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					                     Part II
 WHAT IS GPS AND HOW IT WORKS
          GPS ERROR SOURCES
                      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 5.725-
5.850 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
      Spread Spectrum Radio (SSR) Technique 3/3


                                       A Spectrum Analyzer Photo of
                                            a Direct Sequence
                                       (DS) Spread Spectrum signal.




A Spectrum Analyzer Photo of
   a Frequency Hop (FH)
   Spread Spectrum 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


•   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/IIR-M
          • Currently (as of January 4, 2006)
                - 29 satellites Block II/IIA/IIR/IIR-M (the most recent Block
                IIR-M satellite was launched on September 26, 2005 )
                - Oldest satellite: PRN 15 from Block II-9, Oct. 1, 1990
                - AS1/SA capability (to limit the access to the system by
                unauthorized users)
                - multiple clocks onboard
1 Theprocess 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.

2The 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 IIM
   • first launch Sept. 26, 2005
   • multiple Rb clocks
   • first step of GPS modernization program
   • nearly circular orbits, inclination 55 deg
   • Adding a second civil signal
       • C/A-type code at L2 frequency (1227.60 MHz)
       • Low power signal, not intended for precision navigation
   • Adding another military (M) code
   • Future: third civil signal
       • P-type codes (precise) at L5 frequency (1176.45 MHz)
       • Higher power signal, intended for precision navigation
                                   Civil and Environmental Engineering and Geodetic Science
            GPS Constellation
Block IIF
   • planned for launch between 2007 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
                                                                         LAUNCH                   LAUNCH           FREQ
                 GPS Constellation                                       ORDER PRN SVN               DATE           STD       PLANE
                                                                          ---------------------------------------------------------------
     LAUNCH                   LAUNCH             FREQ
                                                                            IIA-16 01 32           22 NOV 92         Cs        F1
     ORDER PRN SVN                DATE           STD       PLANE
                                                                            IIA-17 29 29           18 DEC 92         Rb        F4
       ---------------------------------------------------------------
                                                                            IIA-18 22 22           03 FEB 93         Rb       B1
         ^II-1           14      14 FEB 89        Cs       E1
                                                                            IIA-19 31 31           30 MAR 93         Cs        C3
         II-2      02    13     10 JUN 89        Cs        B3
                                                                            IIA-20 07 37           13 MAY 93         Rb        C4
       ^ 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         28      10 APR 92
                                                                              IIR-3     11 46       07 OCT 99 Rb                D2
         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
                                                                              IIR-5     28 44        10 JUL 00 Rb               B5
                                                                              IIR-6     14 41        10 NOV 00 Rb                F1
                                                                              IIR-7     18 54        30 JAN 01 Rb               E4
  * Satellite is no longer in service.
 ** Unsuccessful launch.
TOTAL: 28 as of January 6, 2003
                                                                  ftp://tycho.usno.navy.mil/pub/gps/gpsb2.txt
                                                                           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

                                      NovAtel Inc.
  Thales Navigation
                                      http://www.novatel.ca
  http://www.thalesnavigation.com/en/

  Garmin                                     Trimble
  http://www.garmin.com                      http://www.trimble.com


  Leica                                      Topcon
                                             http://www.topconps.com
  http://www.leica-gps.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          ~ 54%
•   Navigation                ~ 20%
•   Tracking & Comm           ~18%
•   Military                   ~ 6%
•   Car Navigation             ~ 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
                                                                                    38
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
                                                                           41
             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
                                                                             47
           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
                                                                             48
         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
                                                                           49
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 Science
                                                                            53
      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 Science
                                                                           54
                 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 "Pseudo-
Random".




                               Civil and Environmental Engineering and Geodetic Science
                                                                         55
                A Random Code?

 Since each satellite has its own unique Pseudo-
Random 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
                                                                       56
                  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
                                                                         57
                       GPS Signal


                         Modulation

                                                          C/A code
                                293 m                  (SPS)
L1 carrier
1575.42 MHz                                               P code
 19 cm      19 cm
                                                           (PPS)
                                29.3 m


L2 carrier                                                P code
1227.60 MHz                                               (PPS)
 24 cm     24 cm
                                29.3 m




                                Civil and Environmental Engineering and Geodetic Science
                                                                          58
       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
                                                                               59
                 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
                                                                          60
               Atomic Clock Technology

 The development of reliable, stable, compact, space-
qualified 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
              Rubidium Atomic Clocks




Cesium clocks are the best
time keeping devices with a
drift of 2-3 * 10-14/day
Rubidium clocks can drift
by 2-3 * 10-13/day
                              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 Science
                                                                             64
                  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 Science
                                                                              65
                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 Science
                                                                           66
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.

                                                                           67
                                 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
                                                                            69
       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
                                                                             70
    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
                                                                           71
            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
                                                                            72
              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
                                                                              73
       Summary of GPS Error Sources [m]

                    SA=0                            SA
Satellite Clocks     2.0                            20.0
Orbit Errors         2.1                            20.0
Ionosphere           5.0                            5.0
Troposphere         0.5 (model)                     0.5 (model)
Receiver Noise       0.3                             0.3
Multipath            1.0                            1.0

Typical Position Accuracy
Horizontal            10.0                          41.0
Vertical              13.0                          51.0

                       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
                                                                         75
               Atmospheric Errors on GPS Range

                                                               Boundary between iono
                                                               and troposphere

                 Actual signal path

ionosphere
                                         Geometric distance




 troposphere




                                      Civil and Environmental Engineering and Geodetic Science
      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
ngr  1     2
                 group refractive index (group of waves,such as code GPS signal)
          f
          c
n ph  1  22   phase refractive index
           f
constantc2  40.3N e [ Hz 2 ] thus ngr  n ph since electron density 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
         40 .3              40 .3
iono
  gr     2 TEC and  ph   2 TEC where total electron content TEC
                     iono

          f                  f
TEC   N e ds0 [10 16 electrons per m 2 ] where s0 is the geometric range 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: up to several centimeters
                                              Civil and Environmental Engineering and Geodetic Science
11-year Sun Spot Cycle




          Civil and Environmental Engineering and Geodetic Science
Current cycle of solar activity




                Civil and Environmental Engineering and Geodetic Science
  Estimated Ionospheric Group Delay
            for GPS Signal
                             L1              L2            Residual
                                                          Range Error

      First Order:         16.2 m          26.7 m              0.0
      1/f 2

      Second Order:       ~ 1.6 cm        ~ 3.3 cm          ~ -1.1 cm
      1/f 3

      Third    Order:     ~ 0.86 mm       ~ 2.4 mm         ~ -0.66 mm
      1/f 4

      Calibrated 1/f 3
      Term Based on                                         ~ 1-2 mm
      a Thin Layer
      Ionospheric
      Model


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)

                     trop  d   w
                            p     e     e
               N 0  c1
                 trop
                               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,
 0d , 0w   - vertical dry and wet components, respectively
                                             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 carrier 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 L2 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.

• Using the NGS-derived antenna models takes care of the phase center change as a
function of elevation and azimuth

• 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

				
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