Digital Lifestyles Reference Guide

Aug 27, 2004

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GPS devices figure out your precise location by taking measurements from three or more separate satellites, and then using basic geometry to calculate where you are. The principle involved is called triangulation, and you probably learned about it back in your high school geometry class.

To calculate a position on the ground, the GPS unit must know the distance to at least three geosynchronous satellites. Since all the satellites generate radio signals at exactly the same time, the distance from each one can be calculated by measuring how long it takes for the signal to be received by the GPS device. Satellite signals travel at the speed of light (186,000 miles per second), so the difference in signals from the various satellites is measured in hundredths of a second. As any ninth grader knows, you measure distance by multiplying speed times time — in other words, D(istance) = S(peed) x T(ime). So if it takes 0.09 of a second for a satellite's signal to reach the GPS receiver, the distance between the satellite and the receiver must be 16,740 miles. (That's 186,000 miles per second x 0.09 seconds = 16,740 miles.)

Now, this doesn't mean that the satellite is exactly 16,740 miles overhead. The satellite can actually be located anywhere in a sphere surrounding the receiver with a radius of 16,740. This is why you need measurements from additional satellites to fix a single ground location.

To triangulate your location, your GPS receiver needs measurements from three satellites. Let's continue our example, and say that the signal from a second satellite takes 0.08 seconds to arrive, which puts it 14,880 miles from the receiver. And let's say that the signal from a third satellite takes 0.07 seconds to arrive, which puts that satellite in a sphere 13,020 miles distant from the receiver. Work through the geometry, and you'll find that there are only two possible locations for the GPS receiver. One of these locations is located out in space, which you're presumably not, so the GPS receiver discards that result. The remaining Earth-based location is where you are.

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