Article citation information:
Ziętala,
M. Stability of GPS and GLONASS onboard clocks on a monthly basis. Scientific Journal of Silesian University of
Technology. Series Transport. 2022, 114,
193-209. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2022.114.16.
Michał
ZIĘTALA[1]
STABILITY OF GPS AND GLONASS ONBOARD CLOCKS ON A MONTHLY BASIS
Summary. This paper
presents the stability of the GPS and GLONASS system clocks’ stability.
It describes the construction of these two systems and calculated four
different Allan variances (AVAR), based on the MGEX (the Multi-GNSS Experiment)
clock products. Four used variances allowed making a better analysis of each
GNSS system clock. The results are shown at different averaging times from 5 s
as successive multiples to 655,360 s in a monthly period. The stability of GPS
and GLONASS clocks is included in the range of 10-12~10-14 s. The results
showed that GLONASS clocks are stable (10-12~10-14 s) and are affected with
white frequency noise (WFM). The GPS clock stability models have more
fluctuations for τ > 40,960 s and the mean stability is concluded
between 10-12~10-13 s. Mean frequency accuracy for GPS clocks is related with
WFM and Random Walk Frequency (RWF). The differences in clock stability are
caused by several factors – block type, type of clock and the time of a
satellite in orbit. These factors have an influence on stability results.
Keywords: GPS,
GLONASS, clock, stability analysis, MGEX
Currently, GNSS systems are used in many
areas of human life, for example, safety, transport, shipping, or in many
professions like geodesy, mapping and many other engineering studies (Saleh and
Chelouah, 2004; Borowski, 2013; Maciuk et al., 2021; Kawiecka et al., 2018). Precise time
measurement is the basis for the operation of GNSS systems and, in addition to
the knowledge of satellite coordinates (orbits) allows to determine the user's
position (Maciuk, 2016;
Novak et al., 2020). The first GNSS system was the American GPS
(Global Positioning System), created for military usage and it was not
generally available for civil usage. Today, everyone can use GPS and this
system plays an important role in many real-life applications. Currently, there
are 5 GNSS systems (Rabbou and
El-rabbany, 2016; Jakowski, 2017; Saleh and Chelouah, 2004). There is the American GPS (Global
Positioning System), Russian GLONASS (Global Navigation Satellite System), European Galileo, Chinese
BeiDou, and Japanese QZSS (Ługowska et al., 2011; Perski et al., 2013; Li
et al., 2018). The first two mentioned navigation systems were made and
became fully operational as firsts so far.
Currently, the GPS space segment consists of
31 satellites from which 4 satellite blocks (IIR IIRM, IIF, III) are in use (Tab. 1), from the 8 satellite blocks manufactured
so far. A total of 39 satellites were launched in the already inactive Blocks
I, II and IIA. One of the Block I had a launch failure. In the current blocks,
38 satellites were launched into orbit. Again, one of the IIR Block did not
perform the mission. The first of
the 2R block was launched on July 23, 1997. Since September 25, 2006, an
upgraded 2R-M block has been introduced. 2F satellites were launched between
2010 and 2016, while the latest Block III started launches on December 23, 2018
(Quasi-Zenith Satellite System - 2020; Steigenberger,
Thoelert, and Montenbruck - 2020). In Block IIIF, launches
of satellites will start 2026 and it is planned until 2034 GPS Block IIIF, access date 14 Sep 2021). Tab. 1 shows a total of 30 operational satellites,
with 4 satellites in testing/reserve. The 22 satellites in Block IIIF are
projected to be delivered from 2026, with launches estimated to last through at
least 2034.
Tab.
1.
GPS satellite blocks
|
Block, New |
Launched |
Operational |
Testing/ Reserve |
Retired |
Launch failures |
|
Block I |
11 |
0 |
0 |
10 |
1 |
|
Block II |
9 |
0 |
0 |
9 |
0 |
|
Block
IIA |
19 |
0 |
0 |
19 |
0 |
|
Block
IIR |
13 |
7 |
2 |
3 |
1 |
|
Block
IIRM |
8 |
7 |
1 |
0 |
0 |
|
Block
IIF |
12 |
12 |
0 |
0 |
0 |
|
Block
III |
5 |
4 |
1 |
0 |
0 |
|
Block
IIIF |
0 |
0 |
0 |
0 |
0 |
|
Total |
77 |
30 |
4 |
41 |
2 |
Source: https://en.wikipedia.org/wiki/GPS_satellite_blocks
GLONASS
currently has 26 satellites divided into 7 blocks, of which the 2 operational
blocks are GLONASS M and GLONASS K1 (Li et al., 2019). The
first satellite, which is in reserve now, was launched on December 25, 2006,
and the last had flight tests on October 25, 2020. The new satellites are
planned to be launched in 2022, and after that year, the new Block K2 will
start to launch. Tab. 2 shows the breakdown of GLONASS satellites.
Uragan satellites are divided into 7 blocks, of which 2 are currently in use.
In the inactive blocks I, IIa, IIb, IIv, III were launched a total of 88
satellites, including from block IIb, 6 were lost during launch. The currently
active blocks are Uragan-M and Uragan-K1, where a total of 53 satellites were
launched. In version M, 50 satellites were introduced, only 1 is remaining to
launch. Currently, only 22 are operational, 1 is not used and 6 were lost at
launch. The rest of them are retired. Block K1 has 3 running satellites, where
only 1 is operational and 2 are not used. Further satellites from this block
will be launched by 2033.
Tab. 2.
GLONASS satellite blocks
|
Block, New |
Launched |
Operational |
Not used |
Retired |
Launch failures |
|
Uragan
Block I |
10 |
0 |
0 |
10 |
0 |
|
Uragan
Block IIa |
9 |
0 |
0 |
9 |
0 |
|
Uragan
Block IIb |
12 |
0 |
0 |
6 |
6 |
|
Uragan
Block IIv |
56 |
0 |
0 |
56 |
0 |
|
Uragan
Block III |
1 |
0 |
0 |
1 |
0 |
|
Uragan |
50 |
22 |
1 |
21 |
6 |
|
Uragan-K1 |
3 |
1 |
2 |
0 |
0 |
|
Total |
141 |
23 |
3 |
103 |
12 |
Source: https://en.wikipedia.org/wiki/List_of_GLONASS_satellites
GPS and
GLONASS differ from each other by several factors. As can be seen in the two
tables above, GPS has 7 more operational satellites than GLONASS. For GPS,
there are 4 operational blocks, and there are 2 for GLONASS. Historically, the
Russian system has launched 141 satellites, which is 64 more than the GPS has
launched. These GNSS systems also have technical differences. GPS has better
position accuracy, which is 3.5-7.8 m, while GLONASS
is 5-10 m (Rutkowski, 2019). In the case of
frequencies, GLONASS operates at 1.602 GHz, whereas GPS uses the L1 signal,
operating at 1.57542 GHz (Yunck et al., 1985; Marin et al., 2017). All
GLONASS satellites are equipped with caesium clocks, unlike GPS satellites,
where the majority are rubidium clocks. Despite these differences, there is one
common factor without which the GNSS systems could not work. It is time, which is the key
to work in each GNSS system (Meng et al., 2020). The user position is generated based on the
measuring time at which the signals travel from the satellite to the receiver,
with the assumption of the known speed of the signal, distance is calculated (Galleani and Tavella, 2015). To make it possible there are precise, atomic
clocks onboard each satellite (Daly et al., 1991). These clocks are the basis for all GNSS systems and have an important influence on the accuracy of navigation positioning
(Ye et al.,
2021; Delporte et al., 2012) Atomic clocks have a high level of
stability, but they also have errors. The
stability of onboard clocks can change due to several factors like aging,
sudden breakdowns, radiations, or temperature, which is why there is no perfect
synchronisation between the time of the satellite broadcast signals and
the GNSS system time (Li et al.,
2018). Therefore, it is
important to constantly monitor the performance of satellite clocks to improve
the work of GNSS systems (Delporte et al., 2012). There are several types of GNSS clocks and
each one presents a different performance(Shi et al.,
2019; Walter et al., 2018).
In the case of internal
clocks, we have quartz, rubidium, caesium and hydrogen masers (Roberts, 2019). After 2000, the most common were rubidium clocks because of their lower
costs (Brouwer, 1951). Authors in several articles have provided research on GNSS clock
performance and described the differences in stability between some satellite
blocks. As research shows, the highest stability was confirmed on rubidium
clocks of GPS Block IIA. The rubidium clocks from Block IIA had lower noise
than the clocks from newer Blocks IIR and IIRM for
In this paper, GPS
satellites are mostly equipped with the rubidium type, only numbers 8 and 24
have caesium clocks. The results show that caesium clocks from GPS Block IIF
present lower stability (10-12~10-13 s) than some of the GPS
rubidium clocks (10-12~10-14 s). The GLONASS clocks are all
caesium type, and their stability is in (10-12~10-14 s) level. To estimate the
stability of GNSS clocks, the author made a frequency stability analysis.
Already in the mid-1960’s, the new modern frequency stability analysis
has begun. In those days, new statistics that could better suit common clock noises
became available and better methods were developed for high-resolution
measurements (Nistor, 2016). The new era started in
1966 when the introduction of the two sample Allan variance was summarised by (Stefani 2004). Since then, we can calculate
and illustrate variations with the time of the clock stability with Allan (and
related) Variances (Galleani and Tavella, 2015). These variances can be related to phase
noise power spectral density (Nistor and Buda, 2016). There are many works about
the stability of GNSS onboard clocks and related problems (Xie et al., 2019; Yang et al., 2019; Lyu et al., 2020; Li et al., 2019;
Montenbruck et al., 2017; Shi et al., 2019; Li et al., 2018). In this paper, research was conducted on the
subject.
This article examined the
stability of GPS and GLONASS clocks on a monthly basis (1-31 January 2021),
based on a 30 s sampling interval. Clock stabilities are measured based on
phase-to-frequency data conversion using variances (Huang et al., 2019). In the methods section are used four types:
Allan deviation (ADEV), Overlapping Allan (ODEV), Modified Allan (MDEV) and
Hadamard Allan deviation (HDEV) variances that have been analysed and described
respectively by formulas (2)-(5). In this paper, are explored types of
power-law noises, which are presented in Tables 3 and 4. The calculations of variances
are related with types of noise, as described and presented in Figures 3-10.
In this paper, the author analysed short-term
satellite clock stability (in terms of 1 month) of two fully operational GNSS
– GPS and GLONASS. The special calculations of a few variances were done
to obtain better certainty of the analysis.
Variances are used to
characterise fluctuations in the frequency domain. The most common time domain
measure of frequency stability is the classic Allan Variance (AVAR) and there
are also related versions (variances), that provide better confidence or have
other specifications (Stefani, 2004). The Allan (and related) variances allow analysing the stability of
atomic clocks, including GPS and GLONASS satellites (Zucca and Tavella, 2005; Galleani and Tavella, 2009; Gambis, 2002). Equation (1) presents
frequency data
|
|
|
(1) |
The formula
needed to determine the variance are shown in Figure 1. The x(t) function
presents a simulated plot of time fluctuations calculated from frequency data
y_i. At the bottom left, are equations for the standard deviation, and at the
bottom right are equations, through which we can determine stability in the
field of time (“Section Four”, 1980). The y_i in those calculations
is the ith of M fractional frequency values. The τ interval is the time in
which the data is averaged and analysed.
Fig. 1. Graphical interpretation of standard deviation vs Allan deviation
(Howe
and Allan and Barnes, 1999)
There are several versions of Allan variance
that provide greater statistical accuracy or allow the determining of other
noises. In this paper, the author uses the classic Allan deviation (ADEV),
overlapping Allan deviation (ODEV) and Modified Allan deviation (MDEV) and
Hadamard Allan deviation (HDEV) (Howe and
Peppler, 2001). The classic ADEV is the most common
variance type used to measure frequency stability. It has the advantage of
being convergent for most types of clock noises. Allan’s deviation is
expressed as equation (2):
|
|
|
(2) |
ODEV variance,
|
|
|
(3) |
The modified Allan variance type is used to
distinguish between white noise and flicker PM (Phase Modulation) and can be
expressed as equation (4):
|
|
|
(4) |
Hadamard's variance is characterised by
insensitivity to linear drift. It has a much narrower transfer function, making
it useful for the analysis of rubidium atomic clocks (Stefani,
2004). Hadamard variance can be calculated using
the formula:
|
|
|
(5) |
The noise
power spectral density determines the stability of a satellite’s clock.
Power-law noises have a spectral density of their fractional frequency
fluctuations of the form Sy(f) ∝ fα, where f is the frequency in hertz, and α is the
power-law exponent (Xu and Yue, 2017; Stefani, 2004). The author suited the
four used variances with noises, estimated the stability and modelled it in
Figures 3-10 (Griggs et al., 2015). Several
types of noise are shown in Tab. 3 together with
an exponent corresponding to a given type. In this article, calculated
variances from GPS and GLONASS clocks were associated with WFM and RWF.
Tab. 3.
Type of noise
|
Type of
noise |
α |
|
White PM |
2 |
|
Flicker PM |
1 |
|
White FM |
0 |
|
Flicker FM |
-1 |
|
Random Walk FM |
-2 |
|
Flicker Walk FM |
-3 |
|
Random Run FM |
-4 |
Figure 2 shows
noise types detected by ODEV and MDEV. An additional advantage of Allan’s
modified variance is that one can distinguish white phase and flicker phase
noise.
In this paper, Allan (and related) variations
were calculated based on the MGEX (the Multi-GNSS Experiment) clock products.
Time span covers the first 31 days of the year 2021
(1st-31st January). Daily 30 s clock products for GPS and GLONASS observations
were combined and based on equations 1-5, for each GNSS system were calculated
four different types of the Allan variations for combined clock products for
the whole GPS and GLONASS space segment separately. Moreover, on each graph
were added a graph with noises characterising each space segment.
Fig. 2. Noise type graphs detected by the overlapping Allan deviation (left)
and the modified Allan
deviation (right)
(Physique
and Lasers, 2019)
A total of 8 figures was presented showing the stability of GPS and GLONASS clocks using 4 different types of Allan’s variances. The stability is shown at different averaging times from 5 as successive multiples to 655,360 seconds. The clock stability was calculated for 32 GPS satellites from four operational blocks: IIR, IIRM, IIF and III. The oldest operational satellite is from Block IIR, and it has been orbiting for 24 years (since 1997). In the GLONASS case, calculations were made for 21 satellites from blocks M and K1. The oldest satellite has been flying for over 14 years (since 2007).
Figures 3 and 4 present values of ADEV. In Figure 3, we related mean-variance (yellow line) to white frequency modulation (WFM) in the range of 5 < τ < 40,960 s. WFM is marked with a longer dashed black line and random walk frequency (RWF) is presented with a dotted black line. We can see that stability fluctuates for τ > 40,960 s and its connection with (RWF). The GPS clocks stability is increasing from level 10-12 s to 10-14 s in the range of τ = 5 s to τ = 40,960 s, and for τ > 40,960 s, the stability drops to 10-13~10-12 s. It is mostly visible for satellites G14, G23, G32.
Figure 4 shows GLONASS clocks stability using ADEV. Mean-variance is related with WFM and stability is about 10-12~10-13 s for 5 < τ < 40,960 s, and for τ > 40,960 s, it is increasing even to 10-14 s. We can see that the three clocks from satellites R11, R13, R2 have worse stability compared to the others and R11 has a fluctuating frequency drift. The rest GLONASS clocks stabilities are close to each other and the lines presenting frequency accuracy have a similar course.
Figures 5 and 6 present stability results using HDEV.
As the charts show, for both GPS and GLONASS satellites, the mean stability has
convergence with WFM. In Figure 5, it is visible that stability fluctuates
respectively after τ > 40,960 s. It is shown that GPS satellites, G24
and G8 have worse stability, which is caused by the caesium clock type, for
τ = 5 s, it is between 10-11~10-12 s, and it
rises to 10-13 s for τ = 655,360 s. The clocks from satellites G27 and G30
reach the best stability, which is 10-15 at τ = 655,360 s. The mean
frequency drift for GPS clocks increases from 10-12 to 10-14 s, respectively,
with τ increase.
Fig. 3. ADEV of GPS space segment with mean value
(yellow line)
and assigned noise types (black lines)
Fig. 4. ADEV of GLONASS space segment with mean
value (yellow line)
and assigned noise types (black lines)
Whereas in Figure 6, there are lower fluctuations
compared to the GPS drift. We also can see fluctuations after τ = 40,960
s, but they are not as high as GPS ones. The mean stability drift is associated
with WFM. GLONASS clocks stability is between 10-11~10-12
s for τ = 5 s, and it increases to the range of 10-13~10-14 s at τ =
655,360 s. Further, it should be noted that the clock from the R21 satellite
reaches the best 10-15 s stability at the end of τ range. The differences
in stability between the HDEV and ADEV methods are little for GLONASS
satellites.
Fig. 5. HDEV of GPS space segment with mean value (yellow
line)
and assigned noise types (black lines)
Fig. 6. HDEV of GLONASS space segment with mean value (yellow line)
and assigned noise types (black lines)
The next two charts represent clock stability after
modified Allan variance. We can see a similar stability model in this method
and ADEV. In Figure 7, mean-variance is fitted with WFM and RWF noises. It is
visible that half of the GPS clocks have worse stability, which is close to
10-12 s, and the rest have better stability on the level between 10-12~10-13 s,
where 5 < τ < 1.280 s. The biggest changes in line course begin for
τ > 40,960 s, where the fluctuation starts, and the stability result
drops from 10-13 to 10-12 s for the clock from Satellite G14. Mean frequency
accuracy of GPS satellite clocks starts at level 10-12 s for τ = 5 s and
reach almost 10-14 s for τ = 40,960 s, and then decrease, respectively, to
10-13 s.
Fig. 7. ADEV of GPS space segment with mean value (yellow
line)
and assigned noise types (black lines)
In Figure 8, we can see GLONASS clock stability and
again it has a more uniform course than the GPS. Similarly, in the MDEV method,
it is visible that the clocks frequency accuracy slowly getting better from
10-12 to 10-14 s, respectively, with τ increase. The stability is slightly
better at τ = 5 s than it was in HDEV and ADEV variations. The stability
of the R11 satellite clock stands out from the rest mostly in the range 320
< τ < 20,480 s, and it is around 10-12 s. The mean-variance has
convergence with WFM in the studied τ range.
Fig. 8. MDEV of GLONASS space segment with mean value (yellow line)
and assigned noise types (black lines)
The last type of variation used by the author is the
ODEV variance. Figure 9 shows a similar stability model of GPS clocks to the
rest Allan variances. The difference between the clock G24 with the worst
stability, and presenting the higher accuracy G30, is 10-1 s in the range where
5 < τ < 40,960 s. The divergence between these two clocks is caused
by the time each satellite is in orbit and also, the clock type is the reason.
The higher fluctuations in stability are visible after τ > 40,960 s,
where the differences in stability between satellites grow, and the most reach
10-2 s for G14 and G20 satellites. The mean-variance has convergence with WFM
and RWF noises.
Fig. 9. ODEV of GPS space segment with mean value (yellow
line)
and assigned noise types (black lines)
In Figure 10, we can see the similar GLONASS clock
stability fitted to WFM noise as in previous related variances. The last
variation method again shows sticked linear drift, the most similar to the MDEV
variance model. Fluctuations after τ > 40,960 s seconds are not that
much visible as they were in the ADEV and HDEV variations. The most visible
difference between the lowest stability R11 satellite clock and the highest
accuracy R21 is almost 10-1 s in the range 2,560 < τ < 5,120 s. The
mean stability for GLONASS clocks using the ODEV method concluded between 10-11~10-12 s for τ = 5 s, and then increase,
respectively, with time to level 10-13~10-14 s at τ = 655,360 s.
Table 4 shows individual values of clock stability depending on the variance type and the GNSS system. It is visible that as with τ multiplies, the stability of clocks is increasing. In the range 10< τ < 2,560 s, the accuracy of clocks stands on level 10-12~10-13 s. As the τ increase to 40,960 s and then gets 655,360 s, the stability is improving up to 10-14 s and stands on a similar level. It should be noticed that the mean stability of GPS is higher for each variance used than GLONASS clocks, where 10< τ < 40,960 s. The change appears at τ = 163,840 s, where GLONASS has better accuracy than GPS using MDEV, and at τ = 655,360 s GLONASS presents higher stability than GPS clocks for ADEV, MDEV and ODEV.
The presented figures show us the differences in the
stability of GLONASS and GPS satellite clocks. We can conclude that GLONASS
figures present a more consistent course of variations than the GPS figures. In
the GPS, the fluctuations and differences between some satellite frequency
stabilities are more visible and its mean stability is associated with WFM and
RWF for 3 variances. The GLONASS clock stability is related only to WFM for 4
used variations. The mean stability for both satellite systems clocks is
similar and varies in the range 10-12~10-13 s for GPS and 10-12~10-14 s for
GLONASS clocks. From the four methods of variances used, the most distinctive
stability model for GPS is HDEV, while the rest three are similar. Whereas for
GLONASS, we can see the resemblance in the various models between ADEV and HDEV
and between MDEV and ODEV.
Fig. 10. ODEV of GLONASS space segment with mean value (yellow line)
and assigned noise types (black lines)
Tab. 4.
GPS and GLONASS mean clock
stability determined by ADEV, HDEV, MDEV, ODEV
deviations for selected averaging times
|
Variance |
System |
10 s |
40 s |
160 s |
640 s |
2,560 s |
10,240 s |
40,960 s |
163,840 s |
655,360 s |
|
ADEV |
GPS |
1.944E-12 |
1.65E-12 |
7.92E-13 |
2.87E-13 |
1.06E-13 |
6.03E-14 |
2.55E-14 |
3.07E-14 |
8.26E-14 |
|
GLONASS |
4.383E-12 |
2.17E-12 |
1.06E-12 |
5.71E-13 |
2.7E-13 |
1.49E-13 |
6.11E-14 |
3.16E-14 |
1.45E-14 |
|
|
HDEV |
GPS |
1.76E-12 |
1.62E-12 |
8.13E-13 |
2.95E-13 |
1.06E-13 |
6.07E-14 |
2.27E-14 |
1.48E-14 |
1.06E-14 |
|
GLONASS |
4.39E-12 |
2.17E-12 |
1.06E-12 |
5.73E-13 |
2.63E-13 |
1.39E-13 |
6.09E-14 |
3.13E-14 |
1.3E-14 |
|
|
MDEV |
GPS |
1.645E-12 |
1.27E-12 |
5.35E-13 |
1.71E-13 |
6.54E-14 |
4.34E-14 |
1.92E-14 |
2.7E-14 |
8.08E-14 |
|
GLONASS |
3.412E-12 |
1.51E-12 |
7.42E-13 |
3.93E-13 |
2.08E-13 |
1.04E-13 |
4.45E-14 |
2.25E-14 |
1.2E-14 |
|
|
ODEV |
GPS |
1.948E-12 |
1.65E-12 |
7.91E-13 |
2.87E-13 |
1.08E-13 |
6.14E-14 |
2.52E-14 |
3.03E-14 |
8.21E-14 |
|
GLONASS |
4.382E-12 |
2.15E-12 |
1.06E-12 |
5.49E-13 |
2.89E-13 |
1.49E-13 |
6.58E-14 |
3.26E-14 |
1.69E-14 |
In this article, GPS and GLONASS clocks stability were analysed. Four variances Allan (and related) were calculated based on the MGEX clock products. Operational satellites from two GNSS systems were chosen for this research and each satellite clock performance was presented at different averaging times, from 5 as successive multiples to 655,360 s. The analysed 32 satellites from GPS concluded mean stability between 10-12~10-13 s and influenced WFM and RWF. The exception was HDEV calculation, where mean variation was associated with WFM, and the stability was approximately 10-12~10-14. The 21 GLONASS satellites also had stability at the level 10-12~10-14 s and were related with WFM noise. The main differences between these two systems are that GLONASS clocks frequency is more consistent, and stability improves with averaging time increasing, whereas GPS clocks are not as compatible as their Russian counterpart, having higher fluctuations for τ = 40,960 s and above. The reason for these differences is that GLONASS satellites use only caesium atomic clocks free from frequency drift. The differences between some GPS satellite clocks are visible in the range 5 < τ < 1,280 s, where half of all satellites have better stability about 10 times than the others. This may be caused by the different times that each satellite is in orbit. This means that the satellites from older blocks have worse stability than the recently launched ones. From the four variances calculated for GPS clocks, three of them gave very similar results. Only HDEV variation differs more from the others, cause its stability consists of averaging time increasing also after τ = 40,960 s, and it is only affected by the WFM noise. For GLONASS satellite clocks, the ADEV and HDEV variations showed higher fluctuations. Whereas the other two methods, ODEV and MDEV, presented similar and more consistent stability. The analyses showed that the mean stability of the presented GNSS system clocks is on a similar level, but GLONASS is more stable and consistent. Four calculated variances were compared to each other and allowed for even deeper analysis.
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Received 09.10.2021; accepted in
revised form 26.11.2021
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0
International License
[1] AGH University of Science and Technology, Mickiewicza 30 Av., 30059 Krakow, Poland. Email: oregal116@wp.pl. ORCID: https://orcid.org/0000-0003-0354-3687