=Paper=
{{Paper
|id=Vol-2880/paper11
|storemode=property
|title=Analysis of Galileo NeQuick ionospheric model based on the station position error
|pdfUrl=https://ceur-ws.org/Vol-2880/paper11.pdf
|volume=Vol-2880
|authors=Anna Świątek,Leszek Jaworski,Paulina Woźniak
|dblpUrl=https://dblp.org/rec/conf/icl-gnss/SwiatekJW21
}}
==Analysis of Galileo NeQuick ionospheric model based on the station position error==
https://ceur-ws.org/Vol-2880/paper11.pdf
Analysis of Galileo NeQuick Ionospheric Model Based on the
Station Position Error
Anna Świąteka, Leszek Jaworskia and Paulina Woźniaka
a
Space Research Centre, Polish Academy of Sciences, Bartycka 18A, Warsaw, 00-716, Poland
Abstract
The ionosphere, as a dispersion medium for electromagnetic waves in the L-band, affects the
calculated GNSS position. One of the ways to remove the influence of the ionosphere on
position computation is computation based on dual-frequency observation. In the case of
single-frequency measurements the ionospheric error compensation method is the correction
calculated from the ionospheric model. For navigation measurements, the model transmitted
by GNSS satellites is adopted. Galileo satellites broadcast a NeQuick model adapted to
navigational messages and called NeQuick-G. The Galileo performance analysis carried on in
the Galileo Reference Centre - Member States (GRC-MS) project consist of analyses of various
Key Performance Indicators. Two of them concern the error of horizontal and vertical position
and were carried out for a single frequency (E1) and a combination of frequencies (E1E5a and
E1E5b).
Analyses were performed for selected permanent GNSS stations attending the project and
observing the Galileo signal. The stations are located at different latitudes and longitudes
around the world.
The NeQuick-G model, for navigation purposes is broadcasted as parameters divided into 5
areas parallel to the geomagnetic equator. The results of the analyses presented in the article
show the spatial heterogeneous of accuracy of the NeQuick-G model.
Keywords 1
Galileo, Key Performance Indicators, NeQuick-G, ionospheric models
1. Introduction
The problem of precise positioning and ionosphere error mitigation is well known and described in
many papers such as [1]–[3]. It is estimated that about 75% of all GPS (Global Positioning System)
receivers in market are those single frequency [4]. When using a dual-frequency receiver for
positioning, the precise position is calculated using the frequencies combination which removes the
ionospheric time-delay. For a single-frequency receiver it is necessary to use the ionospheric model.
Calculation in post-processing mode gives the possibility to use different and sometimes very
complicated models, however, real-time position calculation requires the model that is simple and
directly received by the device. For such transmission is used the navigation message in Global
Navigation Satellite Systems (GNSS). The Galileo system, just like GPS, has an ionosphere model
transmitted as a number of parameters broadcasted by satellites, which are used for ionospheric
correction calculation [5], [6]. In the GPS system the Klobuchar model, described in [7] was applied.
The Klobuchar model is defined as a single layer model. It is accepted that this model corrects the
ionospheric time-delay RMS (Root Mean Square) in 50% or better. In the European GNSS system
Galileo – the NeQuick model was applied, its algorithm is described in [8].
NeQuick is developed by the Aeronomy and Radiopropagation Laboratory (T/ICT4D Laboratory)
of the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy, and by the
I
CL-GNSS 2021 WiP Proceedings, June 01–03, 2020, Tampere, Finland
EMAIL: ana@cbk.waw.pl (A. 1); pwozniak@cbk.waw.pl (A. 3)
ORCID: 0000-0002-8659-4545 (A. 1)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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Institute for Geophysics, Astrophysics and Meteorology of the University of Graz, Austria. Based on
the ionosonde parameters foE, foF1, foF2 and M(3000)F2, peaks of the ionosphere layers E, F1 and F2
are determined, they are the anchor points of the model. The output is the electron concentration
anywhere in the ionosphere, and from this the Total Electron Content (TEC) along ground-to-satellite
ray-path by means of numerical integration is also determined. The resulting values depend on solar
activity (based on the monthly average number of sunspots R12 or 10.7 cm solar radio flux F10.7), as
well as on the month and time of the day [9].
Space Research Centre of the Polish Academy of Sciences (SRC PAS) team is involved in the
Galileo Reference Centre – Member States (GRC-MS) project granted by European GNSS Agency
(GSA). One of the objectives of the work Package they are working in is the Key Performance
Indicators analysis.
One of them was the analysis of horizontal and vertical position error. The results obtained in the
research allow to present the NeQuick-G behaviour in various region of the Earth.
2. Data
For station position error analysis stations located around the world on various latitudes and
longitudes were selected. The location of stations selected to analysis is presented in Figure 1, and their
details – in Table 1.
The stations were selected so that they were located in 5 different areas for which the parameters of
the NeQuick-G model are transmitted in the broadcast orbit. This allows the better analysis of the
influence of the ionosphere model on the determined error of station coordinates. The stations equipped
in various receivers were used for analysis. Regarding the Table 1 there are Trimble NetR9, Trimble
Alloy, Septentrio POLARX5/TR and LEICA GR30. Data was collected at intervals of 30 seconds.
Figure 1: Location of stations selected for analysis
Table 1
Details of the selected stations
MODIP Latitude Longitude Height
No Station ID Receiver type
region (deg) (deg) (m)
1 ASCG 3 TRIMBLE NETR9 -7. 91628 -14. 33266 37.953
2 BRST 2 TRIMBLE ALLOY 48. 38050 -4.49660 65.500
3 CBKA 2 TRIMBLE NETR9 52.21473 21.06770 125.738
4 CHPG 4 TRIMBLE ALLOY -22.68227 -45.00238 566.250
5 GAMB 3 TRIMBLE NETR9 -23.13035 -134.96482 80.660
6 HARB 3 SEPT POLARX5TR -25.88696 27.70725 1558.078
7 KOUG 3 SEPT POLARX5TR 5. 09847 -52.63975 107.248
8 KRGG 4 TRIMBLE ALLOY -49.35154 70.25551 72.967
9 MATE 2 LEICA GR30 40.64913 16.70446 535.600
10 METG 2 SEPT POLARX5 60.24197 24.38417 59.672
11 REUN 3 SEPT POLARX5 -21.20833 55.57167 1558.400
12 RGDG 4 TRIMBLE ALLOY -53.78584 -67.75153 32.364
13 YEL2 1 SEPT POLARX5TR 62.48132 -114.48085 181.008
3. POSITION ERROR COMPUTATION
For the KPI10 defined as horizontal and vertical position accuracy calculated for each selected
station the GALAT software was used. The GALAT was designed in SRC PAS for the purpose of
Galileo signal analysis. The input data included the observation files in RINEX v.3 format, consolidated
broadcast orbit files made by CNES and antenna phase centre variation files (IGS14.ATX) from IGS.
The NeQuick-G model was implemented in the software based on the algorithm published in [5].
The computation of position accuracy was carried out as a Single Point Positioning (SPP) for E1b
frequency and E1E5a, E1E5b combinations, according to the project requirements. The sampling
interval for observations was set to 30 seconds and the elevation cut-off was 5°. The observations were
weighted regarding the elevation using cos 𝑧 function. The influence of troposphere was mitigated by
a priori Saastamoinen model [10], [11] with applied Global Mapping Function (GMF) [12]. During the
computation process the receiver coordinates and clock corrections were estimated in the epoch-wise
mode. The estimation is prepared for observation meeting condition PDOP (Position Dilution of
Precision) lower than 6.
4. RESULTS ANALYSIS
Analysing the Horizontal and Vertical Position Error (respectively: HPE and VPE) defined as a
value corresponding to 95% of the observations, some regularities can be find. The considered stations
were grouped according to the modified dip latitude (MODIP), which combines the geomagnetic dip 𝐼
and the geographic latitude 𝜑 [13]:
𝐼
𝑀𝑂𝐷𝐼𝑃 = arctan
√cos 𝜑
MODIP is expressed in degrees, a table grid of MODIP values versus geographical location is
provided together with the NeQuick-G model. In the area of the globe, five regions are defined on the
basis of their MODIP (relating to the geomagnetic field, Table 2); they differ in the characteristics and
intensity of ionospheric processes. [5].
Table 2
MODIP region ranges depending on geomagnetic latitude
region range
1 60° < MODIP ≤ 90°
2 30° < MODIP ≤ 60°
3 -30° ≤ MODIP ≤ 30°
4 -60° ≤ MODIP < -30°
5 -90° ≤ MODIP < -60°
Selected stations are located in MODIP regions no. 1, 2, 3 and 4. Inside each of the MODIP regions
results show certain similarity of behaviour. In this paper results for MODIP 2 and 3 are presented. In
addition, a comparative analysis of the NeQuick-G model is performed in the context of the Total
Electron Content (TEC) values.
4.1. HPE and VPE variability analysis in different MODIPs
For MODIP 2 HPE values are on the level of 1.5 m and VPE less than 3 m. The HPE and VPE
values decrease as the number of satellites increase. For most stations HPE and VPE is lower for single-
frequency computation with model. This suggests a very good fitting the NeQuick-G model to real
conditions in the area of Europe. The following Figures 2-5 show the time series of HPE and VPE,
covering the period from 4th quarter 2018 to 3rd quarter 2020, for the single-frequency (E1) results and
the dual-frequency combination (E1E5b). The provided time series present results for the following
days, these are values that cover 95% of all parameters observed over the day (at 30 s rate). The peaks
visible in the graphs for both single- and dual-frequency results are caused by errors related to the
system, the SIS (Signal in Space) status flag advising not to use the results has not been introduced in
the broadcast orbit. When it comes to a bias in the first part of the considered period (systematically
worse results until 11 February 2019), the decrease in positioning errors is due to the increase in the
number of satellites available (four Galileo satellites began work in the operational mode). Table 3
below shows the mean HPE and VPE values for individual stations. The results presented therein
indicate that the NeQuick-G model is very well suited in the case of the Europe area, and the greater
mean values in the case of a dual-frequency combination result from greater observational noise.
Table 3
Mean HPE and VPE calculated for stations located in MODIP 2 for whole analysed period and for period
from 2019-02-11 (22 operating Galileo satellites)
4th quarter 2018 - 3rd quarter 2020 from February 11th 2019
mean HPE 95% mean VPE 95% mean HPE 95% mean VPE 95%
Station E1b E1E5b E1b E1E5b E1b E1E5b E1b E1E5b
BRST 1,351 1,524 2,097 2,477 1,272 1,450 2,037 2,369
CBKA 1,464 1,950 1,945 2,727 1,376 1,828 1,882 2,551
MATE 1,524 0,887 2,794 1,787 1,470 0,810 2,816 1,664
METG 1,320 1,513 1,933 2,107 1,255 1,369 1,820 1,922
Figure 2: Horizontal Position Error – single-frequency: E1 (INAV) for stations located in MODIP 2
Figure 3: Vertical Position Error – single-frequency: E1 (INAV) for stations located in MODIP 2
Figure 4: Horizontal Position Error – dual-frequency: E1E5b (INAV) for stations located in MODIP 2
Figure 5: Vertical Position Error – dual-frequency: E1E5b (INAV) for stations located in MODIP 2
For MODIP 3 HPE and VPE values for single-frequency computations are greater than for MODIP
2 area. They are also greater than for dual-frequency results. The HPE and VPE values are decreasing
when the number of satellites is increasing. Similarly to the MODIP 2 results presented above, the
Figures 6-9 below illustrate the time series of HPE and VPE for the same time range and the same
frequencies, while the mean values of these parameters are shown in Table 4.
The station KOUG is the special case. We observe the higher values for HPE than for VPE. Because
they are strongly better for dual-frequency results this suggest that in vicinity of station KOUG the
NeQuick-G model is not well fitted to real local ionospheric conditions. It is also seen in seasonal
variability of HPE values.
Table 4
Mean HPE and VPE calculated for stations located in MODIP 3 for whole analysed period and for period
from 2019-02-11 (22 operating Galileo satellites)
4th quarter 2018 - 3rd quarter 2020 from February 11th 2019
mean HPE 95% mean VPE 95% mean HPE 95% mean VPE 95%
Station E1b E1E5b E1b E1E5b E1b E1E5b E1b E1E5b
ASCG 1,816 1,394 3,603 2,969 1,809 1,325 3,473 2,737
GAMB 2,261 1,452 3,551 2,848 2,030 1,355 3,194 2,691
HARB 1,481 0,962 2,614 1,855 1,412 0,894 2,507 1,764
KOUG 3,239 1,032 2,950 2,150 3,315 0,966 2,816 2,023
REUN 1,501 1,604 2,874 3,249 1,444 1,441 2,812 2,977
Figure 6: Horizontal Position Error – single-frequency: E1 (INAV) for stations located in MODIP 3
Figure 7: Vertical Position Error – single-frequency: E1 (INAV) for stations located in MODIP 3
Figure 8: Horizontal Position Error – dual-frequency: E1E5b (INAV) for stations located in MODIP 3
Figure 9: Vertical Position Error – dual-frequency: E1E5b (INAV) for stations located in MODIP 3
4.2. Comparison of the NeQuick-G model in various conditions and locations
One of the considered aspects is the evaluation of the NeQuick-G model results against the model
provided by International GNSS Service (IGS) in the IONEX files, the solution by Astronomical
Institute of the University of Bern (AIUB) was used. TEC values for the following locations were
compared: near the equator (KOUG – Kourou, French Guiana) and in the central Europe (CBKA –
Warsaw, Poland).
In the first stage, statistical parameters for the following hours of the day were considered,
independently for each month. Based on the results for 2019, it was decided to perform the analysis for
the month of July, when the ionosphere was relatively quiet and the differences in TEC values were
low. Similarly, as an example of a month with higher ionosphere activity and high variability of the
TEC parameter throughout the day (and in the level of discrepancy between models, as well), the month
of October was chosen. The following Figures 10 and 11 show the average values of the TEC coefficient
during the day, in July and October 2019, respectively, for both considered stations, as well as for both
models and the differences between them.
Comparing the differences in the values of NeQuick-G and AIUB solutions, it can be noticed that
for stations in Europe they reach the ceiling of 20 TECU only during the period of disturbed ionosphere,
while near the equator they differ by only a slightly smaller value even during the quiet season.
Meanwhile, in the more active October, for station in Kourou the amplitude of differences between the
models, in particular around 13-14 LT (Local Time), are close to 30 TECU on some days. It is also
worth paying attention to the following tendency, especially noticeable for the presented October 2019:
while the TEC parameter value for the Warsaw station in the case of the NeQuick-G model is
consistently higher than the AIUB result, for the Kourou station it is the other way round – the result of
the NeQuick-G model turns out to be underestimated compared to the AIUB model. Moreover, taking
into account the local time, it can be noticed that for KOUG station the difference in mean values is
positive during the daytime (TEC values for AIUB model are higher than for NeQuick-G model),
however, after sunset there is a sharp decrease in this parameter and the difference takes a negative sign.
IGS/AIUB NeQuick-G ∆!"#$%&'()*+,
CBKA
KOUG
Figure 10: Mean TEC parameter for consecutive hours during the day – July 2019
IGS/AIUB NeQuick-G ∆!"#$%&'()+*,
CBKA
KOUG
Figure 11: Mean TEC parameter for consecutive hours during the day – October 2019
The results obtained in the discussed stage of the research allowed to indicate the time of day when
the ionosphere is characterized by the lowest and the highest activity (approximately). A common hour
for the whole year was consistently used, the presented examples of results refer to the same concerned
months - July and October 2019. As the hour with the lowest TEC values 4 LT was assumed (2 UTC
and 7 UTC for stations CBKA and KOUG, respectively), while as the period of the highest TEC values
– 14 LT was chosen (12 UTC and 17 UTC for stations CBKA and KOUG, respectively).
For both selected hours, the course of the TEC differences between NeQuick-G and AIUB models
was visualized. The charts below present this parameter for the combination of both months and both
models, wherein Figure 12 shows the results for 4 LT and Figure 13 - for 14 LT. The difference between
the results for day- and night-time is clear, especially in the case of KOUG station. At night, the TEC
differences do not exceed a few TECU for both months concerned. Otherwise it is during the daytime:
in July the differences are greater and amount to 12 TECU, and in October they are at the level of 15 to
almost 30 TECU. Moving on to CBKA station, the diversity is slightly smaller. A greater dynamics of
the time series for the daytime period is also noticeable.
Figure 12: TEC parameter differences for the time with the lowest TEC values during the day (CBKA –
2 UTC, KOUG – 7 UTC)
Figure 13: TEC parameter differences for the time with the highest TEC values during the day (CBKA –
12 UTC, KOUG – 17 UTC)
4.3. HPE and VPE variability considering various computation approach
For 2019 HPE and VPE were calculated for example station from MODIP 2 and MODIP 3. As the
example of station located in MODIP 2 CBKA station was selected, while for MODIP 3 – KOUG
station. Various calculation methods were considered: dual-frequency combination (E1E5a and
E1E5b), single-frequency E1b with various ionospheric models (NeQuick-G, Klobuchar and IGS
obtained in IONEX format). Results are presented below (Figures 14-17).
Figure 14: Horizontal Position Error using various calculation approaches, station: CBKA (MODIP 2)
Figure 15: Vertical Position Error using various calculation approaches, station: CBKA (MODIP 2)
Figure 16: Horizontal Position Error using various calculation approaches, station: KOUG (MODIP 3)
Figure 17: Vertical Position Error using various calculation approaches, station: KOUG (MODIP 3)
For CBKA station it can be noticed, that:
• best results are obtained for computations on single frequency with IGS model both for HPE
and VPE,
• for VPE, the highest error relates to single-frequency calculated using the Klobuchar model.
In the case of KOUG station:
• similarly to results from CBKA station, best results are obtained for computations on single
frequency with IGS model both for HPE and VPE; however the dual-frequency results are very
similar and only slightly worse,
• for HPE the results for single-frequency computation with NeQuick-G model are significantly
worse than for other methods.
5. Conclusions
The analysis of the first results show that NeQuick-G model performance is heterogeneous. There
are areas where the model is very well adapted to the real ionospheric conditions (MODIP 2 in the
Europe), but it is also seen that in the equatorial region the areas of reduced accuracy of reflecting real
conditions could be found. This is especially important in the vicinity of the KOUG station (northern
part of South America) where the NeQuick-G model causes increased errors in determining the
horizontal position.
It is planned to extend the current investigation to different MODIP and areas in the world.
6. Acknowledgements
Research work financed from the GSA grants in 2018-2020 in the Galileo Reference Centre –
Member States project.
Research work financed from the Polish Ministry of Education and Science funds for science in
2019-2020 allocated to the implementation of an international project co-financed.
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