How GPS Works

1
How GPS Works

• Kristine M. Larson
• Professor of Aerospace Engineering Sciences
• University of Colorado

2
Outline

• What is GPS
• How GPS works
• How GPS codes work
• Why I use GPS for my research

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The Global Positioning System is a constellation
of 31 satellites that is used to calculate your
position.
How do you use these satellites to calculate your
position?
4
Instead of satellites, lets use transmitters on
the ground.
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Grand Junction sends a signal to Radons GPS.
What kind of signal?
it puts the time on the signal.
GPS
Grand Junction Transmitter
Radon in Boulder
For this to work, well need for both the
transmitter and Radon to have clocks.
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When Radons GPS receiver gets the signal, he
compares the time on the signal with the time on
his clock.
Time Difference (in seconds) 2.99792458 108
meters/second Distance (in meters)
So, a GPS signal tells you how far you are from
the transmitter.
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If the distance from the GPS transmitter is 250
miles, that means you are somewhere on a circle
of radius 250 miles.
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Now add a 2nd transmitter in Ft. Collins.
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Radon is at the intersection of the 3 circles
And a third transmitter in Pueblo
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This only works if

• You know where the transmitters are.
• GPS signals also transmit the satellite
  locations.
• Everyone has good clocks.
• The GPS satellites have very good clocks. A GPS
  user can use a 4th signal to piggy-back onto the
  GPS satellite clocks.
• And you can tell the transmitters apart.
• The signals are made in a way so that you can
  tell which transmitter sent them.
• For real problems, we use the intersection of
  three spheres, not three circles.

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Intersecting Spheres
But only 1 point is on the Earth
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When GPS receives a signal

• It compares that signal with all the known codes
  (there are currently 37).
• The receiver determines which satellite it is.
• It decodes the timing information, multiplies by
  the speed of light to find the radius of the
  sphere.
• Once it has done that for 3 satellites, it can
  determine the location.

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How do GPS signals send all this information?

• They use codes! Binary codes.
• Each satellite has a different code.

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For example, here are the first 1000 numbers of
the code for satellite 1
00001000101001110000111001001000100001000101011000
111101110010101101100111101011 001011001010011001
11111011001111001001100110100011100010010001011000
101101110000 001101100100010001011010001010010000
00011111000110001011111011111100110111001011
0111100011111101010010100001010100111000011010011
1011000111101111100001111111111
0100100100100110011101010111110000100010110100111
1110000100110111100111000110110
1011011010100001011010010100010100100011100111000
1010010111010111010101000001011
0111001101100110100000000000111011101100011011010
1010110110001110001100110011111
0101111100111010101000001111110010010100000011101
0001111011010010110110000010010
0100110000110110000111101110111000110111011010011
1001000110101010000110110100101
1100101111111110110001110000001101110001100000010
0000000100000110101000101011110
1100011101101000110010101111100111101000000011011
1100110011101011110000011110110
0100010010101110000000010000101010100111110110011
1011011111100101111000100110101
This is the code for satellite 6
10011110111010001001101111111110111100101101111011
001101111101010100011111011000 110001001100110100
00100000101111111000010000110101101011101011010011
000001101000 011000101010110010001001000001100000
11110000111010000011100100111011000000010110
0111100010010101011111010100111100101111101100101
0001011100001001110000111110111
0101110101101100111100100110101110010001101101111
1011001101011100001110101110001
1000111100000100011101101110001000001101001100100
1110000100010111000100100011011
1110001110101010011000000001100111100111010100001
0010001110010101010011100101101
1111001111111001101001110110011101100101001010011
0010101110111001110001101111001
1000001010001111001101111011001111010011011101001
1100110101010110100000101110001
1100011101011000111100010010100111010101100001100
0100011001010111001100001111100
0001111100010010001101000101000101001001000110000
1100100000110001100010100001101
1001011010011001100010110111001111001000101001010
0011110011101100001111101100101
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Strategy

• First we need to learn how GPS creates these
  codes
• Then we need to come up with a way to quickly
  tell the codes apart.

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How do you create codes?

• You use binary addition rules.
• 000
• 101
• 011
• 1110 (but only use the last bit, 0)
• GPS uses shift registers.
• The more shift registers you have, the more
  complicated you can make your code.

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Here is an example with 3 shift registers
Start with all 1s in your shift registers
Add Register 1 and Register 3
For this example, 11 10 gt 0
The answer 0 goes into Register 1 and everything
shifts to the right.
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Resulting in
1
1
1
0
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Next 011
1
0
1
1
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After 2N -1 steps (N is the number of registers),
the code repeats
For 3 shift registers, the code repeats after 7
steps.
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Real GPS

• Uses 10 shift registers.
• They add different registers to produce the codes
  for different satellites.
• Satellite 1 uses 2 and 6.
• Satellite 2 uses 3 and 7, and so on.
• A 10-shift register code repeats after 210-1, or
  1023.

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How do you compare codes?
100111101110100010011011111111101
000010001010011100001110010010001
Every time the numbers agree, add 1.
Every time the numbers disagree, subtract 1.
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This example 2 different satellites
100111101110100010011011111111111 0000100010100111
00001110010010001
14 agree
Total score 3
11 disagree
Perfect agreement would be 35
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This example same satellite codes, but shifted
Not so good - score of -3.
01100010101011001000100100000110000011110000 11000
101010110010001001000001100000111100001
But if you recognize they are shifted by 1
01100010101011001000100100000110000011110000
11000101010110010001001000001100000111100001
Agreement is perfect
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Its useful to have a computer to do these
comparisons, especially since you have to test a
lot of different shifts. Then you can plot how
good the agreement is as a function of shift.
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Satellite 9 compared to Satellite 10 code
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Satellite 10 compared to Satellite 10 code
Very good agreement here.
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Satellite 10 compared to Satellite 10 code that
has been shifted by 200.
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Why two peaks?
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Why are the codes shifted? The shift gives the
GPS receiver the time difference.
Time Difference (in seconds) 2.99792458 108
meters/second Distance (in meters)
What is a typical Time Difference? GPS
satellites are 20,000,000 meters above the Earth.
20,000,000/300,000,000 70 milliseconds
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Plate tectonics
The Earth is a spherical jigsaw puzzle.
Different tectonic plates move in different
directions at different speeds.
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I mostly use GPS to study how the Earth changes.
I study plate tectonics, volcanoes, and
earthquakes.
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Southern California
Iceland
We have GPS receivers operating all over the
world.
Holland
Australia
Hawaii
Antarctica
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Lets use a GPS site in Canada as an example
Churchill, Manitoba
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Each red dot tells you the position of a GPS
receiver on a single day.
Churchill is moving 1.9 cm/yr west, 0.6 cm/yr
south, and 1.1 cm/yr up.
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Churchill, Manitoba
The North American plate is rotating about the
blue triangle
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All the plates together
Blue boundaries are the different plates
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Why is Churchill going up 1.1 cm/yr?
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Canada was covered by ice 11,000-14,000 years ago.
And ice is very heavy.
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Postglacial rebound