## The Global Positioning System

### What is GPS?

The Global Positioning System (GPS) is a worldwide radio-navigation system formed from a constellation of 24 satellites and their ground stations.

 GPS satellites orbiting Earth

### How does GPS work?

A GPS receiver measures the distance to a satellite using the travel time of radio signals. By accurately measuring the distance from 3 satellites it is possible to find your position anywhere on Earth.  For GPS to work we must be able to 1) measure travel time very accurately, 2) know the exact location of a satellite in space, and 3) understand the delays the signal experiences as it travels through the atmosphere.

Suppose we measure our distance from a satellite and find it to be 18,000 km (11,000 miles). Knowing that we are 18,000 km from a particular satellite narrows down our possible locations to the surface of a sphere centered on the satellite with a radius of 18,000 km as shown to the right.

If we measure our distance from a second satellite, we now know that we are somewhere on a second sphere centered on the second satellite.  We can thus narrow our location to be on the circle where the two sphere's intersect. This is the same thing as when you blow bubbles and two of the bubbles come together. There connection is along a circle.

If we measure our distance from a third satellite, we know that our location is one of 2 points where the 3 spheres intersect. The intersection of 3 spheres is illustrated to the right. We will be able to reject one of the points because it will be off the Earth's surface; the other point is our location on Earth.

### Measuring travel time and converting it to distance

The distance to a satellite is determined by measuring how long a radio signal takes to reach the receiver from the satellite. A radio signal travels at the speed of light or roughly 300,000 km/sec (186,000 miles/sec).

Multiply travel time by the speed of light to get distance.

GPS satellites have atomic-accuracy clocks and so their timing is very accurate.  GPS receivers do not have these clocks, otherwise they would be too expensive to buy and use. Receiver clocks don't have to be too accurate though, because an extra satellite distance measurement can be used to remove timing errors. Therefore, although in theory only 3 satellites are needed to locate yourself, in practice 4 satellites are used to reduce errors in measuring travel time. The figure to the left shows the ship receiving signals from 4 GPS satellites.