Time, its scales and part in satellite navigation systems Czas, jego

Transkrypt

Scientific Journals
Zeszyty Naukowe
Maritime University of Szczecin
Akademia Morska w Szczecinie
2010, 20(92) pp. 52–59
2010, 20(92) s. 52–59
Time, its scales and part in satellite navigation systems
Czas, jego skale i udział w Nawigacyjnych Systemach
Satelitarnych
Jacek Januszewski
Gdynia Maritime University, Faculty of Navigation, Ship Operation Department
Akademia Morska w Gdyni, Wydział Nawigacyjny, Katedra Nawigacji
81-345 Gdynia, al. Jana Pawła II 3, e-mail: [email protected]
Key words: timescales, time dilution of coefficient (TDOP), timesystems
Abstract
There are different scales related to time; actually two the most important timescales are the TAI (Time
Atomic International) and the UTC (Universal Time Coordinated). In addition to these times Satellite
Navigation Systems (SNS) have developed their own system time: GPS Time (GPST), the GLONASS
System Time (GLONASSST) and the Galileo System Time (GST). The sources, the generation and the
relation between all these times and timescales are described in this paper. Additionally the time dilution of
precision (TDOP) coefficient and the data concerning the time transmitted in navigation messages by
satellites of different SNS will be presented.
Słowa kluczowe: skale czasu, współczynnik dokładności pozycji użytkownika (TDOP), systemy czasu
Abstrakt
Z czasem związane są różne skale, ale dwie najważniejsze z nich to TAI (Międzynarodowa Skala Atomowa)
i UTC (Czas Uniwersalny Skoordynowany). Nawigacyjne Systemy Satelitarne (NSS) stworzyły jednak własne skale czasu: GPST – czas systemu GPS, GLONASSST – czas systemu GLONASS i GST – czas systemu
Galileo. W artykule omówiono źródła, pochodzenie i relacje zachodzące między wszystkimi ww. czasami
i skalami. Dodatkowo opisano współczynnik dokładności pozycji użytkownika TDOP oraz te parametry dotyczące czasu, które są przekazywane w depeszach nawigacyjnych satelitów poszczególnych systemów.
Introduction
difference between signal reception time, as
determined by the receiver clock, and the
transmission time at the satellite, as market on the
signal. SNS is also a timing system, that is, it can
be used for time synchronization.
Time is a component of the measuring system
(e.g. satellite navigation system) used to sequence
events, to compare the events and the intervals
between them (e.g. time of signal propagation
between satellite and terrestrial receiver), and to
quantify the motions of objects. The use of atomic
properties for time measurements was born in 1955
when the first cesium beam frequency standard
began regular operation in the United Kingdom [1].
As nowadays the satellite position fix is based on
pseudorange measurements (apparent transit time
of the signal from a satellite to the receiver), the
knowledge of all used universal and atomic time
scales and the relation between them is very
important for all users of Satellite Navigation
Systems (SNS). This transit time is defined as the
Universal and Atomic Time scales
Two basic groups of time scales are of importance in satellite navigation systems:
– Universal Time, connected with the diurnal rotation of Earth. The time-dependent orientation
of Earth with respect to the inertial space is
required in order to relate the Earth-based
observations to a space-fixed reference frame.
UT is a modern continuation of Greenwich
Mean Time (GMT);
52
Scientific Journals 20(92)
– Atomic Time, related to phenomena in nuclear
physics. The precise measurement of signal
travel times, e.g. pseudorange in satellite navigation systems, requires a uniform and easily
accessible time scale with high resolution.
The third basic groups of time scales, Ephemeris
(Terrestrial) Time, important in satellite geodesy, in
particular, is derived from the orbital motion of
celestial bodies around the Sun. All these time
scales are based on the observation of uniform and
repetitive astronomical or physical phenomena.
Weights and Measures BIPM (Bureau International
des Poids et Mesures) in Paris, 1967. We can put
the question why in this definition the number of
the periods of the radiation is equal 9,192,631,770?
Because it corresponded exactly with the previous
definition of the second, the ephemeris second.
In practice, atomic time scale are derived from
groups of commercial and laboratory cesium
standards which generate time intervals, based on
the definition of the SI second.
The time scale based on atomic standards is
called International Atomic Time (TAI). TAI is
a uniform time scale based on the atomic second,
which is defined as the fundamental unit of time in
the International System of Units.
TAI is the continuation of time scales which
began with the first cesium atomic clock in 1955
which is not tied to the earth’s rotation on its axis or
its revolution around the Sun.
TAI is computed as the weighted mean of
individual clocks. Therefore TAI is a statistically
formed common time scale for international use.
TAI is referred to as a “paper” time scale since it is
not kept by a physical clock.
The value all existing atomic time scales was
equal to that of UT2 on January 1, 1958, but that
date was before high-precision international coordination of time had begun. The name TAI was
officially proposed in 1970 and adopted in 1971.
Due to the deceleration of Earth’s rotation
the difference between TAI and UT scales is increasing. The difference between TAI and UT1, for
some selected dates, is presented in the table 1.
We must say that large size of these differences
stems from the fact that the unit of the SI–second
was adopted from the length of the ephemeris
second. The latter was derived from the mean
duration of the solar day between 1756 and 1895,
when Earth’s rotation was faster than today [4].
Nowadays there are two different time scales
and two seconds’ definitions, universal and atomic,
while one time scale is required only. This new
scale must provide both a highly uniform time unit
and the best possible adaptation to UT1, and hence
to Earth rotation.
Universal Time (UT) family
Before the acceptance of atomic scales astronomical time scales were used for everyday timekeeping. Although astronomical times are no longer
the best measure of time, they continue to play
a role in current research. These time scales are still
used today, but mostly for applications related to
astronomy. UT is witness to the Earth’s rotation,
whilst serving also to establish Coordinated Universal Time (UTC). They are based on mean solar
time. The mean solar second provides the basis for
Universal Time (UT). We can distinct three principal variations of UT [2, 3]:
– UT0, the original mean solar time scale, based
on the rotation of the Earth on its axis;
– UT1, the principal form of UT, the most widely
used astronomical time scale, it is an improved
version of UT0 with corrections added for polar
motion. UT1 is the same everywhere on Earth.
The correction from UT0 to UT1 is at most
about 0.035 s. The current version of UT1 (since
2003, namely sometimes UT1R) is exactly what
is needed for geophysical investigations. It permits evaluation of the length of the day with
a precision that revels changes due to storm
systems and changes in ocean currents. UT1
drifts with respect to atomic time. This is on the
order of several milliseconds per day and can
accumulate to 1 second in a 1 year period;
– UT2, a smoothed version of UT1 by adding
an empirical formula to remove the effect of the
annual seasonal variations in the rotation of the
Earth. It is mostly of historic interest and rarely
used anymore.
Table 1. The difference TAI–UT1 for selected dates [4]
Tabela 1. Różnica między TAI i UT1 w wybranych dniach [4]
Atomic Time family
Difference [s]
+6.1
+16.4
+23.6
+30.8
+31.9
+32.3
Atomic time scales are derived from groups of
commercial and laboratory cesium standards which
generate time intervals, based on the definition of
the International System of Units (SI). The definition of the second atomic time scale, related to
Cesium 133 atom, has been worked by the 13th
Conference of the International Committee of
Zeszyty Naukowe 20(92)
53
Date
January 1, 1968
January 1, 1978
January 1, 1988
January 1, 1998
January 1, 2001
January 1, 2003
Jacek Januszewski
That’s why, in January 1, 1972, a compromise
time scale, Universal Time Coordinated (UTC),
was introduced. UTC has been run according to the
guidelines in Recommendation ITU–R TF 460–4
of the International Telecommunication Union
(ITU) [1].
The definition of the UTC second is the same as
that for atomic time, and is based on the cesium
atom. UTC is now the scale for public time
throughout the world. We can say that this is the
new GMT.
The acronym UTC is an English-French mixture
for Coordinated Universal Time (CUT) in English
or Temps Universal Coordonne (TUC) in French.
It was internationally agreed to write Universal
Coordinated Time as UTC, rather than CUT or
TUC, making it language–independent.
UTC was set to agree with UT1 at 00 hours on
January 1, 1958. At first the two time scales were
kept close by introducing 0.1 second steps in UTC,
as needed. Since 1972, changes in the Earth’s spin
rate have been accommodated by introducing leap
second (p. 1.3) in UTC. This time is thus obtained
by periodically adding or subtracting one second
from TAI in order to build up a reference time that
follows the Earth’s rotation. That’s why nowadays
UTC and TAI differ by an integer number n of
seconds:
UTC = TAI – n · (1 s)
Differences between TAI and UTC since 1
January, 1972 (from the beginning of UTC) to the
time of this writing is given in the table 2.
Table 2. Difference Δt between TAI and UTC in years 1980–
2010 (in seconds)
Tabela 2. Różnica Δt między TAI a UTC w latach 1980–2010
(w sekundach)
From… to…
01.01.72 – 06.30.72
07.01.72 – 12.31.72
01.01.73 – 12.31.73
01.01.74 – 12.31.74
01.01.75 – 12.31.75
01.01.76 – 12.31.76
01.01.77 – 12.31.77
01.01.78 – 12.31.78
01.01.79 – 12.31.79
01.01.80 – 06.30.81
07.01.81 – 06.30.82
07.01.82 – 06.30.83
07.01.83 – 06.30.85
From… to…
07.01.85 – 12.31.87
01.01.88 – 12.31.89
01.01.90 – 12.31.90
01.01.91 – 06.30.92
07.01.92 – 06.30.93
07.01.93 – 06.30.94
07.01.94 – 12.31.95
01.01.96 – 06.30.97
07.01.97 – 12.31.98
01.01.99 – 12.31.05
01.01.06 – 12.31.08
01.01.09 –
Δt
23
24
25
26
27
28
29
30
31
32
33
34
The USNO determines and distributes the timing and astronomical data required for accurate
navigation and fundamental astronomy, and maintains a UTC time scale that is (by mutual agreement) within 100 ns of UTC(NIST) [3, 5].
In different countries around the world, local
time is attached to UTC corrected by a whole
number of hours. This is sometimes stipulated by
written law (e.g. in France). Legal institutions
sometimes prefer to use the national approximation
to UTC, e.g. in Germany. There are countries
where UTC is not legally recognised, although it is
actually used, since no other time scale is readily
available [1].
The still widespread use of the acronym GMT is
not correct when it is intended to refer to UTC, as it
is the case when expressing the time in general
usage.
After steering corrections, TAI is known from
the values of TAI – UTC(k) at standard dates. Each
laboratory k has a master clock which supplies an
approximation UTC(k) to UTC. This clock serves
as a reference for all local dating procedures. BIPM
publishes the values of UTC – UTC(k) every month
in its Circular T, available by electronic mail. Apart
from this, by tracking GPS and GLONASS satellites for time comparisons, values of UTC – GPS
time and UTC– GLONASS time are provided with
similar uncertainties to those in UTC – UTC(k).
Time signal emissions conform as closely as
possible to UTC. An ITU recommendation fixes
a tolerance of 1 ms. In reality, the discrepancy
is much smaller than this. It is also recommended
(1)
On 1 January 1972, TAI – UTC was equal to
10 s. At the time of this writing (February 2010) the
difference between TAI and UTC was:
TAI – UTC = +34 s
Δt
10
11
12
13
14
15
16
17
18
19
20
21
22
(2)
UTC is generated after the fact on the basis of
the times kept by about 250 cesium clocks and
hydrogen masers located at about 65 different
laboratories located around the world. In the United
States, UTC estimates are generated by the
National Institute of Standards & Technology
(NIST), Boulder, Colorado, and the United States
Naval Observatory (USNO), Washington, D.C.
Both institutions are charged with supplying time
and frequency to the U.S. government and BIPM.
Their UTC estimates are referred as UTC (USNO)
and UTC (NIST). Other countries have similar
institutional arrangement to their national time
standards, which serve as the basis for real-time
estimates of UTC. It takes BIPM about a month to
collect and process the data to generate TAI and
UTC. A monthly bulletin from BIPM reports the
time difference that existed between each of the
contributing clocks and UTC [5].
54
Satellite navigation systems time scales
that the carrier frequency be tuned to the TAI
frequency, with relative frequency offset less than
10–10 [1].
While most clocks in the world are synchronized
to UTC, the atomic clocks on the satellites are set to
own SNS time.
Leap seconds
GPS System Time (GPST)
A leap second is a second added to UTC time
scale to keep the difference between UT1 and UTC
to within ± 0.9 second. The introduction of one
positive or negative leap second must be made
at the end of a UTC month, preferably at the end
of December or June, otherwise at the end of March
or September. The first leap second was inserted
on June 30th, 1972. Since then, they have occurred
at an average rate of less than one per year. All 24
leap seconds were positive, 9 were inserted on June
30th, 15 on December 31st. In February 2010 the 5
last leap seconds were added on December 31st,
1995, June 30th, 1997, December 31st, 1998,
December 31st, 2005 and December 31st, 2008.
Dates for leap seconds are fixed by the International Earth Rotation Service (IERS) and announced
at least 8 weeks beforehand. The announcement
appears in IERS’s “Bulletin C”. This bulletin is
updated every six months, either to announce a time
steep in UTC, or to confirm that there will be no
time step at the next possible date. The probability
that negative leap second will be needed is almost
zero.
Leap seconds are primarily for the benefit
of astronomers: they keep UTC synchronized with
the orbits of the stars and planets. If there were no
leap seconds, then in about 3 000 years from now,
the sun would seem to be rising an hour late [6].
Information about the leap seconds can be found at
the U.S. Naval Observatory Web site, http://maia.
usno.navy.mil.
The current value of UT1 − UTC is called the
DUT1 correction (DUT1 = ± N0.1 seconds, where
N is a digit between 1 and 8) and is obtained from
Time Section of the BIPM. The resolution of the
DUT1 correction is 0.1 s, and represents an average
value for an extended range of dates. Values of
DUT1 and their application date are provided one
month beforehand by the IERS and they are the
same for all emissions.
DUT1 corrections are broadcast among other
things by the stations of NIST, as WWV, WWVH,
and WWVB. The corrections values of DUT1 at
0000UTC of the selected days can be found in the
vol. 2 of ALRS [7], e.g. on Mars 15, 2007 DUT1
was − 0.1 s, on June 14, 2007 it was − 0.2 s. The
knowledge of these corrections allows the user to
correct the value of disseminated UTC.
GPS uses its own particular, continuous time
scale GPS System Time (GPST). It differs from
UTC by a nearly integer number of seconds:
GPStime – UTC = n ∙ s – Ct
(3)
where: n is an integer number, and the correction
term Ct is in the order of several nanoseconds. GPS
system is not corrected to match the rotation of the
Earth, so it does not contain leap seconds or other
corrections which are periodically added to UTC.
GPST is specified to be maintained to within one
microsecond modulo integral seconds, and for the
past ten years it has been maintained to within
( 25 ns) of this goal [8]. GPST is steered to
UTC(USNO) on a daily basis. Over last several
years GPST was kept within a few tens of ns from
UTC(USNO) and TAI (modulo 1 second) [9].
GPST and UTC(USNO) were coincident at 0 h
January 6, 1980. As at this moment the difference
between TAI and UTC was 19 seconds, GPST
remains at a constant offset with TAI:
TAI – GPStime = 19 seconds
(4)
At the time of this writing (February 2010) the
difference between GPST and UTC was 15
seconds. Therefore the reception of GPS signals
provides real-time access to TAI and UTC with
uncertainties below 1 microsecond [4].
The GPST is also a paper time scale; it is based
on statistically processed readings from the atomic
clocks in the satellites and at various ground control
segment components. This time, defined by the
Control Segment, is generated from all the atomic
clocks of the system, including those in the
satellites.
The GPS satellites have rubidium (Rb) and
cesium (Cs) atomic clocks onboard (today’s
satellites block IIa have 2 Cs + 2 Rb, blocks IIR
and IIR–M have 3 Rb). These are kept within
a millisecond of the master clocks at the GPS
master control station.
The largest unit used in stating GPS time is one
week, defined as 604 800 seconds where 000000
seconds is at Saturday / Sunday midnight GPS
Time. Each week at this time, the week number
increments by one, and the seconds into week resets
to 0.
55
Jacek Januszewski
Therefore as opposed to the year, month, and
day format of the Gregorian calendar, the GPS date
is expressed as a week number (WN) and a day of
week number. The WN is transmitted as a ten-bit
field in the C/A and P(Y) navigation messages,
and so it becomes zero again every 1024 weeks
(210 = 1024). GPS week zero started at 00:00:00
UTC (00:00:19 TAI) on January 6, 1980, and WN
became zero again for the first time at 23:59:47
UTC on August 21, 1999 (00:00:19 TAI on August
22, 1999). At this moment the difference between
TAI and UTC was 32 seconds. The number of days
passed since August 21, 1999, divided by 7 gives
the WN, e.g. week 512 is from 15th to 21st June.
In navigation message the data concerning time
are transmitted in the first two and the last two
subframes. Ephemeris parameters in subframe 1
contain estimated group delay differential (eight-bit
information about clock correction term) and four
additional satellite clock correction parameters.
Ephemeris parameters in subframe 2 contain reference time ephemeris. The almanac data provided
in subframes 4 and 5 contain data time also,
reference time almanac (time of applicability) and
two satellite clock correction parameters. The 8
parameters providing the translation of GPST to
UTC time are in page 18 of subframe 4 [10].
All these parameters time permit to calculate the
GPST of transmission from the satellite, which will
be used for calculation of its position and time of
signal propagation from satellite to the user. The
problem of keeping precise time and synchronizing
clocks that are separated by considerable distances
is an old one. The Transit, the first SNS, as terrestrial radionavigation systems (e.g. Loran C) were
capable of time transfer with an accuracy level of
about 1 milisecond.
With the current techniques, GPS can distribute
time with an accuracy of about 30 ns, and can
compare remote clocks with an accuracy of about
5 ns [5].
Unlike the GPS time scale, GLONASS system
time currently implements leap seconds, like UTC,
and it has a constant offset of three hours (difference Moscow time to Greenwich time). This time is
generated and controlled by the GLONASS Central
Synchronizer, based on a set of hydrogen masers.
The relation between UTC and GLONASSSTS is:
UTC = GLONASStime + τc – 3h
(5)
The discrepancy, τc, comes from the different
clock ensembles used and is communicated to the
GLONASS users in frame 5 of the GLONASS
navigation message [4].
GLONASS time is maintained within 1 ms,
and typically better than 1 microsecond (μs) of
UTC(SU) by the control segment with the remaining portion of the offset broadcast in the navigation
message [12]. All GLONASS satellites use cesium
atomic clocks.
In navigation message the data concerning time
are transmitted in the immediate data which include
time marks and synchronization difference between
satellite clock and GLONASS time, and in the nonimmediate data which include raw clock corrections to the GLONASS time and the GLONASS
time correction relative to UTC(SU).
Galileo System Time (GST)
Galileo System Time (GST), modulo 1 second,
is planned to be steered to a prediction taken from
a number of UTC laboratories obtained through
an external Galileo time service provider. GST is
specified to be kept to within 50 ns (95%) of TAI
over any 1–year time interval. The offset between
TAI and GST will be known with a maximum
uncertainty of 28% (2 sigma), assuming the estimation of TAI six weeks in advance. Users equipped
with a Galileo timing receiver will be able to
predict UTC to 30 ns for 95% of any 24 hours
operation [13].
The GST is produced only with terrestrial clocks
available in the two redundant Precise Time
Facilities (PTF) of Galileo. PTF will host an active
H–maser (with necessary hotspares) and an
ensemble of Cesium clocks, and steer the maser
output to TAI. This steered time scale will serve as
a physical representation of GST. Galileo will use a
continuous reference time, like GPS. The first test
Galileo satellite GIOVE–A has on board rubidium
atomic clock, the second satellite GIOVE–B
operates on hydrogen maser atomic clock, for the
first time in history.
The GST is optimized in order to achieve a very
good short-term stability required for the functions
GLONASS System Time (GLONASSST)
GLONASS time, base on an atomic time scale
similar to GPS, is strongly liked to the National
time scale of Russian Federation − UTC(SU) which
is maintained by the Main Metrological Center of
the Russian Time and Frequency service at
Mendeleevo in the Moscow region. On other hand
GLONASS system itself is the most powerful and
accurate mean of UTC(SU) dissemination through
out Russia and the world. That’s why one of
requirements of GLONASS updates is to keep
UTC−UTC(SU) difference within 10 ns [11].
56
associated with navigation. The use of satellite
clocks, as in GPST, has two important aspects: the
internal satellite clock’s frequency drift and the
inherent measurement error associated with satellite
clocks. Both aspects would have had the effect of
decreasing GST accuracy. Therefore, for meteorological aspects, comparisons with clocks external to
Galileo will be used [14].
In Galileo navigation message the data concerning time are transmitted in each subframe,
clock correction and GST status in the page 1, GST
in the pages 2 and 3, GST – UTC conversion, GST
– GPS conversion and Time of Week (TOW) in the
page 4.
The values of all these four parameters (A0, A1, t0U
and ΔtLS) are broadcast by each GPS satellite in its
navigation message (page 18 of subframe 4). The
time tGPS is equal:
tGPS = tS – ΔtS
where tS is the time kept by a satellite clock, and ΔtS
is the satellite clock offset defined by:
ΔtS = αf0 + αf1 (t – t0c) + αf2 (t – t0c)2 + Δtr (10)
where: t0c is the reference epoch, αf0 is the clock
offset, αf1 is the fractional frequency offset, and αf2
is the fractional frequency drift. All these four
parameters are broadcast by each GPS satellite in
its navigation message (subframe 10), Δtr is the
relativistic term calculated from other data.
The rms error in estimation of ΔtS and ΔtUTC is
currently estimated to be about respectively, 5 and
10 ns. As navigation receiver can estimate the
receiver clock bias with a rms error of about 25 ns,
the total error in direct time distribution from GPS
is about 25 ns.
Telecommunications applications typically require synchronization of multiple nodes with an
accuracy of 100 ns, or better. Such synchronization
can be achieved by setting up a GPS antenna at
a fixed, surveyed location at each node, and determining time independently. With antenna position
known, a GPS receiver can determine precise time
by tracking one satellite only [5].
Translation of SNS time to UTC/TAI
UTC is obtained from GPS receiver, and in the
future from Galileo receiver, by adding the integral
number of leap seconds and fine UTC / TAI correction information contained in the navigation data.
In order to provide an estimate of UTC from GPS,
the navigation message broadcast by each GPS
satellite includes estimates of the time difference
between GPST and UTC(USNO) modulo one
second, and its rate. The navigation message also
includes the whole-second difference between the
two time scales due to leap seconds. These parameters allow a receiver clock to calculate an accurate
estimate UTC(USNO).
We know the time kept by a user’s receiver
clock, tu, and we want to generate UTC, tUTC. The
latter can be defined from the following equation:
tUTC = tu – Δtu – ΔtUTC
Time Dilution of Precision (TDOP)
coefficient
(6)
where: Δtu is the receiver clock bias relative to
GPST, and ΔtUTC is the bias between GPST, tGPS,
and UTC(USNO), tUTC.
A GPS navigation receiver computes Δtu in
order to schedule measurements, to time tag
position estimates, and to time-align the measurements for precise relative positioning. The bias
ΔtUTC is equal:
ΔtUTC = tGPS – tUTC
Dilution of Precision (DOP) terms represent the
impact of the geometric scattering of the satellites,
with respect to the receiver’s position, on the
position error, and hence on the accuracy of the
positioning. There is a linear relation between DOP
values and the resulting position accuracy for
a given pseudorange error value σUERE. We can
distinct five DOP coefficients in common use
which are useful to characterize the accuracy of
various components of the position / time solution.
One of these coefficients is TDOP (Time DOP)
which value is defined by the quotient of the square
root of the element of the covariance matrix and the
speed of the radio wave.
In some treatments, DOP is equal to the mentioned above square root only. In this case the variable
c·tb represents a range equivalent of the time bias
error and σctb defined by the product TDOP σUERE is
its standard deviation [5, 8].
(7)
The USNO monitors ΔtUTC and provides this
information to the Control Segment. Its value can
be computed at any instant (defined in GPST) from:
ΔtUTC = A0 + A1(tGPS – t0U) + ΔtLS
(8)
where: A0 and A1 are constant and first–order terms
of polynomial, t0U is reference time for UTC data,
and ΔtLS is the number of leap seconds added to
UTC since 1980 (15 seconds as of 1 January 2009).
(9)
57
Jacek Januszewski
From among all DOP coefficients which
depends on user’s latitude, the least value has
TDOP at equator. For a nominal GPS constellation
(24 satellites fully operational), if all satellites are
in view, TDOP coefficient can be less than 0.8 [15].
modulo 1 second is specified to be less than 5 ns
with 2-sigma confidence interval over any 24 hour
period.
Once Galileo is operational (2015 or later), it
is anticipated by many that most users will use
a combined GPS and Galileo PNT (positioning,
navigation, timing) service. There are two options
for obtaining the GPS–Galileo time offset [13]:
– the user is able to determine this offset in the
position and navigation processing at the cost
of one additional satellite tracked (fifth satellite
when determining a three–dimensional position);
– the offset could be measured by transitional time
transfer techniques (e.g. two way, common way)
or precisely estimated in near real time at the
monitor station of both systems using a integrated GPS / Galileo receiver.
Nowadays the difference between GPS time and
GLONASS time is known with accuracy 30 ns, in
the future 2 ÷ 6 ns [7, 16]. When using GPS and
GLONASS systems jointly, the difference in system time depends on the clocks from both systems
and has to be taken into account.
Satellite navigation system receivers time
Satellite navigation systems receivers display
the time in 12 hour or 24 hour notation, and the
default setting is 24 hour notation. AM or PM is
shown when 12 hour notation is selected. The time
and date are in UTC or in Local Time (LT). The
first time signalized by the receiver is UTC, but this
receiver can also display LT. That’s why the hour
and minute, unlike second, can be changed by the
user by entering a time difference from UTC. Some
SNS receivers can show the time depending on
season of the year, as summer time or winter time.
Time synchronization related errors
As any pseudo–range error leads to user’s position error we can also take into account synchronization errors. The problem of synchronization has
to be clearly distinguished from those of precision
or stability. Synchronization is related to the fact
that all the SNS components deal with a common
timescale. This is of primary importance when carrying out time measurements in the GNSS fields.
We must remember the fact that 1 ns is equivalent
to 30 cm.
The synchronization of satellites’clocks to GPS
time is obtained from the navigation message. The
problem of receiver synchronization must be
carried out on a frequent time base [14].
GPS–Galileo Time Offset
GPS Time and GST will be generated independently from each other. The residual offset between
GST and GPS Time will be probably in the order of
tens of nanoseconds. This GPS–Galileo time offset
(GGTO) will cause a bias between GPS and Galileo
measurements taken by integrated receivers of
these two systems. This will lead to an additional
error in the user’s navigation solution. A similar
effect will appear when users correct pseudorange
measurements to UTC using the broadcast offsets
between GPS and Galileo reference time scales and
UTC.
At user level, GGTO can be estimated from GPS
and Galileo measurements as an additional unknown in the user navigation solution. This would
increase the dimension of the estimation problem,
requiring at least five, and no four, measurements
(pseudo-ranges) to be available to calculate user 3D
position, time offset, and GGTO.
At system level, GGTO can be determined by
the GPS and Galileo ground segments, then predicted for the near future, and finally broadcast in
the navigation messages to all users. Therefore the
users can correct their observations with the received GGTO value and proceed with the “classical”
navigation solution with four parameters; i.e. 3D
position and time offset [9].
Interoperability
Interoperability of satellite navigation systems,
as GPS, GLONASS and Galileo, and satellite–
based augmentation systems, as EGNOS and
WASS can be defined as ability of each of these
systems having independent control loop to operate
jointly with other systems without interfering each
other on condition that signal frequency ranges,
coordinate reference frames and time reference
frame coincide as much possible.
Both GPST and GST are real time versions of
the various UTC(k) laboratories they reflect. If the
offset between these times is made available to
user, interoperability is ensured. The GPS–Galileo
time offset will be easily determined or received by
the user receiver. The U.S. and EU have agreed to
have their satellites broadcast the GPS–Galileo time
offset in the future. The accuracy of this time offset
58
Conclusions
Reference
– All time systems of GPS, GLONASS, and
Galileo are based on UTC, but using individual
realizations of UTC. “Spending” one satellite’s
observations enables a SNS receiver itself to
solve for the time offset between two different
satellite systems;
– typically the internal navigation system time
(e.g. GPST, GLONASS System Time) is only
used as a part of the navigation solution and is
not considered as standard time product;
– with the current techniques, GPS system can
distribute time with an accuracy of about 30 ns,
and can compare remote clocks with an accuracy of about 5 ns;
– the GPS time is a paper time scale (computations performed at the Master Control Station),
while Galileo System time is physically produced at Galileo Precise Timing Facility (PTF);
– the tendency is that most of modern navigation
professional GPS equipment uses GPS time as
the time base. Therefore, the translation from
GPS time to UTC time may no longer be needed
in modern receiver;
– GPS–Galileo time offset (GGTO) can be determined at user level in the user receivers (at least
five measurements are required) and at system
level by GPS and Galileo systems and broadcast
in the navigation message of both systems.
1. AUDIN C., GUINOT B.: The Measurements of Time-Time,
Frequency and the Atomic Clock, Cambridge University
Press, Cambridge 2001.
2. www.ucolick.org
3. www.tf.nist.gov
4. SEEBER G.: Satellite Geodesy, de Gruyter, Berlin / New
York 2003.
5. MISRA P., ENGE P.: Global Positioning System Signals,
Measurements, and Performances, Ganga–Jamuna Press,
Lincoln 2006.
6. VAN DIGGELEN F.: A–GPS: Assisted GPS, GNSS, and
SBAS, Artech House, Boston / London 2009.
7. Admiralty List of Radio Signals. The United Kingdom
Hydrographic Office, 2009, 10, vol. 2.
8. KAPLAN E.D., HEGARTY C.J.: Understanding GPS Principles and Applications, Artech House, Boston / London
2006.
9. MOUDRAK A. et al.: Interoperability on Time GPS–Galileo
Offset Will Bias Position, GPS World, 2005, Vol. 16,
No. 3.
10. BAO-YEN TSUI J.: Fundamentals of Global Positioning System Receivers, John Wiley & Son Inc. New Jersey 2005.
11. www.congrex.nl
12. www.novatel.com
13. HAHN J., POWERS E.: GPS and Galileo Timing Operability,
Global Navigation Satellite System Conference, Rotterdam
2004.
14. SAMANA N.: Global Positioning, Technologies and Performance, John Wiley & Son Inc. New Jersey 2008.
15. GROVES P.D.: Principles of GNSS, Inertial, and
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