61
1 INTRODUCTION
The Galileo satellite navigation system was launched
as part of a joint project of the European Union and
the European Space Agency. It is part of the Trans-
European Transport Network, which aims to solve
navigational and geographic issues. The Galileo
project is an ambitious European venture aimed at
creating the most advanced global positioning
satellite system in the world. Its objectives are to
create an autonomous system that provides
guaranteed global positioning services, as well as
interoperable compatibility with other global
positioning systems, such as GPS and GLONASS.
Galileo satellites permanently transmit three separate
CDMA and right-hand circularly polarized (RHCP)
signals, named E1, E5, and E6. Several studies and
publications have been devoted to the analysis of the
measurement signals of the Galileo system.
In the literature [1-2], models of measurement
signals of some navigation systems are derived. The
authors used these models to evaluate the accuracy of
navigation systems. At the beginning of the system
development, the system structure and signal models
were described in the literature [3], where the author
described the frequency plan and signal structure. The
individual atmospheres of the Earth also have a great
influence on the accuracy of signals. The author of the
article [4] describes how signals behave when passing
through the ionosphere. In the article [5], the author
describes how it is possible to use more than three
frequencies for decimeter positioning accuracy using
Galileo and BeiDou signals. In the study [6], the
authors investigated the positioning performance of
Model of the Random Phase of Signal E6 of the Galileo
S
atellite Navigation System
M
. Džunda, S. Čikovský & L. Melníková
Technical University of Kosice
, Kosice, Slovakia
ABSTRACT: The aim of this paper was to describe the random phase of the E6 signal, the Galileo satellite
navigation system. Based on the available information, mathematical models of the measurement signals of the
Galileo system were created. The frequencies of individual signals were determined and their structure
visualized. A block diagram of the generation of individual signals is also shown. The main contribution of the
paper is the creation of a random phase model of the E6 signal from the Galileo system. In accordance with the
technical data of the Galileo system, the parameters of the random phase model were determined. The
simulation results confirmed that the frequency instability of the continuous signal E6
ωn received from the
satellite is a stationary process. The short-term stability of the
frequency ranges from 10
-13
to 10
-14
. The
simulation results confirmed that the Doppler effect significantly affects the random phase of the E6 signal. This
phenomenon can affect the results of navigation mea
surements using the E6 signal. The modeling and
simulation results of the random phase of the E6 signal presented in the paper can be used to evaluate the
immunity of the Galileo navigation system to interference.
http://www.transnav.eu
the
International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 17
Number 1
March 2023
DOI: 10.12716/1001.17.01.
05
62
GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 in the
conventional PPP mode and single epoch mode using
uncombined coding and phase biases products
generated at The National Center for Space Studies in
France (CNES). The findings of the study revealed
that by using uncalibrated phase and code biases, this
multi-frequency code and phase measurements can be
modeled in in undifferenced and uncombined form
and ionosphere can be estimated. Galileo is currently
developing new services designed to provide greater
security and resistance to attacks, such as the Open
Navigation Message Authentication Service (OS-
NMA) and the Commercial Authentication Service
(CAS). The authors [7] propose a robust and secure
timing protocol independent of external time sources
and at the end perform experimental tests to verify
the proposed protocol. The study [8] is focused on
accurate time transmission through the five-frequency
uncombines Precise Point Positioning (PPP) Galileo
system. The method that was used for the research is
called the backward weighting method, based on
which the short-term frequency stability and accuracy
of the time transmission have been significantly
improved. In the document [9], an analysis of Galileo
clock and ephemeris broadcasts is performed with 43
months of data using the Galileo Receiver
Independent Exchange (RINEX) consolidated
navigation files from January 1, 2017, to July 31, 2020.
Based on these observation results, the Galileo signal
is evaluated in space and the probability of satellite
failure is estimated. One of the main positioning
errors is multipath interference. The improved Galileo
signals are expected to provide greater resistance to
multipath interference effects. The aim of the study
[10], was to verify this hypothesis. The author's
observation results confirm that Galileo codes are
more resistant to the multipath interference effect
than GPS codes. The basic performance limits of
traditional two-step architectures of Global
Navigation Satellite System (GNSS) receivers, which
are directly related to the achievable time delay
estimation performance, are analyzed in the article
[11]. The authors of the article examine GPS signals L1
C/A, L1C, and L5, Galileo E1 OS, E6B, E5b-I, and E5
signals and Galileo meta-signals E5b-E6 and E5a-E6.
The results show that The Alternative Binary offset
carrier modulation (AltBOC) signals (Galileo E5 and
meta-signals) can be used for accurate code-based
positioning, which is a promising alternative to real-
time carrier phase-based techniques. The author of the
work [12] deals with the experimental analysis of
positioning in a harsh environment, where he
calculated parameters for horizontal and vertical
position and speed. The analysis shows that GPS is
not able to transmit continuous signals in a degraded
environment, at the same time the Galileo system
increases the availability of signals in such an
environment. The authors of this article [13],
investigated and analyzed the ionospheric delay
estimation, based on two frequency GNSS signals.
They focused on locations mainly in the middle
latitudes of the Earth. As a result of the analysis,
different ionospheric delay models can be used
depending on the receiver position. There are
different models of Galileo signals. Stochastic signal
models are described in [14], which aimed to improve
single-frequency GPS/Galileo signals. In addition,
research was also devoted to the elevation angle and
its effect on the satellite. Based on the stochastic
models that have been outlined and used, it is
possible to achieve a composite binary offset carrier
(CBOC) signal are defined in [15] through tracking
algorithms and simulations. The study provided an
experimental as well as a theoretical analysis of the
proposed algorithm for observing the Galileo E1
CBOC signal. In-band pulse interference of the E6
signal and its effect on the control tower (ATC) is
discussed in the study [16]. Through the research, the
authors found out that this type of interference poses
a serious threat to GNSS users. Receiver problems
related to data generation, modulation, and signal
dispersion were investigated in [17]. The results
achieved by the authors can contribute to the redesign
of receivers and transmitters of the Galileo GNSS
system. The authors of the document [18] compare the
performance of GPS and Galileo signals against
altitude. This comparison concluded that the Galileo
system signal is up to 27% more accurate than the
GPS system. The aim of the article [19] was the study
of radio navigation signals of the Galileo system,
which are transmitted by individual constellations of
satellites, where the author represented individual
power spectral densities, modulation schemes, and
autocorrelation functions of the signals. The discovery
of different signals through different GNSS
constellations with amplitudes of millimeter series of
station coordinates was described in the article [20],
where the authors evaluated the contribution of the
multi-constellation of the GLONASS, GPS, and
Galileo systems. In this paper, the measurement
signal models of the Galileo system, including the
random phase model, are presented. The above-
mentioned models can be used in the evaluation of
the accuracy and resistance of the Galileo system to
interference.
2 METHODOLOGY
In this chapter, we will focus on the mathematical
analysis of the measurement signals of the Galileo
system. It is important to know what types of
modulation are used to generate individual GNSS
Galileo signals. We focus on a detailed analysis of the
signals. Galileo satellites transmit coherent navigation
signals on three frequencies in the L band: E1, E5 and
E6. Galileo transmits E6 on a carrier frequency of
1278.75 MHz that contains E6 components E6-A, E6-B
and E6-C. The Galileo E5 signal — which is centred at
1191.795 MHz — contains E5a and E5b signals. E5a
and E5b share a carrier frequency of 1191.795 MHz
and 1176.45 is the center frequency of the E5a signal.
E5a data and pilot components are located 15.345
MHz below the E5 carrier frequency. E5b signals can
be monitored separately, because they are modulated
on two different carrier frequencies in the E5 band
[21]. Long codes allow monitoring of very weak
signals, such as those received inside buildings, but
are difficult to obtain because receivers detect signals
by looking for delays in the received code, and long
codes have more options than short codes. In addition
to being good for quick fixes, shorter codes may lead
to incorrect satellite positioning when the receiver
exchanges signals with two satellites at the same time.
Signal length may not be suitable for all types of users
63
( static users may prefer long codes, while, fast-
moving users may prefer short codes). The answer is
to offer substitute codes with distinct characteristics
for various Galileo transmissions. One of the causes of
the diversity of Gallieo signals naturally offers the
possibility of ionospheric delay correction using
suitable linear combinations. Of course, the
ionospheric error causes a delay in the code range and
a shift of the signal in the phase range. This causes the
code ranges to be too long and uncorrected causes
header errors in processed positions. If the position
error is not corrected, this delay might make the
distance between the user and the satellite as
measured by the receiver appear to be much greater
than it is. Thankfully, this delay varies according to
the signal's frequency, with low-frequency delaying
communications more than high-frequency signals.
The ionospheric delay error can be removed from
another measurement by merged values of all
transmitted GNSS signals on at least 2 frequencies in
order to correct the main ionospheric delay term by
linear combination. The effectiveness of this
cancellation will increase with the distance between
the two frequencies. Galileo services are typically
implemented as pairs of signals due to this [22].
2.1 Signal E1
The Galileo E1 signal is modulated by BOC, which is a
binary offset carrier. BOC uses carrier shift
modulation to shift the energy from the middle of the
band away from the band. This is important because it
allows the same band to be used for multiple GPS
systems. BOC modulations use two independent
design parameters. One is the carrier frequency of the
auxiliary signal, fs, in MHz. The other is the code rate
of code shift, fc, in mega chips per second. This gives
the signal two parameters that can be used to
manipulate the signal's power in specific ways. This is
intended to reduce interference from other signals on
the same band. Additionally, the redundant upper
and lower sidebands of BOC modulations provide
advantages in signal processing by receiver
acquisition, carrier tracking, code tracking and data
demodulation [23]. The entire transmitted Galileo E1
signal consists of the following components [27]:
Figure 1. E1 signal modulation scheme [24].
Figure 1 shows the modulation scheme of signal
E1. E1 open service data channel e
E1-B(t) is generated
from I / NAV navigation data stream D
E1-B(t) and
measurement code C
E1-B(t), which are then modulated
by subcarriers SC
E1- B,a(t) and SCE1-B,b(t). The open
service pilot channel E1 e
E1-C(t) is generated from the
range code C
E1-C(t), including its secondary code,
which is then modulated by subcarriers SC
E1-C,a(t), and
SC
E1-C,b(t), in antiphase [27].
The Galileo E1 signal is modulated at a medium
frequency such as [24]:
(
) (
)
( )
( ) ( )
( ) ( ) ( ) ( )
cos 2
ττ τ
τ τ τ πθ
−
+
= − − −+
−− − − +
DD
P c IF
s t A C t d t CBOC t
c t S t CBOC t x f t
(1)
where:
( ) ( ) ( )
16
10
1
11 10
−
= −CBOC t BOC t BOC t
(2)
( ) ( ) ( )
16
10
1
11 10
+
= +CBOC t BOC t BOC t
(3)
( )
( )
( )
6
sin .2 .1 .023 .
π
=
x
BOC t sign x e t
(4)
A is the amplitude of the input signal at the input of
the correlator,
C
P a CD are extended sequences that carry pilot and
data components,
d
D represents the navigation message symbol of the I /
NAV modulated data component.
S
c represents the secondary code present on the pilot
component,
τ is a sequence delay,
f
IF is the center frequency,
θ is the phase shift of the carrier frequency.
GPS C / A and Galileo BOC (1,1) share the L1 / E1
spectrum, which is shown in Figure 2. The mean
frequency of the E1 / L1 signal is 1575.42 MHz. It is
important to remember that the current E1 band was
given the name L1 band for a long time, analogous to
GPS, until 2008, when the name of the L1 signal was
changed to the current E1.
Figure 2. Structure of signal E1 [24].
Figure 2 shows that the carrier frequency of the E1
/ L1 signal is centered on 0 MHz. The signal for PRS
Galileo is shifted by 10 MHz to the right and -10 MHz
to the left of the carrier frequency. The spectral power
density of the E1 / L1 signal is -65 dBW.
2.2 Signal E5
The Galileo E5 signal consists of the signals E5a, E5b
(and the modulation product signal) and is
transmitted in the 1164 - 1215 MHz frequency band.
Galileo satellites transmit navigation signals in the E5
band (1164-1215 MHz) using the AltBOC modulation
64
scheme. The E5 signal is modulated and multiplexed
in AltBOC. Each of the recording and pilot channels
are in-phase and quadrature components because
they are signals in complex envelope format. These
properties enable code range measurements at the
centimeter level and allow for better mitigation of
multipath effects [25]. The following Figure 3 shows
the modulation of the E5 signal, which is modulated
using the AltBOC modulation scheme.
Figure 3. E5 signal modulation scheme [24].
The whole transmitted signal E5 consists of the
following components [27]:
e
E5a-I from the F / NAV navigation data stream DE5a-I
modulated with the unencrypted measurement code
C
E5a-I.
e
E5a-Q (pilot component) from unencrypted
measurement code C
E5a-Q
e
E5b-I \ from the I / NAV navigation data stream DE5b-I
modulated by the unencrypted measurement code
C
E5b-I.
e
E5b-Q (pilot component) from unencrypted
measurement code C
E5b-Q.
The transmitted signal of the Galileo E5 system can
be represented as [27]:
( ) ( )
2f
55
π
=
c
t
jt
EE
S t AR S t e
(5)
( )
( )
( )
5 5I 5
−−
= +
t
E E EQ
S t S t jS t
, (6)
where A is the amplitude of the signal; f
s is the carrier
frequency that is selected as 1191.795 MHz; R is a real
function.
The baseband envelope S
E5(t) is given by [25]:
( ) ( ) ( )
( )
( )
( ) ( )
( )
( )
( ) ( )
( )
( )
( ) ( )
( )
,5
5 55 5 5
,5
55 5 5
,5
55 5 5
55
1
4
22
1
4
22
1
–
4
22
1
22
−− − −
−− − −
−− − −
−−
= + − −+
+ ++
+ −+
++
sE
E EaI EaQ E s E s
sE
EbI EbQ E s E s
sE
EaI EaQ E p E p
EbI EbQ
T
S t e t je t SC t jSC t
T
e t je t SC t jSC t
T
e t je t SC t jSC t
e t je t S
( )
,5
55
4
−−
+−
sE
Ep Ep
T
C t jSC t
(7)
In this equation, the signal components e
E5a-I, eE5a-Q,
e
E5b-I a eE5b-Q carry the navigation message codes. While
the intermittent components e
E5a-I, eE5a-Q, eE5b-I and eE5b-Q
indicate signal products. Symbols SC
E5-s and SCE5-p
indicate the four-valued subcarrier functions for
single-signal sidebands and product signal sidebands.
The spectrum is divided into two side lobes, which
are completely symmetrical due to the existence of
subcarrier signals. These two lateral lobes are called
E5a and E5b and are midway from the carrier
frequency [25].
Figure 4. Structure of signal E5 [24].
Figure 4 shows that the signal power spectral
density (PSD) is -80 dBW for Galileo channels E5a I
and E5b I. For channels E5a Q and E5b Q, the PSD is -
85 dBW. Channels E5a Q and E5b Q are shifted by -
15MHz left and 15MHz right to the carrier frequency.
2.3 Signal E6
Galileo satellites use E6-B and E6-C radio navigation
signals to identify their position. These signals are
sent in the E6 band at 1278.75 MHz, and contain data
and authentication. The data component of the E6-B
signal is transmitted by each satellite at approximately
500 bits per second. The authentication is created
using spread code encryption and is based on the
satellites' precise positions. There are several benefits
and drawbacks to this band of signals. One big
advantage is the fact that this band is relatively new.
One drawback is the presence of radio and radar
interference. Additionally, this band of Galileo has
higher bit rates than other bands. The E6 band is 1260-
1300 MHz, and it contains two components: E6-B and
E6-C. E6-B transmits 448 bits per second and E6-C
transmits a pilot signal. E6 signals are using BPSK
binary phase shift key technology at the signal level.
The modulation scheme of the E6 signal is shown in
Figure 5 [28]. The transmitted Galileo E6 signal
consists of the following components, both (pilot and
data components) being combined on the same carrier
component, with 50 percent energy sharing [27]:
Figure 5. E6 signal modulation scheme [24].
eE6-B from navigation data stream C / NAV DE6-B
modulated by encrypted measurement code C
E6-B
e
E6-C (pilot component) from the range code CE6-C [25].
The E6 signal is generated by a combination of
components B and C according to the equation [25]:
65
( ) ( ) ( )
6 66
1
,
2
−−
= −
E EB EC
S t e te t
(8)
where
( )
[ ]
( )
,6
6
6
6 ,6
6,
6,
,
∞
∞
−
−
−
+
−−
−
−
−
= −
∑
CE B
L
DC
EB
EB
EB T CEB
E Bi
E Bi
e t C d rect t iT
(9)
( )
( )
,6
6
6 ,6
6,
∞
∞
−
−
+
−−
−
−
= −
∑
CE C
L
EC
EC T CEC
E Ci
e t C rect t iT
(10)
D
E6-B is the navigation data flow of the C / NAV of
component B,
C
E6-B is the range code of component B,
C
E6-C is the range code including its secondary
component code C,
e
E6-B(t) is a binary navigation signal, modulated by
component B, including range code, sub-carrier, and
navigation message data. (e
E6-B(t) = CE6-B(t)DE6-B(t)),
rect
Tc(t) is a rectangular function that equals 1 for 0 <t
<T and equals 0,
[i]
DC E6-B: is an integer part of i/DCE1-B,
T
C,E6-B is the length of the component B measurement
code chip (second),
e
E6-C(t): is a binary navigation signal, modulated by
component C, including range code and subcarrier.
(e
E6-C(t)) = CE6-C(t).
Figure 6. Structure of signal E6 [24].
It can be seen from Figure 6 that the PSD of the
signal E6 is -70 dBW. The Galileo PRS channel is
shifted by 10Mhz to the right and at the same time by
-10Mhz to the left of the carrier frequency and has a
value of -70 dbW. GNSS receivers use Direct Sequence
Spread Spectrum (DSSS) modulation features to
collect signals from multiple satellites and process
them independently. The independent processing of
the various signals is based on quasi-orthogonal codes
used to modulate the various components of the
signal. For this reason, the signal from one satellite
will be considered in the following equation. The
continuous signal received from the satellite can be
modelled as the sum of L useful components, which
can be expressed as [29]:
( )
( ) ( )
( )
1
,
0
2 (2 )
τπ ϕ
−
=
= − + ++
∑
L
j j j FR j j
j
y t C e t cos f f t j n t
, (11)
Where L is the total number of signals transmitted by
the satellite. The expressions e
j(t) represent the various
components of the GNSS baseband signal modulated
by the propagating code and carrying the navigation
message. For each signal component identified by the
subscript j, C
j, the power is received and fFR,j is the
center frequency, while τ
j, φj and fj the code delay,
carrier phase and Doppler shift introduced by the
propagation channel. Finally, n(t) is the zero average
additive white Gaussian noise (AWGN) introduced
by the propagation channel and with a spectral
density N
0. The signal power ratio, Cj and N0, defines
the power-to-noise spectral density ratio (C/N0), one
of the main signal quality indicators used in GNSS
signal processing.
When only Galileo E6-B / C signals are considered,
the signal can be expressed as [28]:
( )
( ) ( )
( )
( ) ( )
6 60 60
,6 0
2 2 ·
· (2
−−
= −− −
+ ++
E DE B pE C
RF E
y t Ce t τ Ce t τ
cos πf fttnt
(12)
where
ϕ
(t) is random phase of signal E6.
This signal is given by a combination of pilot and
data components, which have the same power [29]:
= =
DP
CCD
(13)
3 RESULTS
In some tasks of the analysis and synthesis of satellite
navigation systems, it is necessary to create models of
the measurement signals of these systems and their
parameters. In this paper, models of the measurement
signals of the Galileo satellite navigation system have
been presented. One of the parameters of the
developed signal model y(t), which is described by
relation (11), is the random phase of this signal
ϕ
j(t)
3.1 The random phase model of the signal E6 received
from the satellite
The random phase model of the signal E6 received
from the satellite
The change in the signal y(t) phase may be due to
the instability of the control signal generator due to
thermal noise of its elements. We consider the random
phase
ϕ
j(t) from relation (11) to be a diffusion process,
which we can express in the form:
( )
( )
ϕ
=
F
t
nt
dt
(14)
The spectral power density of the n
F(t); process can
be assumed to be constant over the entire Galileo
receiver bandwidth. Therefore, we approximate the
n
F(t); process by white Gaussian noise with known
characteristics:
(
)
( )
( ) ( )
( )
( )
0
1 2 21
0;
2
F FF
N
Ent Ent nt t t
δ
= ⋅ =⋅−
(15)
where N
0=const. is the power spectral density of the
process n
F(t).
66
We consider the initial phase ϕ
j(0) to be random,
having a uniform probability distribution on the
interval [ - π, π ]. The variance of the phase σ
ϕ
2
increases with time therefore the random phase
ϕ
(t) is
a non-stationary process. Fluctuations in the phase of
the received signal (11) may be caused by a change in
the frequency
ω
0 of the signal generator, for example,
due to a change in the external conditions of its
operation. This change can be described by the
stochastic differential equation:
( )
( )
0.5
2
n
ω n ω ωn
d
· 2· · · t
dt
ω
ω
γω γσ
=−+ n
, (16)
where
ω
n — expresses the instability of the frequency
of the continuous signal received from the satellite
y(t); n
ω
(t)—white Gauss noise with zero mean value
and an intensity equaling to one; γ
ω
−1
—is the time of
correlation of processes
ω
n; σ
ω
n
2
—dispersion of the
y(t) signal frequency fluctuation.
Among the serious factors that affect the phase
change of the useful signal y(t) is the Doppler effect
which manifests itself as a shift of the carrier
frequency f
FR,j by the value of ΩD .
(
)
0
,
Ω = ×
Ω
D
dD t
c dt
(17)
where dD(t)/dt is the radial component of the Galileo
receiver velocity.
In accordance with relations (11), (16) and (17), the
phase fluctuations of the useful signal y(t) can be
described by the relation:
( )
0.5
0
2
ϕϕ
ω
=−× +
Ω
n
dD t
dN
dt c dt
, (18)
where D
F =N
ϕ
/2
γ
ω
is the dispersion of the random
phase
ϕ
j(t) of the signal y(t) during the correlation
time of the process
ω
n.
The process
ω
n is stationary, although its nature
depends on the specification of the initial conditions
for equation (16). We can model the random signal
phase y(t) using relations (16) to (18).
4 DISCUSSION
The random phase model, which is determined by
equations (16) to (18), was verified by simulation.
During the simulations, it was necessary to set the
parameters of the model so that they were consistent
with the parameters of the E6 signal. Some parameters
of the Galileo satellite navigation system signals are
analysed in [31]. The authors of this work investigated
the accuracy of single-frequency time and frequency
transmission using Galileo observations. Based on the
results of this work, the parameters of the random
phase model during simulations were determined in
the following way. The mean frequency of signal E6
was equal to = 1278.75 MHz. Parameter
γ
ω
=0.032 s
-1
.
σ
ω
n
2
- dispersion of the y(t) signal frequency
fluctuation was equal to 2.56x10
-4°2
s
-2
. The dispersion
of the random phase
ϕ
j(t) of the signal y(t) during the
correlation time of the process
ω
n was equal to: DF =
0.032
°2
. The instability of the frequency of the
continuous signal received from the satellite
ω
n(t0)
= 0.0
°
s
-1
. Phase fluctuations of the useful signal
ϕ
j(t0) =
0.0
°
. n
ω
(t) - white Gauss noise with zero mean value
and an intensity equal to one. The Doppler effect was
simulated using a dynamic model of the flying object
movement presented in [2]. Simulations were also
performed without considering the influence of the
Doppler effect. The simulation results are shown in
figures 7 to 11.
Figure 7. The dependence of the frequency
ω
n on time.
Figure 7 shows the dependence of frequency
ω
n on
time. The simulation results have confirmed that the
created model describes the E6 signal generator from
the Galileo system quite accurately. The short-term
relative stability of the frequency f
FR,j ranges from 10
-13
to 10
-14
. The simulation results confirmed that the
process
ω
n is stationary.
Figure 8. Dependence of the random phase
ϕ
j on time
without the influence of the Doppler effect.
Figure 8 shows the dependence of the random
phase
ϕ
j on time without the influence of the Doppler
effect. It is clear from the figure that the random phase
of the signal changes with time almost linearly in the
range from 0 to 1.0°. This is because the E6 signal
generator is stable.
Figure 9. Dependence of the random phase
ϕ
j on
time for a receiver movement speed of 1.0 m.s
-1
.
The simulation results shown in Figure 9 confirm
that the Doppler effect is applied during the
movement of the receiver of the Galileo system, which
causes the fluctuation of the random phase
ϕ
j. We
assume that the process
ϕ
j is stationary.
67
Figure 10. Dependence of the random phase
ϕ
j on time for
movement speed of 5.0 m.s
-1
.
Furthermore, a simulation of the dependence of
the random phase
ϕ
j was performed for the receiver
movement speed of 5.0 and 10.0 m.s-1. The simulation
results are shown in figures 10 and 11.
Figure 11. Dependence of the random phase
ϕ
j on time for
receiver movement speed of 10.0 m.s
-1
.
From figures 10 and 11, the Doppler effect
significantly affects the phase fluctuations of the E6
signal. Therefore, it is necessary to take this effect into
account in measurements using the E6 signal, as it can
cause large measurement errors.
Figure 12. Dependence of the random phase
ϕ
j on time
when placing the receiver on board of a flying object.
The dependence of the random phase
ϕ
j on time
during the movement of a receiver, which is on board
of the flying object, is shown in fig. 12. The movement
of the flying object was modelled by the dynamic
model presented in [2]. The speed of the flying object
was 265.0 m.s
-1
. Its acceleration was 5.0 m.s
-2
. The
simulation results have confirmed that the Doppler
effect significantly affects the random phase of the E6
signal. This phenomenon can affect the results of
navigation measurements using the E6 signal.
Therefore, it is necessary to take into account the
influence of the Doppler effect when synthesizing the
receiver for processing signals of the Galileo system.
Based on the simulation results, the continuous
signal y(t) (11) received from the satellite can be
expressed as :
( )
( ) ( )
( )
1
,
0
2 (2 )
τπ ϕ
−
=
= − ++
∑
L
j j j FR j
j
y t C e t cos f t j n t
(19)
In this model, the Doppler effect is included in the
phase
ϕ
j (18) model.
5 CONCLUSIONS
In this article, we analyse selected parameters of the
Galileo satellite navigation system signal. Based on
the available information, mathematical models of the
measurement signals of the Galileo system were
created. The frequencies of individual signals were
determined, and their structure visualized. Also
shown is the block diagram of the generation of
individual signals. The results of the modelling of the
Galileo system signals, which are presented in the
paper, can be used to evaluate the resistance of the
Galileo navigation system to interference. The given
images of the Galileo system signals allow a better
understanding of the structures of the individual
signals. The modelling results confirm that the Galileo
system signals have a different structure and a
different frequency spectrum. In further research, it
will be possible to use Galileo signal models to
simulate the effect of intentional jamming on Galileo
accuracy. Also, for modelling the influence of the
atmosphere on the propagation of measurement
signals of the Galileo system. Furthermore, it will be
possible to monitor the debasement of measurement
signals when they are received by navigation
receivers of the Galileo system. Due to the
modulations used in the Galileo system, it is believed
that the signals of the Galileo system may in the
future enable more accurate positioning compared to
other satellite systems. This advantage should be
manifested mainly in dense urban development or in
forest stands. An important advantage of the Galileo
system is the use of a dual frequency for measuring
the position of the user of the Galileo system. The
Galileo system is also expected to be more resistant to
interference. A shortcoming of the mentioned signal
models is the absence of a more detailed description
of the random phase of these signals. In our research
we focused on modelling the random phase of the
Galileo navigation system signals. One of the
parameters of the constructed signal model y(t),
which is described by the relation (11), is the random
phase of this signal
ϕ
j(t). The change in the signal y(t)
phase may be due to the instability of the control
signal generator due to the thermal noise of its
elements. Also due to a change in the external
operating conditions of the carrier signal generator.
As mentioned, the random phase is affected by the
Doppler effect. All the above effects on the random
phase
ϕ
j(t). of the measurement signal y(t) are
considered in the development of the model which is
described by relations (16) to (18). In accordance with
the technical data of the Galileo system, the
parameters of the random phase model were
determined. The simulation results confirmed that the
instability of the frequency of the continuous signal E6
ω
n received from the satellite is a stationary process.
The short-term stability of the frequency f
FR,j ranges
from 10
-13
to 10
-14
. The simulation results have
confirmed that the Doppler effect significantly affects
the random phase of the E6 signal. This phenomenon
can affect the decoding of information from the E6
signal, which will be reflected in the results of
68
navigation measurements. The above model of the
random phase
ϕ
j(t) of the measurement signal y(t) can
be used to assess the accuracy and resistance of the
Galileo satellite navigation system against
interference.
REFERENCES
[1] Dzunda, M; Kotianova, N; Dzurovčin, P. Selected
Aspects of Using the Telemetry Method in Synthesis of
RelNav System for Air Traffic Control. International
journal of environmental research and public health 17
(1), Jan 2020
[2] Dzunda, M; Dzurovcin, P. Selected Aspects of
Navigation System Synthesis for Increased Flight Safety,
Protection of Human Lives, and Health. International
journal of environmental research and public health 17
(5), Mar 2020,
[3] Hein, Guenter W., Godet, Jeremie, Issler, Jean-Luc,
Martin, Jean-Christophe, Lucas-Rodriguez, Rafael, Pratt,
Tony, "The GALILEO Frequency Structure and Signal
Design," Proceedings of the 14th International Technical
Meeting of the Satellite Division of The Institute of
Navigation (ION GPS 2001), Salt Lake City, UT,
September 2001, pp. 1273-1282.
[4] Bidaine, Benoît. Ionosphere Crossing of Galileo Signals,
2006.
[5] Geng, Jianghui, and Jiang Guo. "Beyond three
frequencies: An extendable model for single-epoch
decimeter-level point positioning by exploiting Galileo
and BeiDou-3 signals." Journal of Geodesy, 2020, 94.1,
pp. 1-15.
[6] Zhao, Lei, Paul Blunt, and Lei Yang. Performance
Analysis of Zero-Difference GPS L1/L2/L5 and Galileo
E1/E5a/E5b/E6 Point Positioning Using CNES
Uncombined Bias Products. Remote Sensing, 2020, 14.3,
pp. 650.
[7] Ardizzon, Francesco. Authenticated Timing Protocol
Based on Galileo ACAS. Sensors 2022, 22.16, pp. 6298.
[8] Liu, Gen, Xiaohong Zhang, and Pan Li. "Improving the
performance of Galileo uncombined precise point
positioning ambiguity resolution using triple-frequency
observations." Remote Sensing 11.3 (2019): 341.
[9] Alonso, María Teresa, et al. "Galileo Broadcast
Ephemeris and Clock Errors Analysis: 1 January 2017 to
31 July 2020." Sensors 20.23 (2020): 6832.
[10] Prochniewicz, Dominik, and Maciej Grzymala.
"Analysis of the impact of multipath on Galileo system
measurements." Remote Sensing 13.12 (2021): 2295.
[11] Das, Priyanka, Lorenzo Ortega, Jordi Vilà-Valls,
François Vincent, Eric Chaumette, and Loïc Davain.
"Performance limits of GNSS code-based precise
positioning: GPS, galileo & meta-signals." Sensors 20,
2020, no. 8 , pp. 2196.
[12] Borio, Daniele, and Ciro Gioia. "Galileo: The added
value for integrity in harsh environments." Sensors 16.1
(2016): 111.
[13] J Julien, Olivier, Christophe Macabiau, and Jean-Luc
Issler. "Ionospheric delay estimation strategies using
Galileo E5 signals only." In Proceedings of the 22nd
International Technical Meeting of The Satellite Division
of the Institute of Navigation (ION GNSS 2009), pp.
3128-3141. 2009.
[14] Afifi, Akram, and Ahmed El-Rabbany. Stochastic
modeling of Galileo E1 and E5a signals.International
Journal of Engineering and Innovative Technology
(IJEIT) 3.6, 2013, pp. 188-192.
[15] Jovanovic, Aleksandar, Cécile Mongrédien, Youssef
Tawk, Cyril Botteron, and Pierre-André Farine. "Two-
step Galileo E1 CBOC tracking algorithm: when
reliability and robustness are keys!." International
Journal of Navigation and Observation2012 (2012).
[16] Arribas, Javier, Jordi Vilà ‐ Valls, Antonio Ramos,
Carles Fernández‐Prades, and Pau Closas. Air traffic
control radar interference event in the Galileo E6 band:
Detection and localization. Navigation 66 2019, no. 3, pp.
505-522.
[17] Setlak, Lucjan, and Rafał Kowalik. E1 Signal Processing
of the Galileo System in the Navigation Receiver.
Communications-Scientific letters of the University of
Zilina, 2021, 23.3, E46-E55.
[18] Pascual, Daniel, Hyuk Park, Adriano Camps, A.
Alonso, and Raul Onrubia. "Comparison of GPS L1 and
Galileo E1 signals for GNSS-R ocean altimetry." In 2013
IEEE International Geoscience and Remote Sensing
Symposium-IGARSS, pp. 358-361. IEEE, 2013.
[19] Hein, Guenter W., J. Godet, Jean-Luc Issler, Jean-
Christophe Martin, Rafael Lucas-Rodriguez and Tony
Pratt. The GALILEO Frequency Structure and Signal
Design. (2001).
[20] Sośnica, Krzysztof, Radosław Zajdel, Grzegorz Bury,
Kamil Kazmierski, Tomasz Hadaś, Marcin Mikoś, Maciej
Lackowski, and Dariusz Strugarek. Contribution of the
Galileo system to space geodesy and fundamental
physics. No. EGU22-2477. Copernicus Meetings, 2022.
[21] Galileo navigation signals and frequencies . Available
online:
https://www.esa.int/Applications/Navigation/Galileo/Ga
lileo_navigation_signals_and_frequencies (accessed on
03.11.2022).
[22] EUROPEAN GNSS (GALILEO) OPEN SERVICE
SIGNAL-IN-SPACE INTERFACE CONTROL
DOCUMENT Issue 2.0, January 2021 (accessed on
03.11.2022).
[23] Olivier Julien, Christophe Macabiau, Emmanuel
Bertrand. Analysis of Galileo E1 OS unbiased
BOC/CBOC tracking techniques for mass market
applications. NAVITEC, 5th ESA Workshop on Satellite
Navigation Technologies and European Workshop on
GNSS Signals, Noordwijk, Netherlands, DEC 2010, pp 1-
8, 10.1109/NAVITEC.2010.5708070. hal-01022203
[24] European Commission (2010), European GNSS (Galileo)
Open Service – Signal-In-Space Interface Control
Document Issue 1, February.
[25] Khan, Subhan & Jawad, Muhammad & Safder,
Muhammad & Jaffery, Mujtaba & Javid, Salman.
Analysis of the satellite navigational data in the
Baseband signal processing of Galileo E5 AltBOC signal.
Arctic, 2018, 71. 2-17.
[26] Maufroid, Xavier, Jesús Cegarra, José Caro, Laura
García, and Chiara Scaleggi. The Galileo Return Link
Service Provider in the Works. In Proceedings of the
30th International Technical Meeting of the Satellite
Division of The Institute of Navigation (ION GNSS+
2017), pp. 1333-1346. 2017.
[27] J.A Ávila Rodríguez, Galileo Signal Plan, University
FAF Munich, Germany, 2011
[28] Maufroid, Xavier, Jesús Cegarra, José Caro, Laura
García, and Chiara Scaleggi. "The Galileo Return Link
Service Provider in the Works." In Proceedings of the
30th International Technical Meeting of the Satellite
Division of The Institute of Navigation (ION GNSS+
2017), pp. 1333-1346. 2017.
[29] Elhawary, M., Gomah, G., Zekry, A., & Hafez, I.
Simulation of the E1 and E6 Galileo Signals using
SIMULINK. International Journal of Computer
Applications, 2014, 88(15), 41–48.
https://doi.org/10.5120/15431-4043
[30] Galileo Signal Plan - Navipedia. Available from:
https://gssc.esa.int/navipedia/index.php/Galileo_Signal_
Plan (accessed on 03.11.2022).
[31] Xu, W.; Yan, C.; Chen, J. Investigation of Precise Single-
Frequency Time and Frequency Transfer with Galileo
E1/E5a/E5b/E5/E6 Observations. Remote Sens. 2022, 14,
5371. https://doi.org/10.3390/rs14215371.
