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

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.

Instead of satellites, lets use transmitters on the ground.

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

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) * meters/second = Distance (in meters)

If the distance from the GPS transmitter is 250 miles, that means you are somewhere on a circle of radius 250 miles.

Now add a 2nd transmitter in Ft. Collins.

And a third transmitter in Pueblo Radon is at the intersection of the 3 circles

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.

Intersecting Spheres But only 1 point is on the Earth

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.

How do GPS signals send all this information? They use codes! Binary codes. Each satellite has a different code.

For example, here are the first 1000 numbers of the code for satellite This is the code for satellite 6

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.

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.

Register1Register2Register3Code 111- 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

Resulting in Register1Register2Register3Code

Next 0+1=1 Register1Register2Register3Code

After 2 N -1 steps (N is the number of registers), the code repeats Register1Register2Register3Code For 3 shift registers, the code repeats after 7 steps.

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 , or 1023.

How do you compare codes? Every time the numbers agree, add 1. Every time the numbers disagree, subtract 1.

This example: 2 different satellites agree 11 disagree Total score: 3 Perfect agreement would be 35

Agreement is perfect But if you recognize they are shifted by 1: This example: same satellite codes, but shifted Not so good - score of -3.

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.

Satellite 9 compared to Satellite 10 code

Satellite 10 compared to Satellite 10 code Very good agreement here.

Satellite 10 compared to Satellite 10 code that has been shifted by 200.

Why two peaks? Or is black shifted by 823? Start with 2 codes Is red shifted by 200?

Why are the codes shifted? The shift gives the GPS receiver the time difference. Time Difference (in seconds) * 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

Plate tectonics The Earth is a spherical jigsaw puzzle. Different tectonic plates move in different directions at different speeds.

I mostly use GPS to study how the Earth changes. I study plate tectonics, volcanoes, and earthquakes.

We have GPS receivers operating all over the world. Southern California Hawaii Antarctica Australia Iceland Holland

Let’s use a GPS site in Canada as an example Churchill, Manitoba

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.

Churchill, Manitoba The North American plate is rotating about the blue triangle

All the plates together Blue boundaries are the different plates

Why is Churchill going up 1.1 cm/yr?

Canada was covered by ice 11,000-14,000 years ago. And ice is very heavy.

Postglacial rebound