GTECH 201

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GTECH 201

• Session 08
• GPS

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Global Positioning Systems
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GPS is a Satellite Navigation System

• GPS was originally funded by and controlled by
  the U. S. military.
• GPS provides specially coded satellite signals
  that can be processed in a GPS receiver, enabling
  the receiver to compute position, velocity and
  time.
• Four GPS satellite signals are used to compute
  positions in three dimensions and the time offset
  in the receiver clock.

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The Satellites
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The Satellites
The satellite orbits repeat almost the same
ground track (as the earth turns beneath them)
once each day. The orbit altitude is such that
the satellites repeat the same track and
configuration over any point approximately each
24 hours (4 minutes earlier each day). There are
six orbital planes with four satellites in each
equally spaced (60 degrees apart), and inclined
at about fifty-five degrees with respect to the
equatorial plane. This constellation provides the
user with between five and eight satellites
visible from any point on the earth.
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GPS Receivers
GPS receivers convert the satellite signals into
position, velocity, and time estimates. Four
satellites are required to compute the four
dimensions of X, Y, Z (position) and Time.
Navigation in three dimensions is the primary
function of GPS. Precise positioning is possible
using GPS receivers at reference locations
providing corrections and relative positioning
data for remote receivers. Surveying, geodetic
control, and plate tectonic studies are examples.
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Standard Reception
Without further techniques, the accuracy is
approximately   100 meter horizontal
156 meter vertical
The position of the receiver is where the signals
from a set of satellites intersect.
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Standard Reception
The position is determined from multiple
measurements at a single measurement epoch. The
measurements are used together with satellite
position estimates based on the precise orbital
elements (the ephemeris data) sent by each
satellite. This orbital data allows the receiver
to compute the satellite positions in three
dimensions at the instant that they sent their
respective signals. Four satellites (normal
navigation) can be used to determine three
position dimensions and time. Position dimensions
are computed by the receiver in Earth-Centred,
Earth-Fixed X, Y, Z (ECEF XYZ) coordinates.
Three satellites are used to compute a
two-dimensional, horizontal fix (in latitude and
longitude) given an assumed height. This is often
possible at sea or in altimeter equipped
aircraft. More satellites can provide extra
position fix certainty and can allow detection of
out-of-tolerance signals under certain
circumstances.Position in XYZ is converted
within the receiver to geodetic latitude,
longitude and height above the ellipsoid.
Latitude and longitude are usually provided in
the geodetic datum on which GPS is based
(WGS-84). Receivers can often be set to convert
to other user-required datums. Position offsets
of hundreds of meters can result from using the
wrong datum.
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Carrier Phase Tracking (Surveying)

• Accuracies of millimeters under special
  circumstances
• Ionospheric delay differences
• Two receivers be within about 30 km of each
  other
• Real-Time-Kinematic (RTK)

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GPS Error Sources
GPS errors are a combination of noise and bias.
Noise and bias errors combine, resulting in
typical ranging errors of around fifteen meters
for each satellite used in the position solution.
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GPS Error Sources

• Noise errors
• Bias errors
• Ephemeris (orbital sphere) data errors
• Tropospheric delays
• Ionosphere delays
• Multipath

Noise and bias errors combine, resulting in
typical ranging errors of around fifteen meters
for each satellite used in the position solution
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Geometric Dilution of Precision (GDOP) and
Visibility

• GPS ranging errors are magnified by the range
  vector differences between the receiver and
  satellites.
• The volume of the shape described by the
  unit-vectors from the receiver to the satellites
  used in a position fix is inversely proportional
  to GDOP.

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Geometric Dilution of Precision

• Poor GDOP, a large value representing a small
  unit vector-volume, results when angles from
  receiver to the set of satellites used are
  similar.

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Geometric Dilution of Precision

• Good GDOP, a small value representing a large
  unit-vector-volume, results when angles from
  receiver to satellites are different.

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Geometric Dilution of Precision

• GDOP is computed from the geometric relationships
  between the receiver position and the positions
  of the satellites the receiver is using for
  navigation. For planning purposes GDOP is often
  computed from Almanacs and an estimated position.
  Estimated GDOP does not take into account
  obstacles that block the line-of-sight from the
  position to the satellites. Estimated GDOP may
  not be realizable in the field.

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Differential GPS Techniques

• Relative to a known position
• Differential corrections may be used in real-time
  or later, with post-processing techniques

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Combined Error
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Differential Carrier GPS (Survey)