The Basics of the Global Positioning System

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The Basics of theGlobalPositioningSystem

• by Matt Higgins
• B App Sc Surv, M Surv and Map Sc, F.I.S.A.
• Vice Chair FIG Commission 5
• Dept of Natural Resources and Mines Queensland

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Outline of Seminar

• Basics of GPS
• Measurement Techniques
• Coordinates and Heights
• Practical Exercise

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Basics of GPS
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3 Segments of GPS
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GPS Satellite Constellation

• 21 3 Satellites
• 6 orbital planes
• 20,000 km high
• 12 hour orbits
• At least 4 Satellites in view 24 hours per day
• Any weather

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Launched on Delta Rockets
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The GPS Satellite

• 3 atomic clocks
• L Band Radio Signals - 19cm Wavelength
• Codes on the signal
• Time signal takes to reach the receiver
• Satellite Position
• Also give health of system

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The GPS Satellite
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3 Types of GPS Positioning

• Single Point Positioning
• Differential GPS
• GPS Surveying

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1 Receiver - Single Point Positioning (SPP)

• Basic technique for which GPS was designed
• Basic Civilian Receivers lt 500

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The Pseudo-range

• Difference between what it should hear and what
  it does hear is the time delay (5 units in
  diagram)
• Range Distance Time Delay Speed of Light
• Not the true range part of the time delay is due
  to Receiver Clock Offset hence pseudo-range
• Unknowns are Lat, Long, Height and this receiver
  clock offsethence need 4 satellites 4
  equations in 4 unknowns

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The GPS Measurement in 3 Dimensions
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Computing a Position
(Pseudorange creceiver clock offset)2 (XS
-XR)2 (YS -YR)2 (ZS -ZR)2
Need 4 Equations to solve 4 Unknowns Need
Pseudoranges to 4 Satellites
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Some Errors Sourcesin Satellite Positioning
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Satellite Geometry
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Multipath
Direct path from satellite
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Atmospheric Corrections

• Satellite signals are delayed by the ionosphere
  and troposphere
• Receiver can estimate corrections based on models
• 2nd frequency can eliminate most of ionospheric
  effect

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Military vs Civilian Accuracy

• Military Users - Precise Positioning Service
  (PPS)
• /- 15m for Military Users
• Uses P Code which has high resolution
• Good accuracy Satellite Positions (Ephemeris)
• Civilian Users - Standard Positioning Service
  (SPS)
• C/A code 10 times less resolution than P code
• Under policy of Selective Availability - SA,
  Code and/or Ephemeris accuracy can be downgraded
• Until May 2000, /- 100m 2D 95 of the time
• Since May 2000, SA set to zero and civilian users
  now officially getting /- 20-25m 2D 95 of the
  time - but testing showing better than that -
  say 10m or better 2D
• NOTE Military retains right to degrade in
  regions
• Ionosphere can give worse in high and low
  latitudes

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Error Budget for SPP
Langley, 1997
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SA and Single Point Positioning

• SA dithered the orbit info (less recent times)
• SA dithered the satellite clocks and thus the
  accuracy of the observed pseudo-range
• It is this dithering that has been stopped

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SA - Before and After
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How good is Single Point Positioning now?

• The official line is that GPS Point Positions
  should now be better than 25m (95 confidence).
• Testing showing significantly better than that -
  say, better than 10m BUT remember
• Military can still deny accuracy in regions if
  required
• Ionosphere can be an issue, especially in low and
  high latitudes (no C/A on L2 yet)

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SPP Accuracy - UNSW Tests
Single-epoch SPP coordinate accuracy using
different ephemerides, satellite clock correction
and ionospheric bias information, 95 CI.
Rizos, C. and Satirapod, C., 2001a
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SPP Averaging - UNSW Tests
Averaged static solution accuracy for varying
window lengths, for both single and
dual-frequency data, 95 CI.
Rizos, C. and Satirapod, C., 2001a
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An Aside How good is Spatial Data?

• If GPS accuracy is better than 10m How much
  spatial data is that good?
• Table shows a common rule of thumb of 0.3mm at
  plot scale.

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Differential GPS

• 0.5m to 5m - depending on correction method
• Real Time or Post Processed

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Differential GPS in Australia

• Require a decoder to obtain corrections via a
  radio signal and input them to a GPS receiver
  capable of taking the corrections
• Various methods for delivering the corrections
• Nationwide base stations with correction signal
  via Optus satellite - pay for decoder and signal
  - Fugro Omnistar or Racal Landstar
• Specific base stations - pay for decoder with
  signal free to air - AMSA
• Specific base stations with correction signal via
  FM pager - AusNav - pay for decoder and signal
• Run your own base station and radio system for
  corrections - or post process

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Surveying with GPS

• Similar to Differential GPS but phase of the
  signal is measured
• Typical accuracy better than 5mm per kilometre
• High productivity - lines lt10km from Real Time
  Kinematic
• Ultra High Precision /- 3cm in 1000 km!

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3 Levels of GPS Accuracy

• Point Positioning - Now 25m 2D 95 of the Time
  for Civilian Users
• Differential GPS - 0.5m to 5m
• GPS Surveying - 5mm per km typical and
  centimetres in thousands of km possible

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From GPSto GNSSGlobal NavigationSatellite
Systems(a more generic term)
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GLONASS

• Russian Federations GLObal NAvigation Satellite
  System
• First launch Oct 1982

• Uses 3 orbital planes rather than 6 with GPS
• GPS - same frequency but different codesGLONASS
  - same code, different frequency
• Channel of Standard Accuracy (CSA) 60m
  horizontal, 75m vertical (99.7 confidence)
• Restricted access - Channel of High Accuracy (CHA)

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Galileo

• European Union wants more autonomy
• Proposing its own system called Galileo
• Estimated system cost of 2.2 to 3 billion Euros
• Justified in land transport savings alone - 77
  of the Market Volume in Road Traffic segment
• 2005 to 2025 indirect savings of 200 billion
  Euros in the European economy for every 1 saving
  in road travel time
• 2005 to 2025 a market of 270 billion Euros
• European market for equipment 88 billion Euros
• European market for services 112 billion Euros
• Export market for equipment 70 billion Euros

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Coordinates and Heights
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Coordinate Systems and GPS
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Satellite Motion

• Satellites travel around the centre of mass of
  the earth
• They are affected by the Earths gravity field
• Computations need to be related to gravity -
  geoid
• A purely mathematical figure approximating the
  geoid is the ellipsoid

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Ellipsoids and Geoids
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World Geodetic System 1984

• WGS84 - Reference Frame for GPS
• Established by National Imaging and Mapping
  Agency (NIMA nee DMA)
• Realization of the International Terrestrial
  Reference Frame (ITRF) but not exactly the same
• WGS84 improvements - Revised gravity model and
  tracking station coords (processed with IGS sites)

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Geocentric Datum of Australia (GDA)
Link to ITRF by GPS observations at IGS sites and
the Australian National Network (500km). Then
further densified by State GPS Networks (e.g.
100km Network in Qld) GDAs link to ITRF makes it
compatible with WGS84
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Datum Transformation

• 3D Transformation between WGS84 and AGD84
• 7 Parameters 3 Shifts, 3 Rotations and 1 Scale
• Until recently used Higgins 1987 Parameters
• New Parameters - Late 1997
• Supplemented by a grid of corrections to model
  remaining distortion due to errors in AGD84

Rz
Ry
Dz
Dx
Dy
Rx
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More on these Distortions
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Distortions between AGD84 and GDA94
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Distortion Grid
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Using the Distortion Grid
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Coordinates Systems and Projections
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Coordinates Systems and Projections
NMGA
EMGA
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Terminology
Universal Transverse Mercator
Std. 6 Degree Zones, with the same Central
Meridians etc.
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Heights from GPS
Topography
Geoid
Ellipsoid
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Want Height above Geoid - H
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GPS gives Ellipsoidal Height - h
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Need Geoid Ellipsoid Separation - N

• AUSGEOID98 Model Used in Australia

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Conclusion

• Basics of GPS
• Measurement Techniques and 3 levels of accuracy
• Coordinates and Heights now ...
• Discuss Your Applications
• Practical Exercise