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
3. How do you use these satellites to calculate your position?
The Global Positioning System is a constellation of 31
satellites that is used to calculate your position.
5. Grand Junction sends a signal to Radon’s GPS.
What kind of signal?
Grand Junction
Transmitter
Radon in Boulder
it puts the time on the signal.
For this to work, we’ll need for both the
transmitter and Radon to have clocks.
GPS
6. When Radon’s GPS receiver gets the signal, he
compares the time on the signal with the time on his
clock.
So, a GPS signal tells you how far you are from
the transmitter.
Time Difference (in seconds) * 2.99792458 108 meters/second =
Distance (in meters)
7. If the distance from the GPS transmitter is 250 miles, that means
you are somewhere on a circle of radius 250 miles.
9. And a third transmitter in Pueblo
Radon is at the intersection
of the 3 circles
10. 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.
12. 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.
13. How do GPS signals send all
this information?
• They use codes! Binary codes.
• Each satellite has a different code.
15. 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.
16. How do you create codes?
• You use binary addition rules.
• 0+0=0
• 1+0=1
• 0+1=1
• 1+1=10 (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.
17. Register1 Register2 Register3 Code
1 1 1 -
Start with all 1’s in your shift registers
Add Register 1 and Register 3
The answer 0 goes into Register 1 and
everything shifts to the right.
Here is an example with 3 shift registers
For this example, 1+1 =10 ==> 0
20. After 2N -1 steps (N is the number of
registers), the code repeats
Register1 Register2 Register3 Code
1 1 1 -
0 1 1 1
1 0 1 1
0 1 0 1
0 0 1 0
1 0 0 1
1 1 0 0
1 1 1 0
For 3 shift registers, the code repeats after 7 steps.
21. 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.
22. How do you compare codes?
100111101110100010011011111111101
000010001010011100001110010010001
Every time the numbers agree, add 1.
Every time the numbers disagree, subtract 1.
23. This example: 2 different satellites
100111101110100010011011111111111
000010001010011100001110010010001
14 agree
11 disagree
Total score: 3
Perfect agreement would be 35
25. It’s 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.
29. Why two peaks?
Or is black shifted by 823?
Start with 2 codes
Is red shifted by 200?
30. 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
31. Plate tectonics
The Earth is a spherical jigsaw puzzle. Different tectonic plates
move in different directions at different speeds.
32. I mostly use GPS to study how the Earth
changes. I study plate tectonics,
volcanoes, and earthquakes.
33. We have GPS receivers operating all over the world.
Southern California
Hawaii
Antarctica
Australia
Iceland
Holland
34. Let’s use a GPS site in Canada as an example
Churchill, Manitoba
35. 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.