Transcript TRANSIT - Geodesy

Part II
WHAT IS GPS AND HOW IT WORKS
GS608
Reference materials can be found at:
www.gmat.unsw.edu.au/snap/gps/about_gps.htm
More GPS links are provided on the course web page
Civil and Environmental Engineering and Geodetic Science
Global Positioning System (GPS)
The NAVSTAR Global Positioning System (GPS) is a
satellite-based radio-positioning and time-transfer system,
designed, financed, deployed and operated by the US
Department of Defense.
However, the system has currently significantly larger
number of civilian users as compared to the military users.
Civil and Environmental Engineering and Geodetic Science
Global Positioning System (GPS)
 The NAVSTAR Global Positioning System (GPS)
program was initiated in 1973 through the combined efforts
of the US Army, the US Navy, and the US Air Force.
 The new system, designed as an all-weather, continuous,
global radio-navigation system was developed to replace the
old satellite navigation system, TRANSIT, which was not
capable of providing continuous navigation data in real time
on a global basis.
Civil and Environmental Engineering and Geodetic Science
GPS – Objectives 1/2
 Suitable for all classes of platform: aircraft, ship, land-based
and space (missiles and satellites),
 Able to handle a wide variety of dynamics,
 Real-time positioning, velocity and time determination capability
to an appropriate accuracy,
 The positioning results were to be available on a single global
geodetic datum,
 Highest accuracy to be restricted to a certain class of user,
 Resistant to jamming (intentional and unintentional),
 Redundancy provisions to ensure the survivability of the
system,
Civil and Environmental Engineering and Geodetic Science
GPS – Objectives 2/2
 Passive positioning system that does not require the
transmission of signals from the user to the satellite(s),
 Able to provide the service to an unlimited number of users,
 World-wide coverage
 Low cost, low power, therefore as much complexity as
possible should be built into the satellite segment, and
 Total replacement of the Transit 1 satellite and other terrestrial
navaid systems.
Civil and Environmental Engineering and Geodetic Science
GPS Receiver Requirements
GPS user hardware must have the ability to track
and obtain any selected GPS satellite signal (a
receiver will be required to track a number of
satellites at the same time), in the presence of
considerable ambient noise
This is now possible using spread-spectrum and
pseudo-random-noise coding techniques
Civil and Environmental Engineering and Geodetic Science
Spread Spectrum Radio (SSR) Technique 1/2
 Spread Spectrum Radio (SSR) was almost exclusively used by military
until 1985, when FCC allowed spread spectrum’s unlicensed commercial
use in three frequency bands: 902-928 MHz, 2.4-2.4835 GHz and 5.7255.850 GHz.
SSR differs from other commercial radio technologies because it spreads,
rather than concentrates, its signal over a wide frequency range within its
assigned bands.
A key characteristic of spread spectrum radios is that they increase the
bandwidth of the transmitted signal by a significantly large ratio to the
original signal bandwidth.
 The main signal-spreading techniques are direct sequencing and
frequency-hopping
Civil and Environmental Engineering and Geodetic Science
Spread Spectrum Radio (SSR) Technique 2/2
 Direct sequencing continuously distributes the data signal across a broad portion
of the frequency band; it modulates a carrier by a digital code with a bit rate much
higher than the information signal bandwidth (used by GPS).
 Alternatively, frequency-hopping radios move a radio signal from frequency to
frequency in a fraction of a second.
 The spread spectrum receiver has to reconstruct the original modulating signal
from the spread-bandwidth signal by a process called correlation (or de-spreading).
The fact that the interference remains spread across a large bandwidth allows the
receiver to filter out most of their signal energy, by selectively allowing through only
the bandwidth needed for the de-spread wanted signal.
 Thus, the interference is reduced by SSR processing. Transmitting and receiving
SSR radios must use the same spreading code, so only they can decode the true
signal.
Civil and Environmental Engineering and Geodetic Science
TRANSIT as GPS Predecessor
• Researchers at Johns Hopkins observed
Sputnik in 1957.
• Noted that the Doppler shift provided closest
approach to earth.
• Developed a satellite system that achieved
accurate positioning
• Called TRANSIT and provided basic ideas
behind GPS
Civil and Environmental Engineering and Geodetic Science
Development of Basic Navigation
Satellite Concept
1964-1967
•
SYSTEMATIC STUDY OF EVERY WILD IDEA
IMAGINABLE
•
CONVERGED ON “PSEUDORANGING” IN 1967
•
MAJOR STUDY CONTRACTS LET IN 1968 TO TUNE THE
CONCEPT
Civil and Environmental Engineering and Geodetic Science
Motto Adopted by the Joint Program
Office on GPS Program
The mission of this Program is to:
1. Drop 5 bombs in the same hole, and
2. Build a cheap set that navigates (<$10,000),
and don’t you forget it!
Civil and Environmental Engineering and Geodetic Science
Major Issues Identified in 1968 Studies
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•
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CHOICE OF CARRIER FREQUENCY
• L-Band
• C-Band should be studied
DESIGN OF SIGNAL STRUCTURE
• Military and civilian use included
ORBIT/CONSTELLATION SELECTION
Civil and Environmental Engineering and Geodetic Science
Managed Concept Debates
1969-1972
•
•
EXPANDED TRANSIT
• Insisted on worldwide overage
• 153 satellites in 400 mile polar orbits
• Transit carrier frequency
EXPANDED TIMATION
• Initially only a Time Transfer System
• Insisted on worldwide coverage
• Expanded concept to intermediate altitude circular
orbit constellation of 30 to 40 satellites
Civil and Environmental Engineering and Geodetic Science
Convergence on Final System
1973-1974
•
SWITCHED CONCEPT TO 12-HOUR CIRCULAR ORBITS
• 3 planes, 8 satellites each
• i = 63°
•
RETAINED DIRECT-SHIFT KEYED SPREAD SPECTRUM
PN SEQUENCE
•
DUAL FREQUENCY SIGNAL ON L-BAND
•
PICKED INITIAL DEPLOYMENT OF 4+2 ‘BLOCK I”
SATELLITES
Civil and Environmental Engineering and Geodetic Science
PHASE I DESIGN 1974-1980
•
•
BLOCK I SATELLITE CONTRACTS WITH ROCKWELL
INTERNATIONAL
• 6 satellites followed by 6 more
• All satellite performance projections achieved. 3dB more transmitted power
then required
-13
• Exceptional (1x 10 ) on-orbit Rubidium clock performance achieved.
DETAILS OF SIGNAL STRUCTURE & NAV MESSAGE DEFINED
• C/A code designed with civil sector in mind
• “P-Code” designed by Magnavox
• Navigation message identical on both signals
Civil and Environmental Engineering and Geodetic Science
PHASE II DESIGN 1981-1989
•
•
BLOCK II SATELLITES
• Rockwell International
• Selective Availability and Anti-Spoof (Y-Code) Implemented
• Constellation downsized to 21 satellites (6 planes)
• Nav message slightly modified
OPERATIONAL CONTROL SEGMENT
• Monitors at Ascension, Diego Garcia, Guam, Hawaii, and Colorado
Springs
• 24-satellite ephemeris (orbit) determination
•
PHASE II/PHASE III USER EQUIPMENT
• Rockwell Collins, Magnavox and Teledyne Systems
• Rockwell Collins and Magnavox
• Rockwell Collins
Civil and Environmental Engineering and Geodetic Science
GPS Satellite System – Final Design 1/2
 24 satellites
 altitude ~20,000 km
 12-hour period
 6 orbital planes, inclination 55o
 Applications: practically unlimited!
•
•
•
•
•
•
Positioning and timing
Navigation
Mapping and GIS data collection
Engineering and communication
Agriculture
ITS
Civil and Environmental Engineering and Geodetic Science
GPS Satellite System – Final Design 2/2
 continuous signal transmit
 fundamental frequency 10.23 MHz
 almost circular orbit (e = 0.02)
 at least 4 satellites visible at all times from
any point on the Earth’s surface (5-7 most of
the time)
Civil and Environmental Engineering and Geodetic Science
GPS Policy Board*
•
•
•
•
•
•
•
Department of Agriculture
Department of Commerce
Department of Defense
Department of Interior
Department of State
Department of Transportation
NASA
*created to give larger voice to civilian applications of GPS.
Civil and Environmental Engineering and Geodetic Science
GPS Constellation
• Block I (not operational)
• Block II/IIA/IIR
• Currently
- 28 satellites Block II/IIA/IIR
- AS1/SA capability (to limit the access to the
system by unauthorized users)
- multiple clocks onboard
1 The
process of encrypting the P-code by modulo-2 addition of the P-code and a secret encryption W-code.
The resulting code is called the Y-code. AS prevents an encryption-keyed GPS receiver from being
“spoofed” by a bogus, enemy-generated GPS P-code signal. Y-code is not available to the civilian users.
2
The Department of Defense policy and procedure of denying to most non-military GPS users the full
accuracy of the system. SA is achieved by dithering the satellite clock and degrading the navigation
message ephemeris. Turned to zero on May 2, 2000.
Civil and Environmental Engineering and Geodetic Science
GPS Constellation
Block I
• vehicle numbers (SVN) 1 through 11
• launched between 1978 and 1985
• concept validation satellites
• developed by Rockwell International
• circular orbits
• inclination 63 deg
• one Cesium and two Rubidium clocks
• design life of 5 years (majority performed well
beyond their life expectancy)
Civil and Environmental Engineering and Geodetic Science
GPS Constellation
Block II
• vehicle numbers (SVN) 13 through 21
• launched between 1989 and 1990
• full scale operational satellites
• developed by Rockwell International
• nearly circular orbits
• inclination 55 deg
• two Cesium and two Rubidium clocks
• design life of 7.3 years
• AS/SA capabilities
Civil and Environmental Engineering and Geodetic Science
GPS Constellation
Block IIA
• vehicle numbers (SVN) 22 through 40
• launched since 1990 (18 out of 19)
• second series of operational satellites
• developed by Rockwell International
• nearly circular orbits
• inclination 55 deg
• two Cesium and two Rubidium clocks
• design life of 7.3 years
• AS/SA capabilities
Civil and Environmental Engineering and Geodetic Science
GPS Constellation
Block IIR
• vehicle numbers (SVN) 41 through 62
• total of 7 launched (1 unsuccessful)
• operational replenishment satellites
• developed by Lockheed Martin
• nearly circular orbits
• inclination 55 deg
• one Cesium and two Rubidium clocks
• design life of 7.8 years
• AS/SA capabilities
Civil and Environmental Engineering and Geodetic Science
GPS Constellation
Block IIF
• will be launched between 2001 and 2010
• operational follow on satellites
• nearly circular orbits
• inclination 55 deg
• design life of 12.7 years
• will carry an inertial navigation system
• will have an augmented signal structure (third frequency)
Civil and Environmental Engineering and Geodetic Science
GPS Constellation
Block III
In November 2000, Lockheed Martin and Boeing
were each awarded a $16-million, 12-month study
contract by the Air Force to conceptualize the next
generation GPS satellite, which will be known as
GPS Block-3.
Civil and Environmental Engineering and Geodetic Science
Current GPS Constellation
LAUNCH
LAUNCH
ORDER PRN SVN
DATE
FREQ
STD
LAUNCH
PLANE
--------------------------------------------------------------*II-1
LAUNCH
ORDER PRN SVN
DATE
FREQ
STD
PLANE
---------------------------------------------------------------
14
14 FEB 89
Cs
E1
IIA-19 31 31
30 MAR 93
Cs
C3
Cs
B3
IIA-20 07 37
13 MAY 93
Rb
C4
II-2
02
13
10 JUN 89
*II-3
16
16
18 AUG 89
Cs
E5
IIA-21 09 39
26 JUN 93
Cs
A1
*II-4
19
19
21 OCT 89
Cs
A4
IIA-22 05 35
30 AUG 93
Cs
B4
II-5
17
17
11 DEC 89
Cs
D3
IIA-23 04 34
26 OCT 93
Rb
D4
^II-6
18
24 JAN 90
Cs
F3
IIA-24 06 36
10 MAR 94
Cs
C1
*II-7
20
26 MAR 90
IIA-25 03 33
28 MAR 96
Cs
C2
II-8
21
21
02 AUG 90
Cs
E2
IIA-26 10 40
16 JUL 96
Cs
E3
II-9
15
15
01 OCT 90
Cs
D2
IIA-27 30 30
12 SEP 96
Cs
B2
IIA-10 23 23
26 NOV 90
Cs
E4
IIA-28 08 38
06 NOV 97
Rb
A5
IIA-11 24 24
04 JUL 91
Rb
D1
**IIR-1
42
17 JAN 97
IIA-12 25 25
23 FEB 92
Cs
A2
IIR-2
13 43
23 JUL 97
Rb
F5
*IIA-13
10 APR 92
IIR-3
11 46
07 OCT 99 Rb
D2
28
IIA-14 26 26
07 JUL 92
Rb
F2
IIR-4
20 51
11 MAY 00 Rb
E1
IIA-15 27 27
09 SEP 92
Cs
A3
IR-5
28 44
16 JUL 00
Rb
B5
IA-16 01 32
22 NOV 92
Cs
F1
IIR-6
14 41
10 NOV 00
Rb
F1
IIA-17 29 29
18 DEC 92
Rb
F4
IIR-7
18 54
30 JAN 01
Rb
E4
IIA-18 22 22
03 FEB 93
Rb
B1
* Satellite is no longer in service.
** Unsuccessful launch.
TOTAL: 28 as of October 2, 2001
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
BLOCK I
BLOCK II/IIA
Civil and Environmental Engineering and Geodetic Science
BLOCK IIR
BLOCK IIF
Civil and Environmental Engineering and Geodetic Science
GPS Receiver Manufacturers
Ashtech/Magellan
NovAtel Inc.
http://www.ashtech.com
http://www.novatel.ca
Garmin
Trimble
http://www.garmin.com
http://www.trimble.com
Leica
Topcon/Javad
http://www.leica-gps.com
http://www.topconps.com
Over 67 GPS manufacturers and over 467 types of receivers,
106 antennas ! (GPS World, January 2000)
Civil and Environmental Engineering and Geodetic Science
Who are GPS largest customers?
•
•
•
•
•
Survey & Mapping
Navigation
Tracking & Comm
Military
Car Navigation
~ 54%
~ 20%
~18%
~ 6%
~ 2%
Civil and Environmental Engineering and Geodetic Science
GPS Applications
• military
• civilian aircraft, land mobile, and marine vessel navigation
• time transfer between clocks
• spacecraft orbit determination
• geodesy (precise positioning)
• attitude determination with multiple antennas
• geophysics (ionosphere, crustal motion monitoring, etc.)
• surveying (static and kinematic, also real-time)
• Intelligent Transportation Systems
• GIS, Mobile Mapping Systems
Civil and Environmental Engineering and Geodetic Science
THE DEPLOYED CONSTELLATION
Civil and Environmental Engineering and Geodetic Science
GPS Antenna Coverage
km
25788
13.84°
EARTH
SV
12-hour
orbit
Antenna has ~28° field of view
Civil and Environmental Engineering and Geodetic Science
First GPS satellite Block I was launched in 1978
Air Force-launched Delta II carried the 18th
GPS satellite into orbit in February 1993.
Civil and Environmental Engineering and Geodetic
Science
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Source: http://www.nasm.edu
Civil and Environmental Engineering and Geodetic Science
• Before GPS, pilots relied only on
navigational beacons located across the
country
• Now, with GPS fully operational,
aircraft can fly the most direct routes
between distant airports.
Civil and Environmental Engineering and Geodetic Science
How accurate is GPS?
• Depending on the design of the GPS receiver and the
measurement techniques employed, the accuracy is from
100 meters under Selective Availability (SA) policy (below
10 m with SA turned to zero) to better than 1 centimeter.
• In order to obtain better than 100 (10 with SA turned to
zero) meter accuracy, differential GPS must be used (two
simultaneously tracking receivers or differential services).
Civil and Environmental Engineering and Geodetic
Science
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Why is GPS so accurate ?
• The key to GPS accuracy is the fact that the signal is
precisely controlled by the highly accurate atomic
clock
• Atomic clock’s stability is 10-13 – 10-14 per day (this
means that the clock can loose 1 sec in 3,000,000
years!)
• This highly accurate frequency standard produces
the fundamental GPS frequency, 10.23 MHz, which is
a basis for derived frequencies L1 (1575.42 MHz =
=154*10.23) and L2 (1227.60 MHz = 120*10.23)
Civil and Environmental Engineering and Geodetic Science
• The basis of GPS is
"triangulation" from satellites.
• To "triangulate," a GPS receiver measures distance using the
travel time of radio signals.
• To measure travel time, GPS needs very accurate timing, which it
achieves with some tricks
• The primary unknowns are three coordinates of the receiver
antenna (user)
Civil and Environmental Engineering and Geodetic Science
• Mathematically we need four satellite ranges to
determine exact position.
• Three ranges are enough if we reject ridiculous
answers or use other tricks.
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
Source: http://www.nasm.edu
Civil and Environmental Engineering and Geodetic Science
How distance measurements from three
satellites can pinpoint you in space 1/3
Suppose we measure our distance from a satellite and
find it to be 11,000 miles. Knowing that we're 11,000
miles from a particular satellite narrows down all the
possible locations we could be in the whole universe to
the surface of a sphere that is centered on this satellite
and has a radius of 11,000 miles.
Civil and Environmental Engineering and Geodetic
Science
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How distance measurements from three
satellites can pinpoint you in space 2/3
Next, say we measure our distance to a second satellite and find
out that it's 12,000 miles away.
That tells us that we're not only on the first sphere but we're also
on a sphere that's 12,000 miles from the second satellite. Or in
other words, we're somewhere
on the circle where these
two spheres intersect.
Civil and Environmental Engineering and Geodetic
Science
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How distance measurements from three
satellites can pinpoint you in space 3/3
If we then make a measurement from a third satellite and find
that we're 13,000 miles from that one, that narrows our position
down even farther, to the
two points where the 13,000 mile
sphere cuts through the circle
that's the intersection
of the first two spheres.
Civil and Environmental Engineering and Geodetic
Science
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Finally: In order to find the correct location (out of
two points determined by the observation of three
ranges to three satellites) we may need to make a
fourth observation to the fourth satellite – this way
we get the unique answer to our positioning problem.
But usually one of the two points is a ridiculous
answer (either too far from Earth or moving at an
impossible velocity) and can be rejected without a
measurement.
However, a fourth measurement becomes very handy
for another reason…
Civil and Environmental Engineering and Geodetic Science
 The dashed lines show the intersection point for ideal case (no observation
errors), and the gray bands indicate the area of uncertainty
 Because of errors in the receiver's internal clock, the spheres do
not intersect at one point (the time measurement is used to determine the
distance to the satellite, as explained next)
 If three perfect measurements can locate a point in 3-dimensional space,
then four imperfect measurements can do the same thing
 So, the fourth measurement is used to fix the time (receiver clock) problem,
and find a unique 3-D location in space
Civil and Environmental Engineering and Geodetic Science
Thus: four range measurements to four GPS
satellites are needed for point positioning
But how do we measure the range to the satellite?
By precise measurement of the time that the radio signal takes
to travel from the satellite antenna to the receiver antenna
Civil and Environmental Engineering and Geodetic Science
Measuring distance from a satellite 1/2
 The timing problem is tricky. First, the signal travel times
are going to be very short (about 0.06 seconds), so we need
some really precise clocks.
 But assuming we have precise clocks, how do we measure
travel time?
 Suppose we start generating the same signal at the satellite
and the receiver at the same time.
 The signal (“Pseudo Random Code”) coming from the
satellite is delayed because it had to travel over 11,000 miles.
Civil and Environmental Engineering and Geodetic
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Measuring distance from a satellite 2/2
 If we wanted to see just how delayed the satellite's signal
was, we delay the receiver's version of signal until they fell
into perfect synchronization.
 The amount we have to shift back the receiver's version is
equal to the travel time of the satellite's version.
 So we just multiply that time times the speed of light and
BINGO! we've got our distance to the satellite.
Civil and Environmental Engineering and Geodetic
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A Random Code?
The Pseudo Random Code (PRC) or Pseudo Random
Noise code, PRN, is a fundamental part of GPS.
Physically it's just a very complicated digital code, or in
other words, a complicated sequence of "on" and "off"
pulses. The signal is so complicated that it almost looks
like random electrical noise. Hence the name "PseudoRandom".
Civil and Environmental Engineering and Geodetic
Science
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A Random Code?
 Since each satellite has its own unique PseudoRandom Code, this complexity also guarantees that the
receiver won't accidentally pick up another satellite's
signal.
 So all the satellites can use the same frequency
without jamming each other. And it makes it more
difficult for a hostile force to jam the system.
 In fact the Pseudo Random Code gives the DoD a
way to control access to the system.
Civil and Environmental Engineering and Geodetic
Science
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A Random Code?
 Another reason for the complexity of the Pseudo
Random Code, is crucial to making GPS economical.
 The codes make it possible to use information
theory to “amplify” the GPS signal. And that's why
GPS receivers don't need big satellite dishes to receive
the GPS signals.
Civil and Environmental Engineering and Geodetic
Science
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GPS Signal
Modulation
L1 carrier
1575.42 MHz
 19 cm
 293 m
C/A code
(SPS)
P code
(PPS)
19 cm
 29.3 m
L2 carrier
1227.60 MHz
 24 cm
24 cm
 29.3 m
P code
(PPS)
Civil and Environmental Engineering and Geodetic
Science
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Getting Perfect Timing
 On the satellite side, timing is
almost perfect because they have
incredibly precise atomic clocks
on board.
 But what about our receivers here on the ground?
 Remember that both the satellite and the receiver need to be
able to precisely synchronize their pseudo-random codes to
make the system work.
Civil and Environmental Engineering and Geodetic
Science
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Atomic Clocks
 Atomic clocks don't run on atomic energy. They get the
name because they use the oscillations of a particular atom
as their "metronome” (device for marking time by means of
a series of clicks at precise intervals).
 This form of timing is the most stable and accurate
reference man has ever developed.
 With the development of atomic clocks a new era of
precise time-keeping had commenced. However,
before the GPS program was launched these precise
clocks had never been tested in space.
Civil and Environmental Engineering and Geodetic
Science
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Atomic Clock Technology
 The development of reliable, stable, compact, spacequalified atomic frequency oscillators (rubidium, and then
cesium) was therefore a significant technological
breakthrough.
 The advanced clocks now being used on the GPS satellites
routinely achieve long-term frequency stability in the range of a
few parts in 1014 per day (about 1 sec in 3,000,000 years!).
 This long-term stability is one of the keys to GPS, as it
allows for the autonomous, synchronized generation and
transmission of accurate timing signals by each of the GPS
satellites without continuous monitoring from the ground.
Civil and Environmental Engineering and Geodetic Science
Quartz Crystal Oscillator Technology
In order to keep the cost of user equipment down,
quartz crystal oscillators were proposed (similar to
those used in modern digital watches),
Besides their low cost, quartz oscillators have
excellent short-term stability.
However, their long-term drift must be accounted for
as part of the user position determination process –
this is where the fourth range measurement becomes
handy!
Civil and Environmental Engineering and Geodetic Science
Getting Perfect Timing
 If our receivers needed atomic clocks (which cost upwards of
$50K to $100K) GPS would be a lame duck technology. Nobody
could afford it.
 Luckily the designers of GPS came up with a brilliant little trick
that lets us get by with much less accurate clocks in our receivers.
 The secret to perfect timing is to make an extra satellite
measurement (remember the fourth range observation that we need
to get precise position in space?)
 By using an extra satellite range measurement and a little algebra
a GPS receiver can eliminate any clock inaccuracies it might have.
Civil and Environmental Engineering and Geodetic
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Getting Perfect Timing
 Since any offset from universal time (UTC, the civilian time
system that we use) will affect all of our measurements, the
receiver looks for a single correction factor that it can subtract
from all its timing measurements to make them correct.
 That correction brings the receiver's clock back into sync with
universal time, and BINGO! - you've got atomic accuracy time
right in the palm of your hand (especially if you're using one of
the hand-held receivers!)
 Once it has that correction it applies to all the rest of its
measurements and now we've got precise positioning.
Civil and Environmental Engineering and Geodetic
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Getting Perfect Timing
 One consequence of this principle is that any decent GPS
receiver will need to have at least four channels so that it can
make the four measurements simultaneously.
 But for the triangulation to work we not only need to
know distance, we also need to know exactly where the
satellites are.
Civil and Environmental Engineering and Geodetic
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What else do we need to navigate
(position) with GPS?
• Along with distance, you need to know exactly where
the satellites are in space. High orbits and careful
monitoring are the secret.
• Finally you must correct for any delays the signal
experiences as it travels through the atmosphere.
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Civil and Environmental Engineering and Geodetic
Science
Getting Satellite Position in Space 1/3
Successful operation of GPS depends on the precise
knowledge and prediction of a satellite's position with
respect to an earth-fixed reference system.
Tracking data collected by ground monitor stations are
analyzed to determine the satellite orbit over the period of
tracking (typically one week).
This reference ephemeris is extrapolated into the future
and the data is then up-loaded to the satellites.
Prediction accuracies of the satellite coordinates, for one
day, at the few meter level have been demonstrated.
Civil and Environmental Engineering and Geodetic Science
Getting Satellite Position in Space 2/3
• The Air Force has injected
each GPS satellite into a
very precise planned orbit.
• GPS satellites are so high up
that their orbits are very
predictable.
• On the ground all GPS receivers have an almanac programmed
into their computers that tells them where in the sky each
satellite is.
• Minor variations in satellite orbits are measured by the
Department of Defense (data from permanently tracking stations
allow determination of satellite position and speed)
Civil and Environmental Engineering and Geodetic
Science
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Getting Satellite Position in Space 3/3
 These errors (variations from the ideal orbit) are caused by
gravitational pulls from the moon and sun and by the pressure of
solar radiation on the satellites.
 That information is sent back up to the satellite itself. The
satellite then includes this new corrected position information in
the timing signals it's broadcasting.
 So a GPS signal is more than just pseudo-random code for
timing purposes. It also contains a navigation message with
ephemeris information as well.
 Now we are almost ready for perfect positioning, but there is
one more trouble...
Civil and Environmental Engineering and Geodetic
Science
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Getting Errors Corrected
 A GPS signal doesn’t travel
in vacuum!
 We've been saying that you
calculate distance to a satellite by
multiplying a signal's travel time
by the speed of light. But the speed of light is only constant in
a vacuum.
 As a GPS signal passes through the charged particles of the
ionosphere and then through the water vapor in the
troposphere it gets slowed down, and this creates the same
kind of error as bad clocks.
Civil and Environmental Engineering and Geodetic
Science
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Getting Errors Corrected 1/2
 Some errors can be factored out using mathematics and
modeling.
 Another way to get a handle on these atmosphere-induced
errors is to compare the relative speeds of two different signals.
This "dual frequency" measurement is very sophisticated and is
only possible with advanced receivers.
 Problem on the ground -- is called multipath error and is
similar to the ghosting you might see on a TV.
 Good receivers use sophisticated
signal rejection techniques to
minimize this problem.
Civil and Environmental Engineering and Geodetic
Science
69
Getting Errors Corrected 2/2
 Other error sources: satellite position.
 Intentional errors: the policy is called "Selective
Availability" or "SA" and the idea behind it is to make sure that no
hostile force or terrorist group can use GPS to make accurate
weapons.
 DoD introduces some "noise" into the satellite's clock
data which, in turn, adds noise (or inaccuracy) into position
calculations. DoD may also be sending slightly erroneous orbital
data to the satellites
 Military receivers use a decryption key to remove the SA errors
and so they're much more accurate.
 Differential GPS can eliminate almost all error sources.
 SA was turned down to zero on May 2, 2000
Civil and Environmental Engineering and Geodetic
Science
70
Summary of GPS Error Sources [m]
Satellite Clocks
Orbit Errors
Ionosphere
Troposphere
Receiver Noise
Multipath
SA=0
2.0
2.1
5.0
0.5 (model)
0.3
1.0
Typical Position Accuracy
Horizontal
10.0
Vertical
13.0
SA
20.0
20.0
5.0
0.5 (model)
0.3
1.0
41.0
51.0
Civil and Environmental Engineering and Geodetic Science
Atmospheric Errors on GPS Range
Boundary between iono
and troposphere
Actual signal path
ionosphere
Geometric distance
troposphere
Civil and Environmental Engineering and Geodetic Science
Summary of GPS Error Sources
Typical Error in Meters (per satellite)
Standard GPS
Differential GPS
Satellite Clocks
1.5
0
Orbit Errors
2.5
0
Ionosphere
5.0
0.4
Troposphere
0.5
0.2
Receiver Noise
0.3
0.3
Multipath
0.6
0.6
SA
30
0
Typical Position Accuracy (under SA)
Horizontal
50
1.3
Vertical
78
2.0
3-D
93
2.8
Civil and Environmental Engineering and Geodetic
Science
73
GPS Errors: An Overview
• Bias errors - can be removed from the direct
observables, or at least significantly reduced, by using
empirical models (eg., tropospheric models), or by
differencing direct observables
- satellite orbital errors (imperfect orbit modeling),
- station position errors
- propagation media errors and receiver errors
• White noise
Civil and Environmental Engineering and Geodetic Science
GPS Error Sources
•
•
•
•
•
Satellite and receiver clock errors
Satellite orbit errors
Atmospheric effects (ionosphere, troposphere)
Multipath: signal reflected from surfaces near the receiver
Selective Availability (SA)
- epsilon process: falsifying the navigation broadcast data
- delta process: dithering or systematic destabilizing of the
satellite clock frequency
• Antenna phase center
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Timing errors: receiver and satellite, including SA
• satellite clock (as a difference between the precise
and broadcast clocks ): 0.1-0.2 microseconds which
corresponds to 30-60 m error in range
• first-order clock errors are removed by differencing
technique
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Orbital errors and Selective Availability (SA)
• nominal error for the broadcast ephemeris: 1-5 m on
average
• precise (post-mission) orbits are good up to 5-10 cm
and better; available with 24-hour delay
• Selective Availability: not observed on the orbit
• first-order orbital errors are removed by differencing
technique
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Propagation media
• ionosphere (50-1000km)
• the presence of free electrons in the geomagnetic field causes a
nonlinear dispersion of electromagnetic waves traveling through the
ionized medium
• group delay (code range is measured too long) and phase advance
(phase range is measured too short) , frequency dependent; can
reach ~150 m near the horizon;
c2
  group refractiveindex (group of waves, such as code GP S signal)
2
f
c
n ph  1  22   phase refractiveindex
f
ngr  1 
constantc2  40.3N e [ Hz 2 ] thus ngr  n ph since electrondensity N e is always positive
Civil and Environmental Engineering and Geodetic Science
Propagation media cont.
• the propagation delay depends on the total electron content (TEC)
along the signal’s path and on the frequency of the signal itself as
well as on the geographic location and time (ionosphere is most
active at noon, quiet at night; 11-year Sun spot cycle)
• integration of the refractive index renders the measured range, and
the ionospheric terms for range and phase are as follows:
measured distance s   n ds

iono
gr
40.3
40.3
iono
 2 TEC and  ph   2 TEC where totalelectroncontentT EC
f
f
T EC   N e ds0 [1016 electronsper m 2 ] where s0 is thegeometricrange at zenith
• differencing technique and ion-free combination of observations on
both frequencies eliminate first-order terms, secondary effects can be
neglected for the short baselines
• differential effect on the long baselines: 1-3 cm
Civil and Environmental Engineering and Geodetic Science
11-year Sun Spot Cycle
Civil and Environmental Engineering and Geodetic Science
Estimated Ionospheric Group Delay
for GPS Signal
First Order:
1/f 2
Second Order:
1/f 3
Third
1/f 4
Order:
Calibrated 1/f 3
Term Based on
a Thin Layer
Ionospheric
Model
L1
L2
Residual
Range Error
16.2 m
26.7 m
0.0
~ 1.6 cm
~ 3.3 cm
~ -1.1 cm
~ 0.86 mm
~ 2.4 mm
~ -0.66 mm
~ 1-2 mm
The phase advance can be obtained from the above table by multiplying each
number by -1, -0.5 and -1/3 for the 1/f 2, 1/f 3 and 1/f 4 term, respectively
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Troposphere (up to 50 km) - frequency-independent, same for all
frequencies below 15 GHz (troposphere is not dispersive for frequencies
below 15 GHz )
• group and phase delay are the same
• elimination by dual frequency is not possible
• affects relative (differential) and point positioning
• empirical models (functions of temperature, pressure and relative
humidity) are used to eliminate major part of the effect
• differential effect is usually estimated (neglected for the short baselines
with similar atmospheric effects)
• total effect in the zenith direction reaches 2.5, and increases with the
cosecant of the elevation angle up to 20-28 m at 5deg elevation
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• The tropospheric propagation effect is usually represented as a function of
temperature, pressure and relative humidity
• Obtained by integration of the refractivity Ntrop
trop   10 6 N trop ds
where integration is performed along the geometric path
• It is separated into two components: dry (0-40 km) and wet (0-11km)
tro p  d   w
N 0trop  c1
p
e
e
 c2  c3 2
T
T
T
• Represents an example of refractivity model at the surface of the earth; c1, c2, c3
are constants, T is temperature in Kelvin (K), e is partial pressure of water vapor
[mb], p is atmospheric pressure [mb]
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• The dry component, which is proportional to the density of the gas molecules
in the atmosphere and changes with their distribution, represents about 90%
of the total tropospheric refraction
• It can be modeled with an accuracy of about 2% that corresponds to 4
cm in the zenith direction using surface measurement of pressure and
temperature
• The wet refractivity is due to the polar nature of the water molecules and the
electron cloud displacement
• Since the water vapor is less uniform both spatially and temporally, it
cannot be modeled easily or predicted from the surface measurements
• As a phenomenon highly dependent on the turbulences in the lower
atmosphere, the wet component is modeled less accurately than the dry
• The influence of the wet tropospheric zenith delay is about 5-30 cm that
can be modeled with an accuracy of 2-5 cm
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• The tropospheric refraction as a function of the satellite’s zenith distance
is usually expressed as a product of a zenith delay and a mapping function
• A generic mapping function represents the relation between zenith effects
at the observation site and at the spacecraft’s elevation
• Several mapping functions have been developed (e.g., by Saastamoinen,
Goad and Goodman, Chao, Lanyi), which are equivalent as long as the
cutoff angle for the observations is at least 20o
• The tropospheric range correction can be written as follows:
 trop  f d  z0d  f w  z0w
where
fd(z), fw(z) - mapping functions for dry and wet components, respectively,
- vertical dry and wet components, respectively
0d , 0w
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• Tropospheric range correction is applied to correct the GSP
measurement before it is used to find your position
•Tropospheric refraction accommodates only the systematic part of the
effect, and some small un-modeled effects remain
• Moreover, errors are introduced into the tropospheric correction via
inappropriate meteorological data (if applied) as well as via errors in the
zenith mapping function
• These errors are propagated into station coordinates in the point
positioning and into base components in the relative positioning
• For example, the relative tropospheric refraction errors affects mainly a
baseline’s vertical component (error in the relative tropospheric delay at
the level of 10 cm implies errors of a few millimeters in the horizontal
components, and more than 20 cm in the vertical direction)
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• If the zenith delay error is 1 cm, the effect on the horizontal coordinates
will be less than 1 mm but the effect on the vertical component will be
significant, about 2.2 cm
• The effect of the tropospheric refraction error increases with the latitude
of the observing station and reaches its maximum for the polar sites. It is a
natural consequence of a diluted observability at high latitudes where
satellites are visible only at low elevation angles
• The scale of a baseline derived from observations that are not corrected
for the effect of the tropospheric delay is distorted; the baseline is
measured too long.
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Multipath - result of an interaction of the upcoming signal
with the objects in antenna surrounding; causes multiple
reflection and diffraction; as a result signal arrives via direct
and indirect paths
• magnitude tends to be random and unpredictable, can reach
1-5 cm for phases and 10-20 m for code pseudoranges
• can be largely reduced by careful antenna location
(avoiding reflective objects) and proper antenna design, e.g.,
proper signal polarization, choke-ring or ground-plane
antennas
Civil and Environmental Engineering and Geodetic Science
Multipath
• As opposed to interference, which disrupts the signal and can virtually
provide no or useless data, multipath would allow for data collection, but the
results would be wrong!
• Existing multipath rejection technology (in-receiver) usually applies to the
C/A code-based observable, and can increase the mapping accuracy by 50%
(differential code positioning with a multipath rejection technology can be
good to 30-35 cm in horizontal and 40-50 cm in vertical directions).
• Signal processing techniques, however, can reject the multipath signal only
if the multipath distance (difference between the direct and the indirect
paths) is more that 10 m.
• In a typical geodetic/surveying application, however, the antenna is about 2
m above the ground, thus the multipath distance reaches at most 4 m;
consequently, the signal processing techniques cannot fully mitigate the
effects of reflected signals.
Civil and Environmental Engineering and Geodetic Science
Multipath
• However, properly designed choke ring antennas can almost entirely
eliminate this problem for the signals reflected from the ground and the
surface waves
• The multipath from the objects above the antenna still remains an
unresolved problem
• The performance of the choke ring antennas is usually better for L2 than for
L1, the reason being that the choke ring can be optimized only for one
frequency. If the choke ring is design for L1, it has no effect for L2, while a
choke ring designed for L3 has some benefits for L1.
• Naturally, the optimal solution would be to have choke rings optimized
separately for L1 and L2, which is the expected direction of progress for the
geodetic antennas.
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
Interference and jamming (intentional interference)
• Radio interference can, at minimum, reduce the GPS signal’s apparent
strength (that is reduce the signal to noise ratio by adding more noise) and
consequently – the accuracy, or, at worse, even block the signal entirely
• Medium-level interference would cause frequent losses of lock or cycle
slips, and might render virtually useless data.
• It is, therefore, important to make sure that the receiver has an
interference protection mechanism, which would detect and eliminate (or
suppress) the interfering signal.
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
Antenna Phase Center Variation
Antenna Phase Center is the point to which the received signal is referred
• It usually does not coincide with the physical center of the antenna, and for GPS
receivers both the L1 and L2 phase centers are generally different
• The magnitudes of these offsets are provided by the manufacturer; however, the
location of the phase center can vary with time (this variation should not exceed 1-2
cm)
• for modern microstrip antennas it reaches only a few millimeters.
• Antenna phase center offset depends on the azimuth and the elevation of the satellite
as well as on the intensity of the incoming signal.
• Similarly, the satellite phase center does not coincide with the spacecraft’s center of
mass. Suggested satellite center of mass corrections for GPS satellites can be found in
IERS Technical Note No. 13 and 21 (IERS Conventions)
Civil and Environmental Engineering and Geodetic Science