When someone uses a GPS receiver, the device finds the four nearest satellites in the GPS constellation and asks each one a pair of simple questions: Where are you? And: What time is it? The receiver uses that information to calculate its own position with a high degree of accuracy. In a mathematics textbook, just three satellites would be sufficient to get a reading, but in a real world filled with imprecision, the fourth satellite is used to increase accuracy.
The key pieces of equipment in the GPS system are the pair of atomic clocks that each satellite carries. Satellites travel in well-defined and precisely monitored orbits, so if you know a satellite’s orbital path (from data that is measured by ground stations, sent to the satellites, and relayed to users) and the time, you know where it is. And if you know how long it took your signal to reach the satellite, you know how far away it is.
And that’s all you need. Microprocessors in the receiver take the four time signals and calculate the user’s position with standard geometrical methods. Since the receiver does not have an ultraprecise atomic clock, there will be some uncertainty in its time readings and thus in the distance readings. That’s where the extra satellite comes in: The receiver corrects its own time up or down until the location comes out the same no matter which subset of three satellites is used.
Obviously, to get an accurate reading, every piece of data must be measured with great precision. An error of one nanosecond—a billionth of a second—translates into an error of about a foot on the ground. The Department of Defense tracks minor perturbations in the satellites’ orbits (from such sources as atmospheric drag and solar radiation) and sends corrections to receivers through the satellites themselves. Other sources of error, less easily corrected, result from waves bouncing off buildings or mountains and interference caused by the earth’s atmosphere.
These inaccuracies can be overcome with Differential GPS (DGPS), in which a fixed receiver with a known location measures its location using GPS and calculates the deviation between the two. The fixed receiver sends the correction factor to other receivers in the area, which adjust their readings accordingly. This explains why GPS data is sometimes quoted with accuracy in feet or yards and sometimes in inches. An uncorrected GPS reading is good to within 20 feet or so, but with DGPS, it can be much more precise.
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