Introduction to NAVSTAR GPS
Scott M. Haag,
Rutgers Center for Remote Sensing and Spatial
Analysis
(Revised from Chuck Colvard and Joe Geib)
Class Schedule
) Computer
Login
) Questions
from last week
) GPS
error budget
) Geographic
Information Systems
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Name
Account
New??
=====================================
Les Small
small
No
Erica Cress
ecress
Yes
Aaron Newland
bcaapi
Yes
Brian Switek
sandshrk Yes
Dan Betz
drbetz
Yes
Zeeshan Khan
zkhan13
Yes
York Bergin-Pugh ruhungry Yes
David Bennet
dbnett
No
David Gates
gates
No
Aaron Love
aalove
No
Anton Getz
agetz
No
Keith Aubin
kaubin
Yes
Questions from Last Week
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Knots and the Rope and how that works?
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A ships speed is determined in nautical miles. A
nautical mile is equal to one minute of latitude.
Since there are 360 degrees and 60 minutes in a
degree, the earth is (360 * 60) or 21,600 knots in
circumference.
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In order to determine speed a ship would throw a
log tied to a rope off the side of the ship.
Questions from Last Week
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This rope had a knot placed every 47 ft 3 inches.
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The amount of knots that were pulled in 30 second
intervals was equal to the speed in knots per hour.
This allowed the navigator to
) fix a dead reckoning position.
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Questions from Last Week
) How
to see the North Star from the South
Pole?
) Well
you can’t do that but most early
navigation took place in the northern
hemisphere, and there are other celestial
objects that can be used in the southern
hemisphere.
Questions from Last Week
) The
equation to converting time to degrees
longitude?
) It
takes the earth 24 hours to completely
turn around. This can be observed for earth
because the sun’s zenith is separated by a
period of 24 hours.
Questions from Last Week
The equation to
So if an observer in New
converting
York has
an accuratetime
clockto
showingdegrees
the timelongitude?
in London
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he-she could calculate the
temporal difference between
solar noon in London and
New York City.
This time difference can be converted to degrees longitude
by the fact that it takes 24 hours for the earth to completely
rotate and has 360 degrees of longitude.
Therefore the sun appear
to be moving at 360/24 or
15 degrees per hour.
Questions from Last Week
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The equation to
So if an observer in New
converting
time4to
York records
solar noon
degrees
longitude?
hours later
then in
London. This observer
would know that they are
15*4 or 60 degrees away
from London.
Also a navigator knows
that as they move towards
home port local noon will
converge temporally with
the home port.
Questions from Last Week
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Link Between GPS and Time? / The mechanics of GPS?
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GPS works by determining the range from know positions
(the satellites).
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In order to determine the range from a known position we
need very accurate clocks because.
y The Satellites are moving (not fixed).
y GPS determines range by measuring how long it takes an
electromagnetic signal to travel from the satellite to the ground
receiver.
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GPS determines the precise position of the Satellites in
space using an almanac which is downloaded from the
satellites.
To find the range to the satellites your GPS receiver uses
something called a Pseudo Random Code.
Each satellite is “singing” a unique PRC that is started at a
specific time. By recording what time this song is heard at
the GPS receiver we can determine how long it took for
the electromagnetic signal to reach the earth.
This Difference in time can then be multiplied times the
speed of propagation of an electromagnetic signal (3.00 X
10 ^8 meters per second) to get the range to the satellite.
Trilateration
Knowing that we're 12,600 miles from a particular satellite
narrows down all the possible locations we could be in the
whole universe to the surface of a sphere that is centered on
this satellite and has a radius of 12,600 miles.
12,600 miles
We’re somewhere
on the surface of
this Sphere
Trilateration
A second measurement
narrows our position down
to the intersection of two
spheres - an imaginary
circle
12,600 miles
16,000
miles
The intersection
of two spheres
is a circle
Trilateration
A third measurement narrows our
possible position to just two
points
12,600 miles
Intersection of
three spheres
is only two points
16,000
miles
14,000
miles
Trilateration
Fourth measurement will decide between two points
Fourth measurement will
only go through one of the
two points
Questions from Last Week
) GPS
Time Correction?
) Small
time Errors cause huge positioning
errors because electromagnetic signals
move so fast.
) Pathfinder
pocket (+-2 to 5 meters)
) Or 0.0000000067 seconds!
Dealing with Clock Errors
Suppose that there were 1 second errors in
your receiver's clock - position calculation
would be way off
5 seconds
wrong time
7 seconds
wrong time
Our true position
This diagram is a 2D analogy - GPS
really works in a 3D world
Bad position - receiver clock
is off by one second =186,000 miles
Dealing with Clock Errors
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With the addition of a third
measurement the receiver
recognizes the timing
problem
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The receiver figures the
error offset, sets its internal
clock to the correct time
(very near atomic accuracy)
and calculates its true
position
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In real world 3-D, this
means using a 4th satellite to
solve for clock errors. The
clock error is the same for
each satellite.
Error Budget
)
y
y
y
y
y
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Error
Typical observed errors
satellite clocks
ephemeris error
receiver errors
atmospheric/iono
S/A
Total (rt sq sum)
y
y
y
y
.8 m
.8 m
1.2 m
4m
30 m
2 ft
2 feet
4 ft
12 ft
100 ft
5-7 m
15-30 ft
Then multiply by GDOP (usu. 4-6)
that gives a total error of:
typical good receiver 20-50M 60-100 ft
worst case
65 M
200 feet
with S/A
120 M 350 feet
S/A
Atmos/Ionos
Receiver
Ephemeris
Sat Clocks
Feet
Meters
0
0
50
100
17
33
More Geometry
) Satellite
geometry matters
) Accuracy is best when
SV’s are spread out
overhead, not bunched
together or down on the
horizon
Good
Bad
DOP
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Dilution of Precision
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A controllable source of error
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Can be predicted
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Two things influence DOP
y Number of satellites in view (line of
sight)
y 3- dimensional Arrangements of
satellites
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Has become less of a problem since
more satellites have been placed in
orbit
Graphic from
http://www.geosun.sjsu.edu/paula/137/pdf/lecture15.pdf
DOP
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Different types of DOP
y HDOP horizontal Dilution of Precision
y VDOP is vertical dilution of Precision
y PDOP Position dilution of Precision (combines HDOP and VDOP)
y TDOP Time Dilution of Precision
y GDOP geometric DOP is a combination of PDOP and TDOP
Measured from high to low- we will come back to this!
Low = 1 high = 8
Selective Availability
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As hard as it may be to believe, the same government that
spent $12 billion to develop the most accurate navigation
system in the world used to intentionally degrading its
accuracy.
The policy was called "Selective Availability" or "SA"
DoD want to make sure that no hostile force or terrorist
group can use GPS to make accurate weapons.
Selective Availability
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DoD introduces some "noise" into the satellite's clock data
which, in turn, adds noise (or inaccuracy) into position
calculations
DoD may also be sending slightly erroneous orbital data to
the satellites which they transmit back to receivers on the
ground as part of a status message.
Together these factors used to make SA the biggest single
source of inaccuracy in the system
Selective Availability
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Military receivers use a separate signal on a
different frequency along with a decryption
key to remove the SA errors and so they're
much more accurate (ten time more accurate)
Selective Availability
• Turned on in late March, 1990
(without notice)
• Turned off on 10 Aug., 1990 for the
Gulf war
*not enough P-code receivers yet in
U.S. military
• Turned on again on 1 July, 1990war over. Turned off again for
Panama, Grenada, and Haiti
SA turned off
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President Clinton ordered Selective Availability
turned off in July, 2000
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Now even low-end units have much greater
accuracy.
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The Federal Government now degrades GPS
locally instead of globally using jamming
technology.