Single station bias calculation using data from calibrated GNSS station for various baseline distances

Abstract

Precise ionospheric TEC can be derived from dual-frequency GNSS carrier phase leveled pseudorange measurements. However, differential code biases (DCB) of satellite and receiver are the main errors that cannot be ignored for precise TEC calculation. We have proposed a method of calculating station DCB using calibrated STEC data from a baseline GNSS station. The method is simply based on the understanding that the ionosphere observed by two baseline GNSS stations at the same universal time (UT) can be considered similar and would pose similar delay to the signals propagating to the two stations. The method is tested for different baseline distances of 250–1000 km and in different latitudinal regions. For 500 km baseline, the average DCB calculation error for one year data is less than 0.22 ns, 0.11 ns, and 0.25 ns for low, mid and high latitude regions, respectively. The most consistent results were obtained from high latitudes where the standard deviation remains less than 0.22 ns. The least accurate were the low latitude results where the spread of error were between 0.29 to 0.50 ns. Results showed that the accuracy and consistency of the DCB estimation reduced with the increasing baseline distance between the two participating GNSS stations. This was specifically true for low latitude regions.

Full text

Shaikh
Progress in Earth and Planetary Science (2023) 10:2
https://doi.org/10.1186/s40645-022-00533-z
METHODOLOGY
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Open Access
Progress in Earth and
Planetary Science
Single station bias calculation using data
fromcalibrated GNSS station forvarious
baseline distances
Muhammad Mubasshir Shaikh1,2*
Abstract
Precise ionospheric TEC can be derived from dual-frequency GNSS carrier phase leveled pseudorange measurements.
However, differential code biases (DCB) of satellite and receiver are the main errors that cannot be ignored for precise
TEC calculation. We have proposed a method of calculating station DCB using calibrated STEC data from a baseline
GNSS station. The method is simply based on the understanding that the ionosphere observed by two baseline
GNSS stations at the same universal time (UT) can be considered similar and would pose similar delay to the signals
propagating to the two stations. The method is tested for different baseline distances of 250–1000 km and in differ-
ent latitudinal regions. For 500 km baseline, the average DCB calculation error for one year data is less than 0.22 ns,
0.11 ns, and 0.25 ns for low, mid and high latitude regions, respectively. The most consistent results were obtained
from high latitudes where the standard deviation remains less than 0.22 ns. The least accurate were the low latitude
results where the spread of error were between 0.29 to 0.50 ns. Results showed that the accuracy and consistency of
the DCB estimation reduced with the increasing baseline distance between the two participating GNSS stations. This
was specifically true for low latitude regions.
Keywords Differential code bias, Single station bias, TEC calibration, GNSS
1 Introduction
e ionosphere is a dynamic region of the earth’s atmos-
phere where conditions change diurnally and seasonally,
particularly with reference to changes in space weather
and geographical location. Total Electron Content (TEC)
is an important parameter for understanding the spatial
and temporal structures and variability of the ionosphere.
TEC can be understood as the line integral of the elec-
tron density along the path of a radio signal. Since the
launch of the Global Navigation Satellite System (GNSS),
global coverage of the ionosphere has become a reality.
Dual-frequency GNSS signals have been widely used to
monitor and model the TEC across the globe (Jakowski
et al. 2002). Precise ionospheric TEC can be derived
from dual-frequency GNSS carrier phase and pseudor-
ange measurements. However, inter-frequency satellite
and receiver differential delay biases (IFBs) are the main
errors that cannot be ignored for precise TEC calcula-
tion. ese biases are also known as differential code
biases (DCB). Previous studies show that DCBs are pre-
sent due to the delays caused by the analog hardware of
satellite and receiver and are instrumental (Lanyi and
Roth 1988). Satellite and receiver DCBs combined could
reach several tens of nanoseconds (ns) or approximately
up to 100 TEC units (TECU); therefore, from GNSS
measurements, DCBs must be removed for both satel-
lite and receiver for precise positioning and accurate TEC
calculation. Satellite and receiver DCBs are assumed to
*Correspondence:
Muhammad Mubasshir Shaikh
mshaikh@sharjah.ac.ae
1 Sharjah Academy for Astronomy, Space Sciences & Technology,
University of Sharjah, Sharjah, United Arab Emirates
2 Department of Electrical Engineering, University of Sharjah, Sharjah,
United Arab Emirates

Page 2 of 9
Shaikh Progress in Earth and Planetary Science (2023) 10:2
be constant for a given time period, typically up to three
days (Brunini etal. 2005).
Receiver DCB for a single station can typically be
calculated by using polynomial of coordinates in solar-
terrestrial reference system by the observations from a
linear system of equations that is solved by least squares
method for the polynomial coefficients and unknown
biases (Lanyi and Roth 1988). Another widely used
method to calculate a single station DCB is the method
of minimization of the standard deviation of vertical
TEC (VTEC) (Ma and Maruyama 2003). Apart from
these commonly known methods, several other meth-
ods for GNSS DCB estimates using multi-frequency
observations have been designed (Schaer 1999; Wang
etal. 2016; Su etal. 2019). ese methods successfully
used various approaches to solve for the station DCB
such as by setting the DCB as a constant during the
TEC estimation or by decreasing the computation costs
by using GIM (global ionospheric maps). Furthermore,
several other techniques that help optimize the DCB
estimation have been adopted such as optimization
on DCB estimation based on regional or single station
ionospheric modeling (Brunini and Azpilicueta 2010;
Nie etal. 2018). However, all these methods come with
some fundamental assumptions, for example, the single-
layer TEC model, the assumption that the satellite and
receiver DCBs remain constant for some days, and a
Lagrange multiplier to separate the satellite and receiver
DCBs generally called ‘zero-mean constraint’ etc. Using
various methods mentioned above, several research
institutes provide satellite and receiver DCB estimates
in the form of IONEX (Ionosphere Map Exchange For-
mat) file format. However, different DCB calculations
provided from various institutes are not always in agree-
ment with each other (Brunini etal. 2005). It is there-
fore understood that DCB estimation suffers similar
shortcomings to TEC assumptions which are generally
present in most of the sources through which we get the
satellite and receiver biases.
We have proposed a simple technique for the com-
putation of single station receiver DCB. e technique
uses the model of STEC computed from the difference
in GPS observables and does not depend on any of the
assumptions made in previous works such as the use of
TEC thin shell model, zero-mean constraint or requir-
ing any external data such as GIM maps to help aid the
DCB estimation process. e accuracy of DCB esti-
mates is evaluated by the Chinese Academy of Sciences
IONEX data files. In the next sections, a brief about the
GNSS TEC calculation model is presented. ‘Data’ sec-
tion presents the data sources used for the application
and analysis of the proposed technique followed by the
description of the proposed technique in the section
‘DCB Calculation’. Performance of the technique is
analyzed under ‘Results and Analysis’ section before
concluding the paper with a brief summary and future
work in ‘Summary and Conclusion’ section.
1.1 GNSS TEC model
Pseudorange measurements from dual-frequency GNSS
receivers can be performed using time delay of GNSS sig-
nals at two different frequencies (Leick 2004). For dual-
frequency GPS receivers, pseudorange measurements,
P1 and P2, and carrier phase measurements, L1 and
L2, are calculated at frequencies f1 (1.575GHz) and f2
(1.227GHz), respectively. e standard model for pseu-
dorange and carrier phase measurements at f1 and f2 is:
where ‘i’ denotes the index for frequency, ‘r’ is receiver
index, ‘s’ is satellite index, ‘R’ is the actual range between
satellite and receiver, ‘

’ and ‘
φ
’ are wavelength and phase
delay, respectively,
′
δ
t′
r
and ‘
δts
’ are the clock errors for
the receiver and satellite, respectively, ‘
ds
trop,r
’ and ‘
ds
ion,i,r
’
are the troposphere and ionosphere group delays, respec-
tively, ‘
DCBr
’ and ‘
DCBs
’ are the frequency-dependent
receiver and satellite differential code biases, respectively,
and ‘N’ is the initial phase ambiguity. e STEC using
code and phase delay observations can be obtained by
using the geometry-free linear combination by ignoring
the higher order effects of the ionosphere as follows:
where ‘
PI
’ and ‘
LI
’ are the ionospheric geometry free lin-
ear combinations for code and phase observations, respec-
tively, ‘
STEC
’ is slant total electron content between each
satellite-to-receiver link. Although unlike code delay
measurements, carrier phase measurements are less prone
to measurement noise and multipath, they are biased by
phase ambiguity (Mannucci et al. 1998). Carrier-to-code
leveling algorithm (Ciraolo etal. 2007) is widely used to
reduce the ambiguities from the carrier phase ionospheric
observables. After obtaining ionospheric observables, as
(1)
Ps
i,r
=R
s
r
+c(δtr−δts)+d
s
trop,r
+d
s
ion,i,r
+cDCBr+DCB
s
(2)
Ls
i,r =iφ
s
i,r =R
s
r+c

δtr−δt
s
+iφ
s
ion,i, r +iφ
s
trop,r
−c

DCB
r
+DCBs

+
i
Ns
i
(3)
P
I=40.3

f2
1−f2
2
f2
1
∗f2
2
STECs
r−c

DCBr+DCBs

(4)
L
I=40.3

f2
1−f2
2
f2
1
∗f2
2
STECs
r−c

DCBr+DCBs

+N
s

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Shaikh Progress in Earth and Planetary Science (2023) 10:2
mentioned in (3) and (4), the average of the differences
between them is computed for every continuous arc as:
where ‘N’ is the number of continuous measurements
contained in a single satellite-to-receiver arc. e sub-
script ‘arc’ refers to every continuous set of carrier phase
observations between the receiver and a particular satel-
lite (i.e., a group of consecutive observations along which
the ambiguities on L1 and L2 do not change). Finally, to
obtain the leveled STEC phase observations:
where ‘
˜
LI,arc
’ is the carrier phase ionospheric observable
leveled to the code-delay ionospheric observable. is
procedure is known as carrier-to-code levelling process.
Using the above-mentioned carrier-to-code levelling
processes, in this work, a simple technique is introduced
which could help calculate the receiver DCB provided
that the leveled STEC data from a baseline station is
available. A detailed description of the proposed tech-
nique is given in the section DCB Calculation.
1.2 Data
All the GNSS data including RINEX (Receiver Independ-
ent Exchange Format) and IONEX data used in this study
has been acquired from NASA’s Crustal Dynamics Data
Information System (CDDIS: https:// cddis. nasa. gov/
archi ve/ gnss/) database. e data period used in this
study is of the year 2019 since it is the low solar activ-
ity year. Only data from GPS constellation has been used
in this work. Initially, we considered using data from 64
IGS stations from different latitudinal regions. However,
since, we have only considered GPS P-code data in this
work, the number of GNSS stations we ended up using
in this work are 19. is gives us 11 different combina-
tions with different baseline distances in pairs of GNSS
stations with which we have tested our technique. Data
observed on days with active geomagnetic conditions,
that is, Dst < -50 nT and Kp > 3 have not been considered
for analysis. e Dst index has been obtained from World
Data Center (Kyoto etal. 2015) and Kp from GFZ Data
Services (Matzka et al. 2021). e minimum elevation
mask for GPS observations used in this work is 30°.
2 Method
e proposed method to estimate the station DCB is
simply based on the understanding that the ionosphere
observed by two baseline GNSS stations at the same uni-
versal time (UT) can be considered similar and would
(5)

LI−PIarc =
1
N
N

1
(LI−PI
)
(6)
˜
L
I
,arc
=LI
,arc
−LI
,arc
−PI
arc
pose similar delay to the signals propagating to the two
stations. at is, if a particular GNSS satellite is visible
to two different GNSS stations present at a certain base-
line at the same UT, their average STEC, calculated using
overlapping STEC arcs, considered as same. In this way,
uncalibrated STEC data for which the receiver DCB is
unknown can be calibrated using the calibrated STEC
data from the other baseline GNSS station and the dif-
ference of their STEC can be used to calculate DCB for
uncalibrated station. STEC arc here is referred to the
STEC data calculated using continuous observation
between a GNSS station and a GNSS satellite. e term
baseline is understood here as the straight-line distance
between the two participating stations, that is, the uncali-
brated GNSS station for which DCB is being calculated
and the calibrated GNSS station from which the data is
taken for the DCB calculation process. For the calibrated
GNSS station, the STEC data is code-to-phase leveled as
indicated in (6). e station from which the calibrated
STEC is obtained will be referred to as ‘Ref’.
Figure 1 (top panel) shows two arcs overlapping in
time observed by two different GNSS stations MAL2 and
MBAR. Station MAL2, used here as Ref, is calibrated for
satellite and receiver biases available from IONEX files
and leveled through carrier-to-code leveling process
using (3), (4) and (6). Station MBAR is only corrected
for the satellite biases available from the same source of
IONEX data. Since the arc observed by station MAL2 is
longer in time than the arc observed by station MBAR,
we have only considered the length of the arcs from the
two stations which are overlapping in time as shown in
Fig.1 (middle panel). ese two arcs overlapping in time
will be referred to as ‘overlapping arcs’. e bias between
the two overlapping arcs is then calculated by taking the
mean of the difference of the two overlapping arcs. is
will be referred to as ‘arc bias’ and calculated as shown
below:
where ‘
LI,arc,uncalib
’ is the uncalibrated phase arc for
which the DCB calculation is being performed, ‘
˜
LI,arc
’ is
the calibrated phase arc of Ref calculated using (6).
Figure1 (bottom panel) shows how the two overlap-
ping arcs look like after the arc bias is removed from
the uncalibrated arc. e process is then repeated for
the calculation of all arc biases using all the overlapping
arcs of STEC for all available GNSS satellites observed
by the two participating stations in a 24-h period. Finally,
the station bias is calculated by taking an average of all
the arc biases. is daily station bias calculation in TEC
unit (TECU) is then divided by 2.86 to convert it to
(7)
arc bias
=LI,arc,uncalib −

LI,arc,uncalib −˜
LI,arc
arc

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Shaikh Progress in Earth and Planetary Science (2023) 10:2
nanoseconds (ns). While applying this technique, we
have used a minimum length of the overlapping STEC
arcs greater than or equal to 1h and minimum of 5 such
overlapping arc must be available for the daily GNSS sta-
tion bias calculation. ese limits are set on the basis of
trial and error. In case of more than one overlapping arcs
present from a particular satellite, referred here as ‘sub-
arcs’, an average of all the individual overlapping sub-arcs’
biases are used to calculate the arc bias. Figure2 shows
a simplified block diagram of the proposed technique.
In this work, we have considered several different base-
line distances between the uncalibrated station and the
Ref. ese baseline distances are varying around 250km
to 1000km and their results are presented in the next
section.
3 Results
We have selected several pairs of GNSS stations from dif-
ferent latitudinal regions to test this method. is was
done to check the validity and robustness of the method
in different latitudinal regions and for different baseline
distances. It was desired that the technique should be
simple enough to be implemented quickly and effectively
without the need of a complicated algorithm or assump-
tions. While selecting the GNSS stations, it was preferred
that different baseline distances of greater than 500km
Fig. 1 Calibration of overlapping STEC arcs of the two participating
stations used to calculate the station bias. The data shown is STEC
arcs obtained from GPS PRN02 on day of year 029. Please note the
changing x- and y-axis in separate panels. Please note that the scale
of x- and y-axes are different in each panel
Daily RINEX observation
file for uncalibrated
GNSS station
Calculate STEC
Find ‘overlapping arcs’
of >1 hour with Ref
Calculate ‘arc bias’
Calculate average of all
the ‘arc biases’ for 24-
hour to calculate the
station dcb
Number of ‘overlapping
arcs’ >5
YES
NO
Fig. 2 Simplified block diagram for the proposed technique to
calculate bias for the uncalibrated GNSS station

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Shaikh Progress in Earth and Planetary Science (2023) 10:2
are selected for the test and analysis. is is important
since there is a limitation of minimum of 5 overlapping
arc be present between both stations on the day on which
the DCB calculation is desirable.
Figure3 shows the DCB estimation error (Δ DCB)
calculated between daily bias estimation using the pro-
posed method and the bias available from the IONEX
files provided by the Chinese Academy of Sciences (file
code casg in CDDIS). Here, only results concerning
stations with baseline distances of approximately
500km are shown. It can be seen that the proposed
technique estimated the DCB accurately at different
latitudinal sectors. Particularly, in mid-latitudes, the
average error is only limited to 0.04–0.11ns compared
to what was estimated in the IONEX files. e results
from the higher latitudes are very consistent for the
whole 1-year period, which can be seen by the small
spread of error as shown in the bottom panel of Fig.3.
Fig. 3 For low-, mid-, and high-latitude station bias calculation. Top row shows results for low-latitude, middle one for mid-latitude and bottom one
for high latitude stations, respectively. Participating station pair’s codes are shown in the top left corner of each panel. Baseline distance between
the two participating stations, mean and standard deviation of calculation errors are also shown at the top left corner. The frequency axis on each
plot is different and set according to the number of days’ data available. The black dotted line in the middle of each plot shows the zero difference
line between calculated and available station bias

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Shaikh Progress in Earth and Planetary Science (2023) 10:2
Even though the baseline distances are larger in higher
latitude stations, the results are still consistent as com-
pared to low- and mid-latitude stations. It is also noted
that bias calculation for southern hemispheric stations
seems to be more consistent as compared to the north-
ern hemispheric stations, as shown in the left column
of Fig.3.
Apart from testing the algorithm for a minimum
baseline distance of 500 km, we have also checked
whether the technique also works with other baseline
distances. As one of our two special cases, we also
checked if the technique generally performs better or
at least equally good if the baseline distance is smaller.
Figure4 is an example of two pairs of stations where
baseline distances are approximately half of what was
used in Fig. 3. Figure 4 clearly shows that the tech-
nique performs better when the baseline distances are
smaller. is may be due to the fact that with more
overlapping arcs and closer ionospheric conditions due
to shorter geographical distances, the overall average of
the day for the station DCB calculation improves sig-
nificantly. Specifically, the spread of the error is limited
to only 0.17–0.18ns in both mid- and high-latitudes
as compared to 0.14–0.30ns in case of 500m baseline
for mid- and high-latitude stations’ pairs as shown in
Fig.3. It was desired that at least on low-latitude pair is
tested for this shorter baseline case, but unfortunately,
the data is not available.
A second special case for longer baseline distances
has also been tested. Figure5 is the DCB calculation for
a baseline distance at least twice the baseline previously
used in Fig.3. e bias calculation error has certainly
deteriorated in low- and high-latitude in terms of aver-
age and spread of error calculation, respectively. How-
ever, the calculation of average bias for low latitude
stations’ pair has shown remarkable results with an
error less than 0.1ns. e best bias calculation results
are again obtained in the mid-latitudes, where the tech-
nique produces a similar error as it was in the case of
Fig. 4 Bias calculation error for shorter baseline case. The top panel is
for mid-latitude and the bottom panel is for the high-latitude stations’
pair. The black dotted line in the middle of each plot shows the zero
DCB error line
Fig. 5 Bias calculation error for longer baseline case. Top row shows
results for low-latitude, middle one for mid-latitude and bottom one
for high latitude stations’ pair. The black dotted line in the middle of
each plot shows the zero DCB error line

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Shaikh Progress in Earth and Planetary Science (2023) 10:2
the 500km baseline. e spread of error over a one-
year period is also less than 0.15ns.
4 Discussion
Considering all the results, it has been concluded that
the proposed technique based on overlapping arcs of
two baseline stations can be effectively used to calculate
the station bias for the uncalibrated station. e maxi-
mum errors in DCB calculation for the 500km baseline is
found to be 0.25ns at high latitude. e standard devia-
tion shows that the maximum spread ΔDCB calculation
is also limited to an average value of 0.35 ns which is
found in low latitude. Two other baseline distances were
evaluated to check the robustness of the technique. For
half baseline case for which baseline distance between
the two stations was limited to approximately 250km,
the results seemed to improve. e average ΔDCB is
found to be 0.01 and 0.08 in mid- and high-latitude sta-
tions, respectively. e spread of the error is also limited
to 0.17–0.18ns for mid- and high-latitude stations’ pair,
respectively. e second special case considered where
the baseline distance is increased to at least double the
500km baseline, that is, approximately 1000km. Mid-
latitude stations’ pairs were most consistent with 0.25ns
average error and spread of only 0.14 ns. Although,
ΔDCB calculation was found to be least in low-latitude
as 0.09ns, the consistency is much worse than mid-lati-
tude, that is, 0.50ns. e high-latitude DCB calculation
was the least accurate among the three with 0.71ns aver-
age. However, the calculations were consistent with only
0.21ns spread.
Table1 shows an overall summary of different GNSS
station pairs used in this work with their geographical
regions and approximate baseline distances mentioned.
e data shown in the table has been taken from
different panels of Figs. 3, 4, 5. e results obtained
from several pairs of GNSS stations separated by differ-
ent baseline distances showed that the method works
accurately. Specifically, for mid-latitudes stations, the
error in calculating station DCB remains less than or
equal to 0.11ns, on average, for less than 500km base-
line distance, when compared to the available IONEX
data taken from the same source with which the STEC
is calibrated for the Ref. It increased to 0.25 when the
baseline increased to more than 1000km. For low-lat-
itude GNSS stations, the maximum error remains less
than 0.22ns at all baseline distances. For high-latitude
stations, the mean error systematically increased with
the baseline distance from 0.08 to 0.71, respectively.
e most consistent results were obtained from high
latitudes where the standard deviation ranges between
0.14 to 0.22ns. e least accurate were the low lati-
tudes results where the spread of error were between
0.29 to 0.50ns. It has been inferred from the results
that, in general, the accuracy and consistency of the
DCB calculation reduce with the increasing baseline.
is is specifically true for low-latitude GNSS stations.
The results obtained after applying a very simple
technique of utilizing overlapping STEC arcs using
calibrated data from a baseline station seems to be
producing the desired results consistently in all latitu-
dinal regions. It is also understood that the technique
can be effectively applied to calculate reliable results
with baseline distances of less than 1000 km in all
latitudinal regions without any complex mathematical
algorithms for averaging or extrapolating the results.
It should not be wrong to conclude that the method
works accurately if the baseline distance between the
two participating stations remains less than or close to
500km.
Table 1 Pair of GNSS stations used to evaluate the technique. In the stations’ pair, in the first column, the first station code is the code
of the uncalibrated station, and the second code is for the Ref
SN GNSS station pair Baseline distance (km) DCB error mean (ns) DCB error standard deviation
(ns) Region
1 MABR-MOIU 516 − 0.04 0.29 Low-Lat
2 ADIS-DJIG 525 0.22 0.42 Low-Lat
3 MBAR-MAL2 1084 − 0.09 0.50 Low-Lat
4 TID1—SYDN 268 0.01 0.17 Mid-Lat
5 CORD-SANT 610 0.11 0.14 Mid-Lat
6 WARN-TIT2 518 0.04 0.30 Mid-Lat
7 BOGI-TIT2 1016 − 0.25 0.14 Mid-Lat
8 KIRU-SOD3 234 − 0.08 0.18 High-Lat
9 MAW1-DAV1 635 − 0.04 0.14 High-Lat
10 EIL4-WHIT 745 − 0.25 0.22 High-Lat
11 YELL-WHIT 1108 − 0.71 0.21 High-Lat

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Shaikh Progress in Earth and Planetary Science (2023) 10:2
5 Conclusions
We have proposed a technique to calculate GNSS station
DCB for TEC calibration. Among all the other techniques
currently in use, this technique is very simple to apply and
does not depend on any of the assumptions such as the
use of the ionospheric thin shell model, zero-mean con-
straint or requiring any external data such as GIM maps to
help aid the DCB estimation process. e purpose of the
technique is to provide a quick way to calculate the sta-
tion DCB for any GNSS station which is within baseline
distance of 250–1000km from a calibrated GNSS station.
e proposed method is simply dependent on the avail-
ability of calibrated STEC data from a baseline GNSS sta-
tion. e technique works by finding ‘overlapping arcs’ of
STEC between the baseline uncalibrated and Ref stations
and then calculating the ‘arc bias’ for each overlapping arc
of at least 1h duration. It is required that, for the calcula-
tion of daily station DCB, at least 5 of such overlapping
arcs must be present between the two baseline stations in
a 24-h period. To have better accuracy, it is strongly rec-
ommended that the calibrated STEC data is also code-to-
phase leveled. Although we have only used GPS data in
this work, it is believed that the proposed technique could
be effectively used to calculate station DCB using data
from other GNSS constellations.
e proposed technique provides an alternate method
of calculating single station DCB without the complication
of previously applied assumptions or using external data.
A comprehensive analysis has been done by applying the
technique with several pairs of GNSS stations at different
latitudinal sectors to check the validity and consistency of
the technique. e results show that the technique works
accurately and consistently up to 1000km baseline dis-
tance. e technique may also work for larger baseline dis-
tances but with lesser accuracy and consistency. is work
will be continued in expanding the scope of the application
of this technique with other GNSS constellation and to
improve the precision and accuracy. Specifically, it would
be interesting to see if the short-term receiver DCB vari-
ability as mentioned by Zhang etal. (2019) would impact
the outcome of the results presented in this paper.
Abbreviations
CDDIS Crustal dynamics data information system
DCB Differential code bias
GIM Global ionospheric map
GNSS Global navigation satellite system
IFB Inter-frequency bias
IONEX Ionosphere map exchange format
STEC Slant total electron content
PRN Pseudorandom noise
RINEX Receiver independent exchange format
TEC Total electron content
TECU Total electron content unit
UT Universal time
VTEC Vertical total electron content
Acknowledgements
Author would like to thank International GNSS Service (IGS) for providing
a comprehensive information about the network of GNSS station which
helped in the selection of GNSS stations used in this work. Author is grateful
for the CDDIS (https:// cddis. nasa. gov/ archi ve/ gnss/) database for providing
global RINEX and IONEX data free of charge for scientific use.
Authors’ Information
Dr Mubasshir is currently working as a research associate and principal
investigator at the Space Weather and Ionosphere (SW&I) laboratory at Sharjah
academy for Astronomy, Space Sciences and Technology (SAASST), Sharjah,
UAE. Before joining SAASST, he completed his doctorate from Politecnico di
Torino, Italy, in the research area of ionospheric physics. He then worked as
a postdoctoral visiting research scientist at the Abdus Salam International
Center for Theoretical Physics (ICTP), Trieste, Italy. His research interests include
ionospheric modeling and data assimilation techniques for ionospheric
empirical modeling.
Author contributions
MMS initiated the idea, designed the methodology, analyzed the data and
wrote the complete manuscript. The author read and approved the final
manuscript.
Funding
No external has been received to conduct the research presented in this
paper.
Availability of data and materials
The RINEX and IONEX data used to perform this research work has been
obtained from CDDIS database at: https:// cddis. nasa. gov/ archi ve/ gnss/.
Declarations
Competing interests
The authors declare that they have no competing interest.
Received: 1 September 2022 Accepted: 29 December 2022
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