Daniel – EPS 2010

How GPS WorksHow GPS Works

What does GPS stand for again?

GPS = Global Positioning System

Trilateration

Measuring distance

Accuracy of time and location of satellites

TrilaterationA method for determining the intersections

of three sphere surfaces given the centers

and radii of the three spheres.

Trilateration Triangulation

Simplifying the problemLet’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

Your location is somewhere on the circumference of the

circle.

Satellite

1

200km

Start with first satellite

Your location must be one of the intersection. (Point A

or B)

Satellite

1

200km

Satellite

2

50k

m

B

A

Second satellite gives two points

Satellite

1

200km

Satellite

2

50k

m

B

A

Satellite

3

150km

Now you know you are on point A.

Third satellite sets the location

Real trilateration in 3D space

The intersection of two sphere is circle. (not two points

as in 2D)

Real trilateration in 3D space

Knowing the distances from three satellites gives you

two points.

Speed Equation

GPS receiver uses speed equation to

calculate the distance to satellites

Distance = Speed ×

Duration

(Time)

Example of speed equationIf you don’t know the distance between pitcher and catcher,

you can calculate it with the speed and duration of the ball

Speed : 150km/h

Distance ???

150km/h ≈ 40m/s

If it took 1 second, the distance is about 40m.

GPS satellites use radio signalInstead 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)

Signal from GPS satellitesEach 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)

Precise calculation of time

• 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