GPS

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GPS
Global Positioning System, as known GPS or
NAVSTAR-GPS (NAVstar System with Timing And
Ranging-Global Positioning System), is a radio
navigation positioning system developed by the
Department of Defence (DoD) to meet the military
needs in 1974. Sivilians were allowed to use GPS
system in 1980.
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Satellite Positioning
1 satellite 2 satellites
3 satellites
Latitude Longitude
Latitude Longitude Height
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Satellite Positioning
4 satellites
Latitude Longitude Height Time or X, Y, Z, t
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Differential GPS
2 - 1 2 - 3 2 - 4 2 - 5
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Most important features of GPS
sea, land space
Cloudy
Rainy
Suny
24 hours
Worldwide
Day night
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GPS Segments
Space Segment Control Segment User Segment
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GPS Space Segment
24 satellites 6 orbiting planes 55 degree
inclination 20200 km above Earth 12 hours of
orbit 5 hours view in horizon
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GPS Space Segment
L1 carrier (15410.23 MHz) P code
C/A code data message L2 carrier (12010.23
MHz) P code data message
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Control Segment
Colorado Springs (Main control monitoring)
Hawai (Monitoring)
Ascension Island in South Atlantic
Ocean (Monitoring and ground control station)
Diego Garcia in Indian Ocean (Monitoring and
ground control station)
Kwajelein in North Pasific Ocean (Monitoring and
ground control station)
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Control Segment
COLORADO SPRINGS
HAWAII
KWAJALEIN
ASCENSION ISLAND
DIEGO GARGIA
MASTER CONTROL MONITORING
UPLOAD DOWNLOAD
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User Segment
Users Civilians (universities, private and
state sectors, etc.) Military Receivers Trimble
Ashtech Rogue Leica Javad etc...
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Accuracy Usage Limitation
SA (Selective availability), removed on May 2,
2000 Error on satellite clocks Error on
satellite coordinates AS (Anti spoofing) no
availability of real P code
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GPS Observables
Phase measurements (Mapping, earth monitoring,
etc.)
Pseudorange measurements (Navigation, car
monitoring, etc.)
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GPS Signals
L1 carrier (15410.23 MHz) P code
C/A code data message L2 carrier (12010.23
MHz) P code data message
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Phase observables
Where,
phase measured at A for k at time t
geometric range from A to k
initial unknown integer number of cycles
between k A
Satellite clock error
Receiver clock error
f frequency of signal c speed of
light
Other errors
Tropospheric refraction ionospheric
refraction noise biases multipathing
effects antenna phase center offset variation
etc..
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Single difference 2 receivers 1 satellite
(substitute 2 phase observable)
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Phase equation for station A and satellite k
(1)
Phase equation for station B and satellite k
(2)
Substituting (1) in (2)
(SINGLE DIFFERENCE EQUATION)
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Double Difference 2 receivers 2 satellites
(substitute 2 single differences)
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Single Difference for satellite k
(3)
Single Difference for satellite m
(4)
Substituting (3) in (4)
(DOUBLE DIFFERENCE EQUATION)
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Generalised Mathematical Model for double
differencing
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where
Phase difference
Rate of change on ranges
Arithmetic mean of the receiver clock errors at A
B
Difference between the two receiver clock errors
Total integer ambiguity
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Surveying Techniques

• Static survey
• Rapid static survey
• Stop-and-go survey
• Continuous kinematics survey
• Real-time kinematic (RTK) survey

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Static survey

• stable platforms or pillars
• Long distances (10 km to thousands of
  kilometres)
• Long occupation time (hours to days)
• Control surveys
• Simultaneous recording at several stations
• Observation rates varying from 5 to 30 seconds
• Reducing multipathing effects
• Post-processing required

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Rapid static survey

• shorter distances (up to 10 km)
• shorter occupation time (10 minutes)
• densification of control networks
• Observation rates varying from
• a second to a few seconds
• Post-processing required
• 2 reference receivers required

Reference receiver 2
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2
3
4
Reference receiver 1
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Stop-and-go survey

• distances less than 1 km
• 1 minute occupation time
• observation rates of seconds
• initialisation required
• repeat initialisation when less
• than 4 satellites are being tracked

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Continuous kinematic survey

• initialisation required
• non-stop occupation
• observation rates of 1 second

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Real-time kinematic (RTK) Survey
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Initialisation Methods

• Static survey
• static survey between any two points (usually
  short baseline) is performed with
• sufficient measurements. Specific details are
  in equipment documentation.

• Known baseline
• survey is performed between any two
• points whose coordinates are
• previously determined. Usually one
• epoch is sufficient. Only ambiguities
• are estimated with constraining the
• position vector.

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Initialisation Methods

• Antenna swap
• Step 1 Reference rover receivers are
  located over well defined marks,
• collecting simultaneous
  observations for a period of 1 minute (A)
• Step 2 Reference rover receivers are
  swapped without changing the
• tripods, collecting observations
  for a period of 1 minute (B)
• Step 3 Reference rover receivers are
  swapped again to return back to
• their original locations, for a
  period of 1 minute (C)
• In general, the first two steps are sufficient to
  resolve the integer ambiguities. However, the
  third step is recommended for a further check.

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Initialisation Methods

• On the fly
• the first three methods require the receivers to
  be stationary
• there are restrictions in some applications,
  such as aerial photogrammetry where camera
  positions are determined with GPS. It is not
  possible to stop the aircraft to perform the
  above initialisation techniques.
• The on the fly method resolves the integer
  ambiguities while the receiver is moving.
• 5 satellites with good geometry are required, 6
  or more are preferred.
• Dual frequency receivers are required.
• Ambiguity resolution in 5 minutes, 2 minutes
  with 6 or 7 satellites.
• Specific details given in the equipment
  documentation.

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GPS COORDINATE TRANSFORMATION
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Transformations

• 3D transformation
• 2D transformation

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Mathematical Model for 3D TRANSFORMATION
(1)
X, Y, Z Local reference system x, y, z
WGS84 reference system, k Scale factor Rx, Ry,
Rz Rotations in radians Xo, Yo, Zo Shifts
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3D TRANSFORMATION PROCEDURE
Gauss-Kruger coordinates of common points in
local system (North, East , Up)
Calculate ellipsoidal coordinates (?, ?, h)
Calculate cartesian coordinates (X, Y, Z)
GPS gives directly X, Y, Z in WGS84
Calculate transformation parameters (3 shifts, 3
rotations, 1 scale)
Using the transformation parameters, transform
the WGS84 coordinates into local system
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2D TRANSFORMATION
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Height Transformation
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Height Transformation
H h - N
H orthometric height h ellipsoidal height N
geoidal height