Transcript Global Positioning Systems

GTECH 201
Session 08
GPS
Global Positioning Systems
X, Y, Z
Measurements of signal phase arrival times from at least f our
GPS is a Satellite Navigation
System
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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.
The Satellites
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.
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.
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.
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 userrequired datums. Position offsets of hundreds of meters can result from using
the wrong datum.
Z
Satellite
X, Y, Z
Receiver
X, Y, Z
Prime
Meridian
0, 0, 0
Y
Equator
X
Earth-Centred, Earth-Fixed X, Y, Z
Pole
Geodetic Height
at Point P
Ellipsoid
Surface
Semi Minor Axis
Normal to
Ellipsoid at
Point P
Point P
Tangent to Ellipsoid
at Point P
Semi Major Axis
Equator
Geodetic Longitude
at Point P
Geodetic Latitude
at Point P
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)
GPS Error Sources
Noise
position
Noise and bias
position estimates
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.
GPS Error Sources
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Noise errors
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Bias errors
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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
Geometric Dilution of Precision
(GDOP) and Visibility
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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.
Geometric Dilution of Precision
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Poor GDOP, a large
value representing a
small unit vectorvolume, results
when angles from
receiver to the set of
satellites used are
similar.
Geometric Dilution of Precision
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Good GDOP, a small
value representing a
large unit-vectorvolume, results
when angles from
receiver to satellites
are different.
Geometric Dilution of Precision
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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.
Differential GPS Techniques
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Relative to a known position
Differential corrections may be used in
real-time or later, with post-processing
techniques
Combined Error
Error source
Clock
Typical range
error
1 m
Ephemeris
1 m
Troposphere
1 m
Ionosphere
10 m
DGPS (code) range error
< 100 km distance
Pseudo-range
noise
Receiver noise
1 m
1 m
1 m
1 m
Multipath
0.5 m
0.5 m
RMS error
15 m
1.6 m
Combined error
60 m
6 m
Differential Carrier GPS (Survey)
Satellite at t2
Satellite at t1
Orbit path
Reference receiver
Remote receiver