by Sandeep Johar

Created on: May 30, 2009

"Turn right on Broadway in one minute", the automated voice announces as you move slowly through the city. The little display showing a map of the area with instructions to your destination. Ever wonder how all this magic works? Well, here is simplified explanation of some very complex algorithms.

The GPS device in your car is a little computer and all it does is calculate your position and give you directions. To do this it uses satellites that are circling the earth at all times. These satellites, in effect, announce themselves by broadcasting a message every couple of minutes to anyone who wishes to hear the message. Your GPS device wants to hear this message as it uses this message to calculate the location of the GPS device.

The satellites announcements consist of messages that contain, among other things, the exact time of the broadcast, the satellite identification and satellite orbit information. The message propagates from the satellite outwards in a virtual sphere, spreading out into space and towards earth. Other satellites are doing exactly the same thing and the system is designed so that each GPS device on earth always can see at least 4 satellites. The system is also designed so that each satellite is at a known location at any given time.

Now when the GPS device receives the signal from a satellite, it first checks the time difference between its clock and the time of the broadcast from the satellite. Using the time difference and position information of the satellite it can calculate how far away the signal has travelled from the satellite. But of course it does not know in which direction the distance it has travelled. So it still does not know exactly where it is located, just knows that it is at a given distance from the satellite. What the GPS device does is to construct a mathematical sphere around the satellite at the calculated distance and knows that it, the GPS device, is somewhere on that sphere.

Fortunately for the GPS device there are other satellites doing the same thing. Each satellite is announcing its position and the GPS uses that information to calculate how far the signal has travelled from each satellite. Mathematically the computer in the GPS device is constructing spheres around each satellites known location. Once it has three spheres it can construct the intersection of the spheres to find its exact location. Of course it already knows that is located on the surface of the earth and uses that information as well.

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