GPS uses trilateration to determine location based on distances to at least three satellites. Each satellite transmits its precise location and time of transmission. The GPS receiver uses the speed of light and transmission time to calculate distances, allowing it to determine its position at the intersection of distance spheres from multiple satellites. Accuracy relies on precise timekeeping of satellites and receivers.

1. Daniel – EPS 2010
How GPS Works

3. What does GPS stand for again?
GPS = Global Positioning System

4.  Trilateration
 Measuring distance
 Accuracy of time and location of
satellites

5. Trilateration
 A method for determining the intersections of
three sphere surfaces given the centers and radii of
the three spheres.
Trilateration Triangulation

6. Simplifying the problem
Let’s assume several factors for easy understanding.
 GPS Satellites are on the ground (3D  2D)
 We know the exact location of satellites
 We can calculate the distance from each of the
satellites

7. Start with first satellite
200km
Satellite 1
Your location is somewhere on the circumference of the circle.

8. Second satellite gives two points
200km
Satellite 1
B
50km
A
Satellite 2
Your location must be one of the intersection. (Point A or B)

9. Third satellite sets the location
200km
Satellite 1
B
50km
A
Satellite 2
150km
Satellite 3
Now you know you are on point A.

10. Real trilateration in 3D space
The intersection of two sphere is circle. (not two points as in 2D)

11. Real trilateration in 3D space
Knowing the distances from three satellites gives you two points.

13. Speed Equation
 GPS receiver uses speed equation to calculate the
distance to satellites
Distance = Speed × Duration
(Time)

14. Example of speed equation
 If you don’t know the distance between pitcher and catcher,
you can calculate it with the speed and duration of the ball
Distance ???
Speed : 150km/h
 150km/h ≈ 40m/s
 If it took 1 second, the distance is about 40m.

15. GPS satellites use radio signal
 Instead of throwing balls, the GPS satellites send radio
wave and GPS receivers catch them.
 Radio wave fly at the same speed of light.
(about 300,000 km/s)

16. Signal from GPS satellites
Each satellites continually transmits messages including :
 the time the message was transmitted
 presise orbital information (location of itself, ephemeris)
 rough orbits of all GPS satellites (the almanac)

17. Precise calculation of time

18. • The key idea of positioning by GPS is ‘Trilateration’
• Two factors for trilateration
1. the location of each satellite (at least three satellites)
2. the distance from the satellite
• Distance = speed of light × duration time
• Satellites send radio signal including time and location