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CS 128/ES 228 - Lecture 10b   1
A guide to GPS theory …




                                          www.usace.army.mil


            CS 128/ES 228 - Lecture 10b                        2
… and practice.
   Recreational

   GIS inputs

   Surveying

   Transportation

   and of course,
    the military

                     CS 128/ES 228 - Lecture 10b   3
A brief history of GPS…
   Forerunners
    - LORAN-C: marine navigation. Used radio
      beacons along shoreline. Localized
      coverage and low accuracy (CEP ~ 200 m)
     - TRANSIT: developed by U. S. Navy. Used
      6 satellites, low orbits. Global coverage &
      high accuracy (sub-meter) but “fix” took
      hours to days

   Department of Defense: 1970s study showed
    ~120 navigation systems in use. Proposed a
    single system, called NAVSTAR
                   CS 128/ES 228 - Lecture 10b      4
The NAVSTAR system
 Military wanted portable,
  fast, passive positioning
  system

 Navstar I launched Feb ’78.
  Now 24 satellites + “spares”

 Global, 24/7 coverage by at
  least 4 satellites
                                               GPS for Land Surveyors. J. Van
                                               Sickle. Ann Arbor Press, 1996




 Satellites carry atomic clocks

                 CS 128/ES 228 - Lecture 10b                                    5
GPS basics




 Both: Differential GPS Explained.
   J. Hurn. Trimble Navigation, 1993

                                       CS 128/ES 228 - Lecture 10b   6
1, 2 …




 Both: Differential GPS Explained.
   J. Hurn. Trimble Navigation, 1993

                                       CS 128/ES 228 - Lecture 10b   7
3!

                                                                       Technically 4
                                                                        satellites are
                                                                        necessary, but
                                                                        normally only 1
                                                                        of the 2 points
                                                                        is on the geoid

                                                                       But, as we’ll
                                                                        see later, a 4th
                                                                        satellite is still
                                                                        useful
     Differential GPS Explained. J. Hurn. Trimble Navigation, 1993


                                               CS 128/ES 228 - Lecture 10b                   8
How to time the signal?
 Standard EDMs bounce a signal off a
  reflector and measure time of return

 But, GPS requires a low-power
  transmission and passive receivers

 Imagine 2 people with synchronized
  stop watches, standing 1 mile apart.
  A gun fires near 1, and each records
  the time when they hear the shot.
  What do the 2 times tell you?

                CS 128/ES 228 - Lecture 10b   9
Pseudocode
 A string of
  pseudo-random
  bits

 Predetermined
  sequence – can
  be generated by
  the satellite and
  the receivers

   GPS: A guide to the next utility. J. Hurn.
      Trimble Navigation, 1993




                                            CS 128/ES 228 - Lecture 10b   10
Code correlation




                                           GPS for Land Surveyors. J. Van
                                           Sickle. Ann Arbor Press, 1996



             CS 128/ES 228 - Lecture 10b                                    11
But wait: for $19.95 you get all
these extra codes …
  C/A (coarse acquisition) code:
   - short (1 ms) & slow (1.023 Mbps)
   - meant to enable receivers to get a
     crude “fix” quickly

  P (precision) code:
   - long (267 d) & fast (10.23 Mbps)
   - permits sub-meter accuracy




                 CS 128/ES 228 - Lecture 10b   12
Why use the P code?
 C/A code bits are ~ 1 µs wide

 Even a good
  receiver can
  be out of phase
  with the code
  by 1-5%

 1% phase error ~ 3 m position
  error

                                      Differential GPS Explained. J. Hurn. Trimble Navigation, 1993


                    CS 128/ES 228 - Lecture 10b                                                 13
Still not sure? There’s more …

  Each code is broadcast on 2
   frequencies, the L1 and L2 bands

  “Dual frequency” receivers utilize the
   frequency difference between L1 & L2
   to compensate for atmospheric
   distortions – more on that later

  Mucho expensive



                 CS 128/ES 228 - Lecture 10b   14
Sources of error
1. [Selective availability]

2. Clock errors

3. Ephemeris errors

4. Atmospheric delays

5. Multipath effects

6. Receiver errors               Differential GPS Explained. J. Hurn. Trimble Navigation, 1993




                  CS 128/ES 228 - Lecture 10b                                                    15
A small clock error matters!
   Microwaves travel at approximately
    the speed of light:

        300,000 km per second

    A clock error of only 1 µs could
    produce a positional error of ~ 300 m!

   How can a $100 GPS receiver have a
    clock that stays accurate to the µs??



                   CS 128/ES 228 - Lecture 10b   16
Voila – the 4th satellite!
A 2-D example:




Clocks synchronized       Clocks not synchronized

                                               Both: GPS: A guide to the next utility.
                                                 J. Hurn. Trimble Navigation, 1993


                 CS 128/ES 228 - Lecture 10b                                             17
If the 4 ranges don’t overlap:
 Receiver adjusts
  its clocks until
  they do

 [Actually: done
  by algebra, not
  trial & error]

 The time on a
  $100 GPS unit is
  really accurate!
                                               Both: GPS: A guide to the next utility.
                                                 J. Hurn. Trimble Navigation, 1993


                 CS 128/ES 228 - Lecture 10b                                             18
Ephemeris errors
Ephemeris: mathematical
description of an orbit




       Trimble Navigation

                                                   GPS for Land Surveyors. J. Van
                                                   Sickle. Ann Arbor Press, 1996




                            CS 128/ES 228 - Lecture 10b                             19
Atmospheric delays
 Signal slowed by:
  - charged particles
    in the ionosphere
  - water vapor in
    the troposphere

 Dual-frequency
  receivers can correct
  for ionosphere
  delays

                                Differential GPS Explained. J. Hurn. Trimble Navigation, 1993


                  CS 128/ES 228 - Lecture 10b                                                   20
Multi-path errors
 Worse:
  - near buildings,
    other obstructions
  - satellites near
    horizon: use
    “elevation mask”

 Better:
  - more sophisticated
     antenna
  - ground plane to block                       Top: GPS: A guide to the
                                                next utility. J. Hurn.

    low-angle reflections
                                                Trimble Navigation, 1993
                                                Bottom: www.gpsw.co.uk



                  CS 128/ES 228 - Lecture 10b                        21
 Typical error “budget” (m)*
                                Standard                   Differential
 Source:                        GPS                        GPS
 Satellite clocks               1.5                        ~0
 Ephemeris errors               2.5                        ~0
 Ionosphere delays              5.0                        0.4
 Troposphere delays             0.5                        0.2
 Multi-path (reflections)       0.6                        0.6
 Receiver errors                0.3                        0.3
 Typical totals                 10 – 15                    1-2
                                Differential GPS Explained. J. Hurn. Trimble Navigation



* Horizontal position; vertical errors typically 2x or greater
                          CS 128/ES 228 - Lecture 10b                                     22
Improving GPS accuracy
   DOP and mission planning

   Differential GPS

   Surveying-grade GPS




                   CS 128/ES 228 - Lecture 10b   23
DOP & “mission” planning
 Dilution of precision:
  a small number of
  satellites or poor
  positions degrades
  accuracy


 Advance software
  lets you plan when
  to use GPS for
  maximum accuracy
  Both: GPS: A guide to the next utility.
    J. Hurn. Trimble Navigation, 1993

                                            CS 128/ES 228 - Lecture 10b   24
“mission” planning software




                                           Pathfinder Office.
                                           Trimble Navigation


             CS 128/ES 228 - Lecture 10b                        25
Differential GPS
 Fixed base station:
  - knows its location
  - records any shifts
    in its readings in
    correction file

 Differential corrections:
  - real time
  - post-processing

                                         Differential GPS Explained. J. Hurn.
                                         Trimble Navigation, 1993




                   CS 128/ES 228 - Lecture 10b                                  26
Real-time DGPS
 Radio link with base
  station

 U. S. Coast Guard
  beacons

 WAAS



                                        GPS: A guide to the next utility. J. Hurn.
                                        Trimble Navigation, 1989




                  CS 128/ES 228 - Lecture 10b                                        27
Coast Guard beacons

                                                               Trimble’s
                                                            Beacon on a Belt




    www.navcen.uscg.gov/dgps/coverage/NYork.htm




                                                                www.trimble.com




                                  CS 128/ES 228 - Lecture 10b                     28
WAAS
 Wide Area Augmentation System

 Designed by FAA &
  DOT for general
  aviation

 25 ground base
  stations collect
  DGPS data & uplink
  to 2 geostationary satellites,
                                                www.garmin.com/aboutGPS/waas.html




  1 over east coast, the other over
  the west coast
                  CS 128/ES 228 - Lecture 10b                                       29
Effectiveness of WAAS
 Corrects for satellite orbit & clock errors, plus
  ionosphere & troposphere distortions

 Capable of improving accuracy to < 3 m for
  WAAS enabled receivers

 Vertical accuracy is not yet sufficient for
  landing airplanes at uninstrumented airports,
  the original program objective

 The eastern satellite (#35) is low on the SE
  horizon and signal can be hard to receive
                   CS 128/ES 228 - Lecture 10b        30
Post-processing
 GPS receiver logs all signals received
  during data collection phase

 Data log compared to similar record from a
  base station receiver

 U. S. NGS operates a series of public base
  stations and an internet file processing
  system (OPUS) for free postprocessing

 www.ngs.noaa.gov/OPUS/What_is_OPUS.html


                   CS 128/ES 228 - Lecture 10b   31
Survey-grade GPS
 Uses high-quality, dual-frequency receivers
  and DGPS

 Carrier phase processing
  - utilizes the L1 or L2
    carrier signal, 1.2 /
    1.5 GHz
                                                 Differential GPS Explained. J. Hurn.

 Can achieve accuracies of < 1cm                  Trimble Navigation, 1993




 Expensive, complex, and requires long
  periods of data collection at each station
                   CS 128/ES 228 - Lecture 10b                                          32
                                             www.garmin.com/aboutGPS/waas.html




The Future of GPS
 Everyday utilities
  (cell phones, car
  navigation systems)

 Integrated GIS/GPS
  units

 GPS stalking??

 ???



                   CS 128/ES 228 - Lecture 10b                                   33

				
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