Shaikh ﻿Progress in Earth and Planetary Science(2023) 10:2
https://doi.org/10.1186/s40645-022-00533-z

Progress in Earth andPlanetary Science

Open Access

METHODOLOGY

Single station bias calculation using datafrom 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 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. Thiswas specifically true for low latitude regions.
Keywords Differential code bias, Single station bias, TEC calibration, GNSS
1 Introduction
The ionosphere is a dynamic region of the earth’s atmosphere 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 electron density along the path of a radio signal. Since thelaunch of the Global Navigation Satellite System (GNSS),*Correspondence:
Muhammad Mubasshir Shaikhmshaikh@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

global coverage of the ionosphere has become a reality.
Dual-frequency GNSS signals have been widely used tomonitor and model the TEC across the globe (Jakowski
et al. 2002). Precise ionospheric TEC can be derived
from dual-frequency GNSS carrier phase and pseudorange measurements. However, inter-frequency satellite
and receiver differential delay biases (IFBs) are the mainerrors that cannot be ignored for precise TEC calculation. These biases are also known as differential code
biases (DCB). Previous studies show that DCBs are present due to the delays caused by the analog hardware ofsatellite and receiver and are instrumental (Lanyi andRoth 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 satellite and receiver for precise positioning and accurate TEC
calculation. Satellite and receiver DCBs are assumed to© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Shaikh ﻿Progress in Earth and Planetary Science(2023) 10:2

be constant for a given time period, typically up to threedays (Brunini et al. 2005).
Receiver DCB for a single station can typically becalculated by using polynomial of coordinates in solarterrestrial 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 usedmethod to calculate a single station DCB is the methodof minimization of the standard deviation of vertical
TEC (VTEC) (Ma and Maruyama 2003). Apart fromthese commonly known methods, several other methods for GNSS DCB estimates using multi-frequency
observations have been designed (Schaer 1999; Wanget al. 2016; Su et al. 2019). These 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 withsome fundamental assumptions, for example, the singlelayer TEC model, the assumption that the satellite andreceiver 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 estimatesin the form of IONEX (Ionosphere Map Exchange Format) file format. However, different DCB calculations
provided from various institutes are not always in agreement with each other (Brunini et al. 2005). It is therefore understood that DCB estimation suffers similar
shortcomings to TEC assumptions which are generally
present in most of the sources through which we get thesatellite and receiver biases.
We have proposed a simple technique for the computation of single station receiver DCB. The techniqueuses the model of STEC computed from the differencein GPS observables and does not depend on any of theassumptions made in previous works such as the use of
TEC thin shell model, zero-mean constraint or requiring any external data such as GIM maps to help aid the
DCB estimation process. The accuracy of DCB estimates 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’ section presents the data sources used for the application
and analysis of the proposed technique followed by thedescription of the proposed technique in the section

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‘DCB Calculation’. Performance of the technique isanalyzed 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 signals at two different frequencies (Leick 2004). For dualfrequency GPS receivers, pseudorange measurements,
P1 and P2, and carrier phase measurements, L1 andL2, are calculated at frequencies f1 (1.575 GHz) and f2(1.227 GHz), respectively. The standard model for pseudorange and carrier phase measurements at f1 and f2 is:
s
s
s
Pi,r
= Rrs + c(δtr − δts ) + dtrop,r+ dion,i,r+ c DCBr + DCBs

(1)

s
s
s
Lsi,r =i φi,r
= Rrs + c δtr − δt s + i φion,i,r + i φtrop,r− c DCBr + DCBs + i Nis





(2)
where ‘i’ denotes the index for frequency, ‘r’ is receiverindex, ‘s’ is satellite index, ‘R’ is the actual range between
satellite and receiver, ‘’ and ‘φ ’ are wavelength and phasedelay, respectively, ′ δtr′ and ‘δts’ are the clock errors forss
the receiver and satellite, respectively, ‘dtrop,r’ and ‘dion,i,r’
are the troposphere and ionosphere group delays, respectively, ‘DCBr’ and ‘DCBs’ are the frequency-dependent
receiver and satellite differential code biases, respectively,and ‘N’ is the initial phase ambiguity. The STEC usingcode and phase delay observations can be obtained byusing the geometry-free linear combination by ignoring
the higher order effects of the ionosphere as follows:f12 − f22
STECsr − c DCBr + DCBs (3)PI = 40.3
22
f1 ∗ f2

f2−f2
LI = 40.3 12 22
f1 ∗ f2


STECsr − c DCBr + DCBs + N s

(4)where ‘ PI ’ and ‘ LI ’ are the ionospheric geometry free linear combinations for code and phase observations, respectively, ‘STEC’ is slant total electron content between eachsatellite-to-receiver link. Although unlike code delay
measurements, carrier phase measurements are less prone
to measurement noise and multipath, they are biased byphase ambiguity (Mannucci et al. 1998). Carrier-to-codeleveling algorithm (Ciraolo et al. 2007) is widely used toreduce the ambiguities from the carrier phase ionosphericobservables. After obtaining ionospheric observables, asShaikh ﻿Progress in Earth and Planetary Science(2023) 10:2

Page 3 of 9

mentioned in (3) and (4), the average of the differences
between them is computed for every continuous arc as:N�LI − PI �arc =1 (LI − PI )
N

(5)

1

where ‘N’ is the number of continuous measurements
contained in a single satellite-to-receiver arc. The subscript ‘arc’ refers to every continuous set of carrier phaseobservations between the receiver and a particular satellite (i.e., a group of consecutive observations along which
the ambiguities on L1 and L2 do not change). Finally, toobtain the leveled STEC phase observations:L̃I,arc = LI,arc − �LI,arc − PI �arc

(6)

where ‘ L̃I,arc’ is the carrier phase ionospheric observableleveled to the code-delay ionospheric observable. This
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 isavailable. A detailed description of the proposed technique is given in the section DCB Calculation.
1.2 Data

All the GNSS data including RINEX (Receiver Independent 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. The data period used in thisstudy is of the year 2019 since it is the low solar activity year. Only data from GPS constellation has been usedin 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 thiswork, the number of GNSS stations we ended up using
in this work are 19. This gives us 11 different combinations with different baseline distances in pairs of GNSS
stations with which we have tested our technique. Dataobserved on days with active geomagnetic conditions,that is, Dst < -50 nT and Kp > 3 have not been considered
for analysis. The Dst index has been obtained from World
Data Center (Kyoto et al. 2015) and Kp from GFZ Data
Services (Matzka et al. 2021). The minimum elevation
mask for GPS observations used in this work is 30°.

2 Method
The proposed method to estimate the station DCB issimply based on the understanding that the ionosphereobserved 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 twostations. That is, if a particular GNSS satellite is visible
to two different GNSS stations present at a certain baseline 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 difference 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. The termbaseline is understood here as the straight-line distance
between the two participating stations, that is, the uncalibrated GNSS station for which DCB is being calculated
and the calibrated GNSS station from which the data istaken for the DCB calculation process. For the calibrated
GNSS station, the STEC data is code-to-phase leveled asindicated in (6). The station from which the calibrated
STEC is obtained will be referred to as ‘Ref ’.
Figure 1 (top panel) shows two arcs overlapping intime observed by two different GNSS stations MAL2 andMBAR. Station MAL2, used here as Ref, is calibrated forsatellite and receiver biases available from IONEX files
and leveled through carrier-to-code leveling processusing (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 islonger in time than the arc observed by station MBAR,
we have only considered the length of the arcs from thetwo stations which are overlapping in time as shown in
Fig. 1 (middle panel). These two arcs overlapping in time
will be referred to as ‘overlapping arcs’. The bias between
the two overlapping arcs is then calculated by taking themean of the difference of the two overlapping arcs. This
will be referred to as ‘arc bias’ and calculated as shown
below:

arc bias = LI,arc,uncalib − LI,arc,uncalib − L̃I,arc
arc(7)
where ‘ LI,arc,uncalib’ is the uncalibrated phase arc forwhich the DCB calculation is being performed, ‘ L̃I,arc’ isthe calibrated phase arc of Ref calculated using (6).
Figure 1 (bottom panel) shows how the two overlapping arcs look like after the arc bias is removed fromthe uncalibrated arc. The process is then repeated forthe calculation of all arc biases using all the overlappingarcs of STEC for all available GNSS satellites observedby the two participating stations in a 24-h period. Finally,
the station bias is calculated by taking an average of all
the arc biases. This daily station bias calculation in TEC
unit (TECU) is then divided by 2.86 to convert it toShaikh ﻿Progress in Earth and Planetary Science(2023) 10:2

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Daily RINEX observation
file for uncalibrated
GNSS station

Calculate STEC

Find ‘overlapping arcs’of > 1 hour with Ref

NO

Number of ‘overlappingarcs’ > 5

YES

Calculate ‘arc bias’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 thechanging x- and y-axis in separate panels. Please note that the scaleof x- and y-axes are different in each panel

nanoseconds (ns). While applying this technique, wehave used a minimum length of the overlapping STEC
arcs greater than or equal to 1 h and minimum of 5 suchoverlapping arc must be available for the daily GNSS station bias calculation. These limits are set on the basis oftrial and error. In case of more than one overlapping arcs
present from a particular satellite, referred here as ‘subarcs’, an average of all the individual overlapping sub-arcs’
biases are used to calculate the arc bias. Figure 2 showsa simplified block diagram of the proposed technique.
In this work, we have considered several different baseline distances between the uncalibrated station and theRef. These baseline distances are varying around 250 km

Calculate average of all
the ‘arc biases’ for 24hour to calculate thestation dcb
Fig. 2 Simplified block diagram for the proposed technique tocalculate bias for the uncalibrated GNSS station

to 1000 km and their results are presented in the next
section.

3 Results
We have selected several pairs of GNSS stations from different latitudinal regions to test this method. This wasdone 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 assumptions. While selecting the GNSS stations, it was preferredthat different baseline distances of greater than 500 km

Shaikh ﻿Progress in Earth and Planetary Science(2023) 10:2

are selected for the test and analysis. This is importantsince there is a limitation of minimum of 5 overlappingarc 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 proposed method and the bias available from the IONEX
files provided by the Chinese Academy of Sciences (filecode casg in CDDIS). Here, only results concerning

Page 5 of 9

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, theaverage error is only limited to 0.04–0.11 ns compared
to what was estimated in the IONEX files. The resultsfrom the higher latitudes are very consistent for thewhole 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 eachplot 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 differenceline between calculated and available station bias

Shaikh ﻿Progress in Earth and Planetary Science(2023) 10:2

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Even though the baseline distances are larger in higher
latitude stations, the results are still consistent as compared to low- and mid-latitude stations. It is also notedthat bias calculation for southern hemispheric stations
seems to be more consistent as compared to the northern hemispheric stations, as shown in the left columnof 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 orat least equally good if the baseline distance is smaller.
Figure 4 is an example of two pairs of stations wherebaseline distances are approximately half of what wasused in Fig. 3. Figure 4 clearly shows that the technique performs better when the baseline distances are
smaller. This may be due to the fact that with more
overlapping arcs and closer ionospheric conditions due
to shorter geographical distances, the overall average ofthe day for the station DCB calculation improves significantly. 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 istested 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 fora baseline distance at least twice the baseline previously
used in Fig. 3. The bias calculation error has certainly
deteriorated in low- and high-latitude in terms of average and spread of error calculation, respectively. However, the calculation of average bias for low latitude
stations’ pair has shown remarkable results with anerror less than 0.1 ns. The best bias calculation results
are again obtained in the mid-latitudes, where the technique produces a similar error as it was in the case of

Fig. 4 Bias calculation error for shorter baseline case. The top panel isfor 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 ofeach plot shows the zero DCB error line

Shaikh ﻿Progress in Earth and Planetary Science(2023) 10:2

the 500 km baseline. The spread of error over a oneyear period is also less than 0.15 ns.

4 Discussion
Considering all the results, it has been concluded thatthe proposed technique based on overlapping arcs of
two baseline stations can be effectively used to calculate
the station bias for the uncalibrated station. The maximum errors in DCB calculation for the 500 km baseline isfound to be 0.25 ns at high latitude. The standard deviation shows that the maximum spread ΔDCB calculationis also limited to an average value of 0.35 ns which isfound 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. The average ΔDCB isfound to be 0.01 and 0.08 in mid- and high-latitude stations, respectively. The spread of the error is also limited
to 0.17–0.18 ns for mid- and high-latitude stations’ pair,respectively. The second special case considered where
the baseline distance is increased to at least double the
500 km baseline, that is, approximately 1000 km. Midlatitude 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-latitude, that is, 0.50 ns. The high-latitude DCB calculation
was the least accurate among the three with 0.71 ns average. 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 geographicalregions and approximate baseline distances mentioned.
The data shown in the table has been taken fromPage 7 of 9

different panels of Figs. 3, 4, 5. The results obtained
from several pairs of GNSS stations separated by different baseline distances showed that the method works
accurately. Specifically, for mid-latitudes stations, theerror in calculating station DCB remains less than orequal to 0.11 ns, on average, for less than 500 km baseline 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 thebaseline increased to more than 1000 km. For low-latitude GNSS stations, the maximum error remains lessthan 0.22 ns at all baseline distances. For high-latitude
stations, the mean error systematically increased withthe baseline distance from 0.08 to 0.71, respectively.
The most consistent results were obtained from highlatitudes where the standard deviation ranges between
0.14 to 0.22 ns. The least accurate were the low latitudes 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.
This 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 latitudinal regions. It is also understood that the technique
can be effectively applied to calculate reliable resultswith baseline distances of less than 1000 km in all
latitudinal regions without any complex mathematicalalgorithms for averaging or extrapolating the results.
It should not be wrong to conclude that the method
works accurately if the baseline distance between thetwo 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 codeof the uncalibrated station, and the second code is for the Ref
SN

GNSS station pair

Baseline distance (km)

DCB error mean (ns)
− 0.04

1

MABR-MOIU

516

2

ADIS-DJIG

525

3

MBAR-MAL2

1084

4

TID1—SYDN

268

0.22

− 0.090.01

DCB error standard deviation Region
(ns)
0.29

Low-Lat

0.42

Low-Lat

0.50

Low-Lat

0.17

Mid-Lat5

CORD-SANT

610

0.11

0.14

Mid-Lat

6

WARN-TIT2

518

0.04

0.30

Mid-Lat−  0.25

7

BOGI-TIT2

1016

8

KIRU-SOD3

234

9

MAW1-DAV1

635

10

EIL4-WHIT

745

11

YELL-WHIT

1108− 0.08− 0.04− 0.25− 0.71

0.14

Mid-Lat0.18

High-Lat

0.14

High-Lat

0.22

High-Lat

0.21

High-Lat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 techniquescurrently in use, this technique is very simple to apply anddoes not depend on any of the assumptions such as theuse of the ionospheric thin shell model, zero-mean constraint or requiring any external data such as GIM maps tohelp aid the DCB estimation process. The purpose of thetechnique is to provide a quick way to calculate the station DCB for any GNSS station which is within baseline
distance of 250–1000 km from a calibrated GNSS station.
The proposed method is simply dependent on the availability of calibrated STEC data from a baseline GNSS station. The 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 calculation of daily station DCB, at least 5 of such overlappingarcs must be present between the two baseline stations in
a 24-h period. To have better accuracy, it is strongly recommended that the calibrated STEC data is also code-tophase leveled. Although we have only used GPS data inthis work, it is believed that the proposed technique could
be effectively used to calculate station DCB using datafrom other GNSS constellations.
The proposed technique provides an alternate methodof calculating single station DCB without the complicationof previously applied assumptions or using external data.
A comprehensive analysis has been done by applying thetechnique with several pairs of GNSS stations at different
latitudinal sectors to check the validity and consistency of
the technique. The results show that the technique works
accurately and consistently up to 1000 km baseline distance. The technique may also work for larger baseline distances but with lesser accuracy and consistency. This work
will be continued in expanding the scope of the applicationof 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 variability 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

Page 8 of 9

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 gratefulfor 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 asa 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 ionosphericempirical modeling.
Author contributions
MMS initiated the idea, designed the methodology, analyzed the data andwrote the complete manuscript. The author read and approved the final
manuscript.
Funding
No external has been received to conduct the research presented in thispaper.
Availability of data and materials
The RINEX and IONEX data used to perform this research work has beenobtained 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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