyayOc 28,saton
EC
ifArtice
cncue
htte
honospheric
ThihSellHigthrteOcg3,t00014o002
3.4xlO'
MntshveahosignOfcat10,f200
NnagOct 10, 2003
0.9I.2l0376xO' Tus nINLB h
esE estimation results
ReeierSttin0ay0
10,200 2003l 1
Oc 31k, 2003ctve0.28
foct102003ou
2003
Octr 10,o 200
Oct
0.244
0.038Xh1,h2
0.044
tta
ume
0.032frncs
0.047TBE
0.025Tu,tanb
D60xlarerelatvely mall therefrelReEs
with03268l2h9XourTEC
xO
o
estmats
.8lO'
459XI2
Z
0.207d
T0.30
0.162
r
,
l
.3l0
. XO2
hieo
Oc 27 2002.38X 054.05l03
ae
0.16
2.53
0.3740
0.026
E
0.083b ued
0.058O 3.6xO
etiats
egto
Eq. (3),E M is the
uing SLiMhemsodel,rinoesphr isptasuedEto bestiatolaerulof
infniesimal thcknsess.eacIonosheric shellahight wisthe heghL o
maimuma D
geogrmaphic loateion
difern ioopeiJelcincoceLuha.1]4,[]
[14]. o Ionos[4],ichosingdiferlengtioopei
rSulatTECTta
estmautesdfor300Eq.
Example
eenhtcEetmtion
smappin functionayand
elevation angle. ~~
stais
~
ns
~
the oaatmellit
D.WigtngGS
~
eEtTC simto dfeene
Signalsi frtomaeltsolowlevtio
susceptibleato multipath
aeltso iheeainage
1]herefore,RgEs
importnthutokappya
minimizekthemulipth effctsIn0 some3 stdis.masrmet
bAiefrom saeltecht
lMitsare vignrd Int [6], a000in1(68 isusdsa0eihtn
fNctiong
whre
cti
athreedifferentteliteD.weighting
esueetiosartiefothRgs
esue
ent
~~~~
it esettoinspei hih
anlsD rmr
tosinas3ro
itr is3100 26 0.4
weghin
effect
compare
electro
drensityanditelismalfunctio
[4]. Vagriousmentwthod
ftmn
intheu lTEraeturemaves
ant appropriate200roedret
[11]
egta are200 below a0etanelvtinanl
dfErencatro2 CoteCU lSEvel
428.k and450g kmnshl apreximgive orn
isctenro
IanFig3,mpRegs
the satelit elevtio anl.0I8hi3tuy
InppFig.3,ifiu
op
resultsarei verycltose to eahouoether.dT otinahquteantitatiave
imeothod.t
Thespweghtng apoptiosare wegiveng
below.et
difeet onsheicsletinchiessuhas[1,[4, 6,
iimzete uliat efct.Insoestdis ma32met
Page 5
1. Weighting Function:
ANKARA
F==71
0,
e,,,
~~~L(n) .1IO'
Wlm(n)
{exp((90 m(f))2n/2 IO') <£(n)<
60.(),(16)
60<nm(n)<90
i

X
2 . W e i g h ti n g F u n c ti o n :
2D ''
/~~r~~~~~~~II
 I
2. Weighting Function:
p0,
e,,(n)< I0° 1(
<em (n)<60 (17)
~~~~~~60'
.O.
w2m(n) =exp((60£m(n)) /2j2I)O
llX
<£m, (n)< 90'
246 10
121416is 2022
24
Fig. 4.
RegEst TEC estimates obtained wl, w2 and w3 weighting
functions for Ankara10.10.2003.
3. Weighting Function:
w3m(n)= sin2(Em (n))
(18)
TABLE 5
RegEst TEC estimation differences with respect to weighting functions wl,
w2 and w3.
Receiver Station
Da
Ankara
Oct 10, 2003
Ankara
Zelenchukskaya
Oct 10, 2003
Zelenchukskaya
Oct 28, 2003
ArtiOct 10, 2003
Arti Oct 31, 2003
Metsahovi Oct 10, 2003
Metsahovi
Oct 28, 2003
Nanyang
Oct 10, 2003
Nanyang
Oct 30, 2003
Thefirst weighting
function
is the one that
is used
previously in RegEst. This function ignores the measurements
below 100 elevation angle. The measurements between 100 and
600 are weighted using a Gaussian function which has a mean
at 900. The measurements above 600 are directly used. The
second weighting function is similar to first one except the
gaussian function has a mean at 600. The third weighting
function is the one that is used in [6]. These weighting options
are tried in RegEst method for various days and receiver
stations that are listed in TABLE 1. An example is provided in
Fig. 4 and TEC estimates for Ankara 10.10.2003 using wl, w2
and w3 are given. In Fig. 4, the estimates obtained by w2 and
w3 weighting functions are close to each other. These two
functions provide smooth transitions in time compared to those
of wl.
following normalized difference functions are defined. The
normalized differences obtained using these three difference
functions are given in TABLE5 for some stations and days as an
example.
D_
N X
X2(
D9E
Nn=1
Xw2
9
9.51x105
1.20xl04 2.34x104
8.69x105
5.14x105
7.77x105
2.67x104
1.53x104
1.62x104
1.71x104
2.78x104
2.34x104
3.06x104
3.3 Ix104
Oct 31, 2003
4.03x104 4.34x104
1.92x104
4.09x104 3.42x104
8.72x104
5.06x104
3.04x104
7.39x104 9.41x104
6.98x104
1.68x104
8.36x104
5.95x104
5.20x104
1.40xIO'
III. CONCLUSION
In order to examine the TEC estimates in detail, the
RegEst,developed in[1], [2],and[3],
resolution, robust TEC estimation technique. In this paper, the
use of satellite and receiver biases, the effects of ionospheric
shell height
and the choice of weighting functions are
investigated for further improvement of RegEst. Although
there is no
i(9)instrumental biases in the literature, two methods foradding
these biases is applied and the results are compared with IGS
analysis centers. The results are consistent with IGS centers
especially with JPL and CODE. The method which estimates
20
TEC closest to IONEX estimates for the use the instrumental
(20)
biases is selected for IONOLAB. In previous studies of Reg
Est, only pseudorange measurement were used as input to the
is a high
standard way ofusing satellite
and receiver
2
2
w2
lXw2
DN <
2
n=1
N2
regularization algorithm. In this paper, phase measurements are
used
technique. The TEC estimation results are very close to the
results of pseudorange measurements but TEC estimates from
phaseleveled measurements are less noisy.
Ionospheric shell height is a parameter used in Reg
Est. In this paper, different ionospheric height values are used
in RegEst method and the TEC estimates are compared. It is
observed thattheRegEstmethod is nearlyindependent ofthe
choice of ionospheric height. Weighting function helps to
reduce the multipath effect in the measurements of satellites
which are at low elevation angles. Three different weighting
1
Xw3Xwl
in RegEst method with
an appropriate
leveling
DI=E
2
(21)
N n=1
Xw2
In TABLE 5, Dg values are smaller than D1o and D1,
which shows that TEC estimation results of w2 and w3 are in
relatively better accordance for all stations compared to results
of wi.
Since w2 provides smooth transitions and reduces
sudden irregularities in TEC estimates, w2 can be used in
IONOLAB.
33
Page 6
options are tried and the weighting function which reduces the
nonionospheric effects best is selected for IONOLAB.
also shown that the TEC estimation results of IONOLAB is
consistent with IGS analysis centers especially with CODE and
JPL. 
It is
ACKNOWLEDGMENT
This study is supported by TUBITAK EEEAG grant no: 105E171.
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34