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How does satellite navigation work?
A look at GNSS systems
Global Navigation Satellite Systems (GNSS), of which the familiar GPS
(Global Positioning System) is but one example, are now ubiquitous and
used in everyone’s daily lives. Most people do not even know the origin or
workings of the location and mapping functions built into the smartphones
that they carry. To them, it’s just ‘there’, and it works. But there is a lot
going on behind the scenes!
By Dr David Maddison
I
n the September 2018 issue of SILICON CHIP, we published an article on Augmented GNSS (siliconchip.
com.au/Article/11222), describing how the accuracy of
satellite navigation systems can be enhanced beyond what
is ordinarily available, through various augmentation systems (eg, SBAS – Satellite-Based Augmentation System).
This augmentation is not needed for ordinary users but
is for applications such as aircraft landing, precision agriculture and self-driving cars etc.
We also looked at a predecessor system to GPS, the terrestrial based Omega Navigation System in the September
2014 issue (siliconchip.com.au/Article/8002).
But so far, we have not actually described in detail how
satellite navigation systems work. This article corrects that
omission. We will go back to basics, to describe how the
regular (non-augmented) GNSS systems operate.
In the beginning . . . the word was the US GPS
The first GNSS system put in place, and the one most
people are familiar with, is the US Global Positioning Sys14
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tem (GPS). This was developed for the US military, both
for navigation and to ensure better accuracy with their
weapons systems (with the benefit of limiting unintended
civilian casualties).
This system was also made available free of charge worldwide, with reduced accuracy at first (“selective availability”), then later with the full available accuracy. The USA
turned off selective availability on 1st May 2000 and undertook never to use it in the future.
Part of the motivation for this was to prevent future tragedies such as Korean Air Lines Flight 007, which was shot
down by the Soviet Union in 1983 after inadvertently flying
into Soviet air space, due to a navigational error.
Newer GPS satellites, or Space Vehicles (SVs) as they are
called, don’t even support selective availability.
While the US Global Positioning System was the first,
the following systems have since come into service, or soon
will be: GLONASS (Russian; fully operational), Galileo (EU,
to be fully operational by 2020) and BeiDou (China, also to
be fully operational by 2020). There are also two regional
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systems: NavIC (India) and QZSS (Japan).
Then there are the following augmentation systems which
provide greater positional accuracy (down to cm or even
mm) and which were described in the September 2018 article: WAAS (USA), EGNOS (EU), MSAS (Japan), GAGAN
(India), SDCM (Russia), WAGE (US Military), SBAS (Australia, test-bed) and the commercial systems StarFire, CNav, Startfix, and OmniSTAR.
Newer satellite navigation receivers are ‘multi-constellation’ types which support more than one of the above
GNSS systems and can have access to over 100 satellites.
This makes position fixes in “urban canyons” and challenging terrain easier, as there is a higher likelihood of having more satellites visible directly overhead, also avoiding
multi-path reflections from satellites that are not directly
in the line of sight.
Basic operating principles
The same basic operational principles apply to all GNSS
systems. Each system has a group of satellites in orbit,
known as a constellation. Each satellite sends a continuous signal to Earth which contains data such as the satellite ID, the current time onboard the satellite, the position
of the satellite and other data. For GPS, this encoded information is called the Navigation Message.
All of the satellites in a constellation are synchronised
with the same time reference, which is achieved using extremely accurate atomic clocks onboard each satellite and
on the ground.
To achieve a full position fix, in theory three satellite signals at sea level are sufficient (where sea level represents
the roughly spherical shape of the Earth, the so-called reference ellipsoid or ‘geoid’ which are accurate models of
the exact shape). Four satellites are required to also compute altitude above sea level.
To get a position fix, two fundamental things need to be
established. The first is the distance from the user’s receiver
to three, four or preferably more satellites.
This is called “trilateration” in the specific case of three
satellites, or “multilateration” for three or more.
Fig.1: the intersection of three spheres, with radii defined
by the distance between a group of satellites and a receiver.
This shows how the intersection of two spheres produces a
circle (blue), and the addition of a third sphere defines two
points on that circle (yellow).
siliconchip.com.au
(Above and opposite): an artist’s impression of the latest
generation GPS Block IIIA satellite by Lockheed Martin,
first launched December 23, 2018. These offer three times
greater positioning accuracy than their predecessors,
increased signal power and much-improved resistance
against jamming. The satellites of the GPS constellation are
named NAVSTAR (Navigation Satellite Time and Ranging)
with various numbers to identify them. See the video titled
“Building the Most Powerful GPS Satellite Ever - GPS III” at:
siliconchip.com.au/link/aavj
This gives a relative position of the receiver with respect
to those satellites at the time of their transmission. To calculate the user’s location, it’s therefore also necessary to
establish the position of the satellites at the time they transmitted their signals, which is encoded in the data stream
along with the time of transmission.
This then gives the approximate location of the receiver
on the Earth’s surface or above it. These measurements are
then followed by many corrections and iterative adjustments to get a more exact positional fix.
Determining the distance to the satellites
Radio signals travel at the speed of light, ie, 299,792,458m/s
Fig.2: the intersection of spheres representing the distance
from a receiver to three satellites, showing the two possible
locations of the receiver with one point being obviously
wrong and rejected. A fourth satellite will establish
additional information such as altitude and help in
calculations to correct the receiver time clock.
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November 2019 15
Fig.3: the structure of GPS signals including a carrier, pseudorandom noise (PRN) code, navigation data (one bit for every
20 PRN cycles) and the resulting combined signal, that is
transmitted by the satellite. C/A stands for coarse/acquisition
code. Image source: José Caro Ramón, Head of GNSS
Augmentation Systems and Services at GMV, PMP; Creative
Commons Attribution-Share Alike 3.0 Unported license.
in a vacuum. If we know the delay between the transmission of a signal from a satellite and it being received on
Earth, we can determine the distance between the transmitter and the receiver.
This propagation delay calculation requires that the time
the signal leaves the satellite and the receipt time at the
receiver be known. The signals leaving the satellite have
a time stamp of the departure time.
Ideally, the receiver would have an atomic clock synchronised to the same time as the satellite clock, but generally, this is not the case; not everybody has pockets large
enough to carry around an atomic clock, or the batteries
required to run it!
We will discuss how that problem is dealt with later.
Knowing the exact time is essential as even a 1ns (onebillionth of a second) clock error at the receiver compared
to the satellite will result in a 30cm positional error; that
is how far radio waves travel in 1ns.
Knowledge of the propagation time of a signal (ie, distance) from one satellite to a receiver locates the receiver on a sphere around the satellite, with its radius being
the calculated distance (see Figs.1 & 2). Knowing you are
somewhere on a sphere is not that useful, so more information is required.
If the distance to a second satellite is known, then the receiver can be determined to be somewhere in a sphere surrounding that satellite as well. The receiver location is on
The full GPS interface specification
If you are interested in seeing the core technical document
that defines everything you need to know about the “interface”
between the “space segment” of the Global Positioning System
and the “user segment”, some of it is contained in the 224-page
document named “Interface Specification IS-GPS-200J, May 22,
2018”, available at: siliconchip.com.au/link/aavk
This describes the structure and content of data transmitted
from GPS satellites on radio frequency links L1 and L2. Related
technical documents can be found at: www.gps.gov/technical/
A useful book on GPS is P. Misra and P. Enge, Global Positioning System: Signals, Measurements and Performance, GangaJamuna Press, 2011.
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Fig.4: how the signal travel time from the satellite to the
receiver is determined. The receiver knows the matching
PRN code expected from each satellite. The PRN code within
the receiver is shifted until the maximum correlation is found
between the received and expected signals, and the offset
required to do this establishes the travel time, ¦t. In this
case, if the receiver code was shifted all the way to the left,
there would be an exact correlation. Figure source: Carlos
Lopez, https://gssc.esa.int/navipedia/index.php/GNSS_Basic_
Observables
the intersection of two spheres, which describes a circle. So
we know the receiver is somewhere on that circle. But that
is still not enough information for a complete position fix.
With a third satellite, we calculate a third sphere, and
this also has to intersect with the circle formed by the intersection of the first two spheres. When a sphere intersects
with a circle, it does so at two points.
So with three satellites we then have two possible positions of the receiver. The question then is how to determine
which of those positions is the actual location.
Usually, the position nearest Earth would be chosen as the
obvious location, and the second position would be rejected.
If a fourth satellite is used, it can unambiguously establish which of the two possible positions is the correct one
without having to guess. The fourth satellite is needed for
another reason as well as will be discussed later.
Note that at this point, only the relative position of the
receiver with respect to the satellites is known. So to determine the actual position of the receiver with respect to
the Earth, knowledge of the satellites’ position is required.
Relativity effects and corrections
Satellite navigation is an everyday situation where Einstein’s theories of Special Relativity and General Relativity have to be taken into account.
Firstly, because the satellites are moving relative to the
observer (about 14,000km/h for GPS), there is a time dilation effect. Special relativity says that the clock on board
the satellite will fall behind ground-based clocks by about
7µs per day. Bearing in mind radio waves travel about
30cm per nanosecond, this would amount to an error of
2.1km per day.
Secondly, massive bodies such as the Earth distort spacetime and the closer to such a body a clock is, the slower
time seems to go relative to an outside observer.
Since the satellites are high above the Earth, an observer
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af0, af1, af2, toc
TGD*
Δtr
–
+ + +
CLOCK
CORRECTION
POLYNOMIAL
ESTIMATE OF SV
TRANSMISSION TIME
Δtsv
CODE PHASE OFFSET
- TRUE SV CLOCK EFFECTS
- EQUIPMENT GROUP DELAY
DIFFERENTIAL EFFECTS
-RELATIVISTIC EFFECTS
+
+ –
Ttropo
+
+ –
Tiono
TROPHOSPHERIC
MODEL
IONOSPHERIC
MODEL*
αη, βη
+
+
+
GPS TIME
+ +
– +
– +
PATH DELAY
- GEOMETRIC
- TROPOSPHERIC
- IONOSPHERIC*
+
+
+ +
PSEUDORANGE
DIVIDED BY THE
SPEED OF LIGHT
–
ERD**
c
+
+
GPS TIME
USER CLOCK BIAS
FILTER AND
COORDINATE
CONVERTER
USER POSITION,
VELOCITY, AND
TIME (CLOCK BIAS)
- RANGE DATA FROM
OTHER SATELLITES
- CALIBRATION DATA
- AUXILIARY SENSORS
* SINGLE FREQUENCY USER ONLY
** OPTIONAL
Fig.5: the mathematical model used by a GPS receiver to
apply correction parameters. Similar procedures apply
to other GNSS systems. SV stands for space vehicle; a10,
a11 and a12 are polynomial coefficients related to satellite
clock error; toc is “time of clock”; ERD is estimated range
deviation; c is the speed of light; t is the true GPS time
at the time of data transmission; tsv is the space vehicle
time; ¦tsv is the difference between the space vehicle
time and the centre of its antennae; ¦tr is the relativistic
correction; α and β are ionospheric parameters; TGD is
the group delay differential; and Ttropo and Tiono are
corrections for tropospheric and ionospheric delays. From
Interface Specification IS-GPS-200K, “NAVSTAR GPS Space
Segment/Navigation User Segment Interfaces”.
on Earth would see the satellite clock running faster than
an Earth-based clock by about 45µs per day.
The combined effect of the satellite clock running slower
due to special relativity and faster due to general relativity from the point of view of an Earth-based observer is a
difference of 38µs or 11.4km per day. Satellite navigation
would therefore be worthlessly inaccurate if these relativistic effects were not taken into account
Another phenomenon that has to be taken into account
is the kinematic “Sagnac effect”. This can amount to a timing error of up to 207ns or up to 62m per day.
Between the satellite and the Earth, there is a rotating
frame of reference. Two electromagnetic beams going in
opposite directions on the same closed path around a rotating object will take different times to complete the trip.
Therefore, the timing has to be adjusted to obtain the exact
propagation time of a signal from the satellite to the receiver.
There are additional corrections which must be made to
get accurate results, which will be discussed later.
The pseudo-random noise (PRN) ranging code
The pseudo-random noise code is what is used to identify
which signals come from which satellites. All satellites in
a GNSS constellation are assigned a unique PRN number.
In the case of GPS, two primary frequencies are used
(with more under development). These are L1 and L2. Civilian GPS mostly uses just L1 (and some L2) and the military use both L1 and L2.
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******** Week 512 almanac for PRN-24 ********
ID: . . . . . . . 24
Health: . . . . . . 000
Eccentricicy: . . . . 0.6661891937E-002
Time of Applicability(s):
319488.0000
Orbital Inclination(rad):
0.9505615234
Rate of Right Ascen(r/s):
-0.7850758266E-008
SQRT (A) (m 1/2): . . 5153. 627930
Right Ascen at Week(rad):
-0.7220151424E+000
Argument of Perigee(rad):
-0.651554227
Mean Anom(rad): . . . -0.5415329933E+000
Af0(s): . . . . . . 0.1974105835E-003
Af1 (s/s): . . . . . 0.3637978807E-011 week: 512
Fig.6: example almanac data for one satellite. Each GPS
satellite transmits almanac data for all GPS satellites. This
allows a receiver to determine which satellites are likely
to be in view, significantly reducing the amount of signal
searching that it needs to do.
EPHEMERIS FOR SATELLITE 24 :
PR.111 number for data . . . . . 24
Issue of ephemeris data . . . . 179
Semi-Major Axis (meters) . . . . 2.65599E+07
C(ic) (rad) . . . . . . . . . . -1.02445E-07
C (is) (rad) . . . . . . . . . . -1.22935E-07
C(rc) (meters) . . . . . . . . . 168.656
C(rs) (meters) . . . . . . . . . 168.656
C(uc) (rad) . . . . . . . . . . -3.48687E-06
C (us) (rad) . . . . . . . . . . 1.1526E-05
Mean motion difference (rad/sec) 3.94802E-09
Eccentricity (dimensionless) . . 0.00623617
Rate of inclination angle (rad/sec)
1.05004E-10
Inclination angle <at> ref. time (rad)
0.976756
Mean Anomaly at reference time (rad)
1.79689
Corrected Mean Motion (rad/sec) 0.000145861
Computed Mean Motion (rad/sec) . 0.000145858
Argument of perigee (rad) . . . -2.06498
Rate of right ascension (rad/sec) -7.67032E-09
Right ascension<at> ref time (rad) -2.4059
Sqrt (1 - e2) . . . . . . . . . 0.999981
Sqr root semi-major axis, (m1/2) 5153.63
Reference time ephemeris (sec) . 252000
Fig.7: an example of GPS satellite ephemeris data, broadcast
from each satellite. PRN is the pseudo-random noise number.
The ephemeris is highly accurate orbital data from which the
exact location of the satellite can be established.
In the civilian case, since all satellites are broadcasting on the same frequency, a way is needed to identify the
signal from each individual satellite from among a whole
jumble of signals.
The GPS date rollover problem
GPS time uses week numbers which started counting at midnight on 5th January 1980 and are numbered from 0 to 1023 (ie,
1024 weeks), after which the week number is reset to zero. The
first rollover occurred on 21st August 1999, and the next one
after that was on midnight 6th April 2019.
The next rollover will occur at midnight on 2nd November
2038. This year, there was a concern that some GPS units might
not handle the rollover correctly and would reset themselves to
1980 or 1999. People were warned about this, but it appears to
have not been a problem as most GPS units were programmed
correctly to handle it.
Editor’s note: we noticed some older GPS modules giving incorrect dates after April 6. Apart from the date being wrong (nearly
20 years earlier than it should be), everything else seems to work,
including location information and the time. These modules were
purchased some years ago; those sold within the last few years
should handle the week rollover seamlessly.
Australia’s electronics magazine
November 2019 17
TABLE I
COMPONENTS OF EPHEMERIS DATA
Name
M0
Δn
e
Description
Mean anomaly at reference
time
Mean motion difference from
computed value
Semicircle
Eccentricity
Dimensionless
m1/2
Semicircle
√a
Ω0
Square root of semimajor axis
i0
Inclination angle at reference
time
Argument of perigee
ω
Units
Longitude of ascending node
of orbit plane at weekly epoch
Semicircle/s
Semicircle
Semicircle
Semicircle/s
&
Ω
Rate of right ascension
IDOT
Cuc
Rate of inclination angle
Cus
Amplitude of sine harmonic
correction term to the
argument of latitude
Rad
Crc
m
t0e
Amplitude of cosine harmonic
correction term to the orbit
radius
Amplitude of sine harmonic
correction term to the orbit
radius
Amplitude of cosine harmonic
correction term to the angle of
inclination
Amplitude of sine harmonic
correction term to the angle of
inclination
Ephemeris reference time
IODE
Issue of data, ephemeris
Dimensionless
Crs
Cic
Cis
Amplitude of cosine harmonic
correction term to the
argument of latitude
Semicircle/s
Rad
m
Rad
Rad
s
Fig.8(a) [left]: the values within the ephemeris (orbital)
data and their meanings. In addition to the ephemeris, the
Navigation Message also contains the following important
clock parameters: t0c (reference time) and a0, a1, a2
(polynomial coefficients for clock correction: bias [s], drift
[s/s], and drift rate/aging [s/s2]). Fig.8(b) [above] explains the
symbols of Figs.8(a) and Fig.9
Fig.9 (opposite): for those interested in the mathematics
behind calculating the satellite position using ephemeris
data, here are the equations used. WGS84 is the World
Geodetic System 1984 coordinate system, and ECEF is Earthcentred, Earth-fixed coordinate system. Table from Ryan
Monaghan. From: siliconchip.com.au/link/aavl
Fig.11: high-orbit GLONASS is a system that will be implemented to provide improved regional coverage over Russia,
much like the Japanese QZSS system. The ground tracks of the orbits are shown in red. Presumably, Australian users will
benefit from this system as with QZSS, as some of the satellites will be visible over Australia.
18
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TABLE 2
ALGORITHM FOR COMPUTING SATELLITE POSITION
Equation
μ = 3.986008 × 1014 m 3 / s 2
& =
Ω
7.292115167 × 10 −5 rad / s
e
Description
WGS 84 value of earth’s
universal gravitational
parameter
WGS 84 value of earth’s
rotation rate
Semimajor axis
a = ( a )2
t=
t − t0 e
n +1
Time from ephemeris
reference epoch
⎧⎪ (1− e2 sin E /(1− e cosE ) ⎫⎪
n
n
f n = tan ⎨
⎬
⎪⎩ (cosEn − e) /(1− e cosEn ) ⎪⎭
True anomaly
−1
En = cos −1 (
=
φn f n + ω
e + cos f n
)
1 + e cos f n
δμ n = CμC cos 2φn + CμS sin 2φn
δrn = CrC cos 2φn + CrS sin 2φn
δin = CiC cos 2φn + CiS sin 2φn
=
μ n φn + δμ n
rn
a (1 − e cos En ) + δrn
=
in i0 + δin + ( IDOT )t n
Eccentric anomaly from
cosine
Argument of latitude
Second-harmonic correction
to argument of latitude
Second-harmonic correction
to radius
Second-harmonic correction
to inclination
Corrected argument of
latitude
Corrected radius
Corrected inclination
xn' = rn cos μ n
X coordinate in orbit plane
yn' = rn sin μ n
& +Ω
& )t − Ω
& t
Ω n= Ω 0 + (Ω
e n
e 0e
Y coordinate in orbit plane
Corrected longitude of
ascending node
=
xn xn' cos Ω n − yn' cos in sin Ω n
ECEF X coordinate
=
yn xn' sin Ω n + yn' cos in sin Ω n
ECEF Y coordinate
z n = xn' sin in
ECEF Z coordinate
CDMA (code division multiple access), a spread spectrum technique, is used to achieve this. CDMA was previously used on some mobile phone networks.
A PRN code is part of the CDMA scheme and is used to
identify the signal of interest. It is a carefully selected binary code and one of a set. The PRN codes are chosen so
that no two are alike.
The PRNs are called Gold codes after the person who invented them, and have “bounded small cross-correlations
within a set” which means that they have the most possible difference between them (see Fig.3 & 4).
The PRN codes are predetermined and stored in both the
satellites and receivers. By knowing the PRN code ahead
of time, a receiver can pick out one signal from many that
are simultaneously being received.
The PRN code is broadcast continuously, and the navigation data (at a much lower bit rate) is superimposed on
that. The transmitted signal has more bandwidth than required for the transmitted navigation data, to allow the
PRN code to be incorporated.
One way of thinking about this is like a room full of
people all speaking different languages at the same time.
If you are only interested in receiving the message of the
speaker of one particular language (the desired PRN code),
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Fig.10: a 10.23MHz rubidium frequency standard (“atomic
clock”) from the late 1970s, by Frequency Electronics, Inc.
These were used on early GPS satellites, although this one
looks more like a prototype. Part of the National Air and
Space Museum collection, Smithsonian Institution,
Washington DC.
the voices of all other speakers are rejected as noise (different PRN codes).
In the case of GPS, the PRN code is 1023 bits long and
repeats every millisecond for civilian users. The military
L1 and L2 signals have PRN sequences that are about 6.2 x
1012 bits long (773 gigabytes) and take one week to transmit, even at a higher bit rate (or chip as it is called).
The civilian PRN is known as the C/A code (coarse/acquisition) and the military the P (precision) code.
There is also a Y and a more modern M code for military
use. These have improved anti-spoofing and anti-jamming
capabilities.
There are also modernised civilian services on later satellites, on the L2 frequency (called L2 CM and L2 CL) which
offer improved navigational accuracy and other benefits.
“Safety of life” signals are also transmitted on more recent
satellites on the L5 band, along with PRN ranging codes.
Apart from enabling multiple signals on one frequency,
The role of GPS in timekeeping
Apart from its obvious role in navigation, GPS also plays a vital role in timekeeping via the very accurate atomic clocks each
satellite has onboard.
GPS can provide accurate time to within nanoseconds, compared to the old radio signals that provided millisecond accuracy.
Many industries use GPS timekeeping services to:
• provide a time stamp on transactional records
• keep mobile phone networks synchronised
• keep power grids synchronised
• keep digital broadcast services operating correctly, allowing efficient utilisation of limited radio spectrum bandwidth
• allow scientific instruments distributed over wide geographic
areas, eg, seismometer networks utilising a common time
reference... and for many other uses.
Australia’s electronics magazine
November 2019 19
An artist’s impression of a Chinese BeiDou satellite
Fig.12: the arrangement of the GPS satellite constellation.
The 24 satellites are in six equally spaced orbital planes
and within each plane, there are four positions or “slots”
occupied by satellites. This arrangement ensures that there
are at least four satellites visible overhead at any point on
the Earth’s surface at all times.
the CDMA technique allows for low transmission power
and resistance to jamming and interference.
Applying time corrections
With the PRN code enabling the identification of individual satellites, and with knowledge of the PRN code expected at a particular time from that satellite in the receiver,
it is possible to determine the offset between two matching
segments of code and thus determine the approximate distance to a satellite. This distance is subject to corrections
and thus called the pseudorange.
A typical receiver such as a hand-held unit, smartphone
or in-vehicle navigation system does not have an atomic
clock due to reasons of cost, size and power consumption.
So the receiver is not precisely synchronised with the clock
on the satellites, leading to uncertainty in the actual distance to the satellites.
The discrepancy between highly accurate clocks on the
satellites and the less accurate clock at the receiver is resolved as follows.
The receiver gets signals from multiple satellites for a positional fix. The spheres representing the distance to three
satellites will always intersect at two points (one of which
is ignored), even if the clock receiver is wrong.
With a fourth satellite and a fourth sphere representing
that satellite, there can only be one value of receiver time
that satisfies the condition of the four spheres intersecting
at one point.
Fig.13: a comparison of GPS, GLONASS and Galileo frequency bands as well as some other frequency allocations.
BeiDou is not included in this diagram. Note several areas of overlap.
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An artist’s impression of
the Galileo system. It is
interoperable with GPS
and GLONASS.
Fig.14: an example of satellites visible from Furuno’s multiGNSS receiver, compared to their GPS-only receiver.
SBAS stands for Satellite Based Augmentation System.
to determine the receiver position.
Establishing the position of the satellites
The receiver adjusts its clock to that value, thus ensuring it is synchronised to the atomic clocks of the satellites.
It must do this constantly due to the inherent inaccuracy
in the receiver clock.
Further corrections
There are signal delays caused by the passage of signals
through the ionosphere, leading to an error of about 83ns
or 25m. Passage through the troposphere leads to an additional 7ns or 2m error.
Other effects taken into account either on the satellite
or user equipment are the space vehicle clock error due to
bias, drift, ageing and group delay (the time delay as a function of frequency for a signal to go through the electronics
of the satellite).
A detailed flow chart for the process is shown in Fig.5.
As can be seen, the process involves calculating the satellite clock bias, group delay, relativistic and other effects;
accounting for delays due to the atmosphere and geometric effects and then correcting pseudorange to give the Estimated Range Deviation (ERD) due to these timing effects.
But there are still more calculations that need to be made
An artist’s impression of a QZSS satellite in orbit.
siliconchip.com.au
We now have explained how the pseudorange is obtained
and how this is adjusted to get the exact propagation time
of the radio signals from the satellite to the receiver. We
still have not established the positions of the satellites from
which we can determine a navigational fix, and that is the
next task. All GNSS systems work similarly but we will look
at GPS as an example.
A GPS satellite transmits both an almanac (Fig.6), which
has general positional data for all satellites in the constellation, and an ephemeris (Fig.7), which is accurate orbital
data specific to itself. Almanac data gives information about
what satellites are in the area of view of the receiver, so that
it doesn’t have to spend extra time looking for satellites that
are not visible.
Almanac data is considered valid for about 180 days, while
ephemeris data is valid for only about four hours. Ephemeris data allows the exact location of a satellite to be established at a given time, and takes into account perturbations
due to gravitational influences on the satellite from bodies
A ground track of one of Japan’s QZSS satellites, showing
that most of Australia is included in its coverage area. This
effectively adds four GPS-compatible satellites.
Australia’s electronics magazine
November 2019 21
DIY GNSS Projects
GPS modules can be purchased from the SILICON CHIP
ONLINE SHOP. If you can afford to wait, they’re also available
quite cheaply on line, for as little as $5 delivered.
SILICON CHIP has published many projects using inexpensive GNSS modules for purposes such as clock and frequency references, or most recently as an accurate speedo
and automatic vehicle audio volume controller (June 2019).
See: www.siliconchip.com.au/project/gps
Here are online articles explaining how to interface these
modules to Arduinos, Raspberry Pis and other similar platforms.
•
To connect to a GNSS module to a PC, you need a USB/
serial converter. Make sure it is the correct voltage for the
module, usually 3.3V. Note that some converters won’t
work with Windows 10; the CP2102-based modules in
our Online Shop are relatively trouble-free.
•
A popular GNSS module brand is u-blox. They make the
VK2828U7G5LF modules sold in our ONLINE SHOP (Cat
SC3362). They have free evaluation software that allows
you to see many aspects of GNSS operation with their
modules.
•
See: siliconchip.com.au/link/aavm (Windows software).
A suitable Arduino library called TinyGPS++
is at: siliconchip.com.au/link/aavn
•
See the videos titled “Playing with GPS: Ublox Neo-7M
and U-Center” at: http://siliconchip.com.au/link/aavo
and “10Hz U-blox binary GPS data in 66 lines of code
(Arduino)” at siliconchip.com.au/link/aavp
•
You can see the position of various GNSS or other satellites in the sky at: siliconchip.com.au/link/aavq
•
Build a geocaching pendant as described at:
siliconchip.com.au/link/aavr
•
RTKLIB (www.rtklib.com) is an open-source program for
high-precision GPS with low-cost devices.
See also: http://rtkexplorer.com/
such as the sun and moon.
Ephemeris data includes the standard six Keplerian
elements, plus ten others, to take into account minor influences which affect the satellite’s orbit.
The orbit of a satellite can be determined using the laws
of physics plus minor deviations from theory due to unknown random forces, which are determined with groundbased radar, providing corrections incorporated into the
ephemerides (the plural of ephemeris). Fig.8 shows the
meanings of the ephemeris parameters, while Fig.9 shows
the calculations involved.
The coordinate system
Once a GNSS system has established the receiver position, it still needs to be placed on a particular reference
frame. The Earth is not a sphere but rather an “oblate spheroid” of 6,378,137m x 6,357,002m.
Various standard reference frames have been developed
for navigation that correctly place coordinates on the Earth’s
true surface.
Typically, WGS84 (World Geodetic System) is used for
22
Silicon Chip
Fig.15: a screen grab of the GPSTest App for Android
showing satellites visible on the phone’s GNSS receiver.
From top to bottom, the constellations are GPS,
GLONASS, Galileo and BeiDou.
GPS for the so-called Earth-centred, Earth-fixed (ECEF) reference frame. In Australia, the standard reference frame for
high precision work is the Geocentric Datum of Australia,
GDA94 but as Australia drifts north due to tectonic plate
movements, this is now out by 1.6m.
GDA2020 is under development; WGS84 still gives acceptable results for most users.
The atomic clocks
GNSS systems would not be possible without the use
Australia’s electronics magazine
siliconchip.com.au
Comparison of satellite navigation systems
Country
GPS
GLONASS
Galileo
BeiDou
USA
Russia
EU
China
total: 32
31 operational
1 in maintenance
Number of satellites
as of 18 June 2019
total: 27
total: 30
24 operational
26 operational
1 in commissioning
4 to be launched
1 spare
(3 of which are spares)
1 in testing
Altitude
20180km
19130km
23222km
Frequencies used
L1: 1575.42MHz
L2: 1227.60MHz
L3: 1381.05MHz
L4: 1379.913MHz
L5: 1176.45MHz
(L1 and L2 are the
primary frequencies,
others are little
used or experimental)
Modernised:
E1: 1575.420MHz
L1: 1600.995MHz
E6: 1278.750MHz
L2: 1248.06MHz
E5: 1191.795MHz
L3: 1202.025MHz
E5a: 1176.450MHz
For future
E5b: 1207.140MHz
interoperability
with other systems:
L1: 1575.42MHz
L3: 1207.14MHz
L5: 1176.45MHz
Signal encoding
CDMA
FDMA
but moving to CDMA
Orbital period
11h 58m
11h 15m
14h 7m
(half a sidereal day)
6 planes in
3 planes separated by 120°,
medium Earth orbit
8 satellites in each plane;
satellite inclination 64.8°
Orbital regime
Accuracy
300-5000mm
First in service
First launch: 1978
Initial operational
capability: December
1993. Fully operational:
April 1995
27 operational
satellites in 3
planes with 56°
inclination to the
equatorial plane
2.8-7.38m,
1m public
next-generation
10mm restricted
GLONASS-K2 from 2019
is intended to reduce
user range error to 300mm
Claimed fully operational
Completion by end
in December 1995 but
2020 but
not globally available
operational now
until the mid-2000s
of extremely accurate atomic clocks. As mentioned above,
radio signals travel 30cm in one nanosecond, so clock accuracy has to be of that order or better to obtain a good
navigational fix.
GPS satellites have four onboard cesium and rubidium
atomic clocks. These are kept in sync and are adjusted by
even more accurate Earth-based atomic clocks. Typical accuracy of the clock on the latest GPS satellites is ±4 nanoseconds, representing about ±120cm of range error.
We published an article in the February 2014 issue which
explained how rubidium atomic clocks work (siliconchip.
com.au/Article/6127).
siliconchip.com.au
CDMA
total: 39
33 operational
6 non-operational
35 to be operational
by 2020
21150km for medium
Earth orbit satellites (MEO)
B1I, B1Q: 1561.098MHz
B1C, B1A: 1575.42MHz
B2B, B2I, B2Q: 1207.14MHz
B2a: 1176.45MHz
B3I, B3Q, B3A: 1268.52MHz
CDMA
For 27 satellites in MEO:
12h 37m
For 2020:
5 geostationary
3 inclined geosynchronous
27 Medium Earth orbit
10m public (global)
5m Asia Pacific region
100mm restricted
Completion by end
2020 but some services
available since
December 2012
GNSS receiver start-up
A receiver usually cannot get a position fix as soon as it is
powered up. There are three distinct start-up situations which
lead to differing power-on times before a fix can be made.
If the receiver is brand new or hasn’t been used for a
long time, that makes it a ‘cold start’. The receiver doesn’t
know where it is, so it has to search for all possible satellites. After a satellite is acquired, it then has to download
the almanac data for all satellites. This takes 12.5 minutes
and gives it the approximate positions of the other satellites.
A ‘warm start’ is where the receiver already knows the
time within 20 seconds and its position within 100km and
Australia’s electronics magazine
November 2019 23
Fig.15: an example of the free u-center evaluation software for Windows, which allows inexpensive u-blox GNSS modules
to be tested and configured. See siliconchip.com.au/link/aavm
has current almanac data.
It can then find the ephemeris data for at least four satellites, which is broadcast every 30 seconds, and then get
a positional fix, usually within a minute.
A ‘hot start’ is where the receiver has current time, almanac, ephemeris, and position to allow rapid acquisition
of new signals, usually within a few seconds. Vehicle GPS
systems which can be “always on” may use this system.
Some GNSS systems used in Smartphones can sometimes start faster, because in addition to the GNSS location, they also use a database of WiFi network locations to
help determine their location earlier than the GNSS signal
would permit.
GPS and leap seconds
The global time standard is UTC or Coordinated Universal Time. Since the Earth’s rotation rate varies naturally by
a slight amount, every so often a leap second is added or
removed to keep Univeral Coordinated Time synchronised
with the Earth’s rotation.
The leap second is not implemented in GPS because of
the navigational errors and confusion this would cause.
Mixing and matching multiple GNSS
systems
Many modern satnav receivers can decode GPS, Galileo, GLONASS and QZSS (Japan’s regional system) signals. An increasing
number of devices can also decode BeiDou.
Multi-GNSS receivers have improved performance due to the
greater number of satellites in view, especially in urban canyons
where the view of the sky is very limited.
You can see what systems your Android smartphone can receive with the free GPSTest App. Note that QZSS, which is visible in most of Australia with standard GPS receivers, effectively
adds four more satellites to the constellation
24
Silicon Chip
The difference between UTC and GPS time was zero when
the GPS clock started on 1st January 1980, but is now 18
seconds.
The GPS Navigation Message broadcasts the difference
between UTC and GPS time, so a receiver can show the
correct UTC or local time.
Mapping errors
Finally, note that while a GNSS fix is generally extremely accurate, the maps used by navigation systems are not
necessarily accurate.
There have been many mishaps due to people following
incorrect maps, only to become stranded, or in some cases,
driven over cliffs or off the end of piers! This is, of course,
a problem of the maps and not the GNSS system itself.
To help ensure the most accurate possible and free maps
the public can contribute to the production of open-source
maps by joining the OpenStreetMap community (www.
openstreetmap.org).
Some maps contribute to specialised interests such as fourwheel-driving, mountain biking, bush walking, etc, while
others concentrate on regular street navigation.
SC
Novel wearable GPS products
One of the more special GPS
products we have seen is the
GPS SmartSole, a GPS unit built into
the sole of any shoe that connects
to the mobile phone network. It
can be used to track loved ones
with memory disorders.
See: siliconchip.com.au/link/aavs
Their tracking services are available in the USA only.
They do not mention whether it is compatible with a shoe
phone, so if you are hot on the heels of a KAOS agent, you had
better do your own testing!
Australia’s electronics magazine
siliconchip.com.au
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