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How GPS Works PowerPoint PPT Presentation

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How GPS Works. Kristine M. Larson Professor of Aerospace Engineering Sciences University of Colorado. Outline. What is GPS How GPS works How GPS codes work Why I use GPS for my research.

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How GPS Works

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How gps works l.jpg

How GPS Works

Kristine M. Larson

Professor of Aerospace Engineering Sciences

University of Colorado

Outline l.jpg


  • 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?

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Instead of satellites, lets use transmitters on the ground.

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Grand Junction sends a signal to Radon’s GPS.

What kind of signal?

it puts the time on the signal.


Grand Junction Transmitter

Radon in Boulder

For this to work, we’ll need for both the transmitter and Radon to have clocks.

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When Radon’s 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













This is the code for satellite 6













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  • 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.

  • 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.

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Here is an example with 3 shift registers

Start with all 1’s in your shift registers

Add Register 1 and Register 3

For this example, 1+1 =10 ==> 0

The answer 0 goes into Register 1 and everything shifts to the right.

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Resulting in





Next 0 1 1 l.jpg

Next 0+1=1





After 2 n 1 steps n is the number of registers the code repeats l.jpg

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?



Every time the numbers agree, add 1.

Every time the numbers disagree, subtract 1.

This example 2 different satellites l.jpg

This example: 2 different satellites



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.



But if you recognize they are shifted by 1:



Agreement is perfect

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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.

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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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Start with 2 codes

Is red shifted by 200?

Or is black shifted by 823?

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


We have GPS receivers operating all over the world.





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Let’s 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

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