EMAT 6700

Final Project


Roy H. Jones, III

The Mathematics of Global Positioning System (GPS)


What is GPS?

GPS, Global Positioning System, is a relatively new technology that was developed by the US military in the 1980's. It allows us to pinpoint locations here on earth using our longitude and latitude coordinate system along with high frequency signals that are transmitted from a set of 24 satellites that orbit the Earth.

GSP version of satellite orbit


Photo courtesy NASA
NAVSTAR GPS satellite


How does GPS work?

In very simple terms, anyone posessing a GPS receiver here on Earth can find there exact location on Earth using a GPS receiver. The receiver intercepts the signals that are being transmitted from the satellites above. The orbits are arranged so that at any time, anywhere on Earth, there are at least four satellites "visible" in the sky. The receiver needs a minimum of 3 satellite signals (4 signals to include altitude) to locate its position. Using the distance formula (distance (d) = rate (r) x time (t)), the receiver is able to calculate its distance from each satellite by calculating how long it takes for the signal from each satellite to reach the receiver. The receiver is programed with the Earths latitude and longitude coordinates (along with sea level coordinates to calculate altitude). Armed with the above information, the GPS receiver uses a mathematical principle called trilateration to calculate it's location on the Earth. Trilateration in three-dimensional space can be a little tricky, so we'll start with an explanation of simple two-dimensional trilateration (see links below).

2-D Trilateration


2-D Trilateration using Geometer's Sketchpad