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  The Big Idea Geometrically:

The Global Positioning System (GPS), is a constellation of 24 satellites (and several backups) that orbit the Earth in a satellite-based navigation system. GPS was developed by the United States Department of Defense for a variety of military applications, but the system has been open to civilian use since the 80's.

Each solar-powered GPS satellite completes two orbits of the earth a day, at a height of 19 300km (12000 miles) above ground. They transmit signal at 1228 MHz and 1575 MHz. Civilian GPS receivers use the latter frequency. Each satellite constantly transmits a long digital pattern called a pseudo-random code, which is an identifying signal unique to each satellite. At the same time, the receiver plays back a stored copy of the pseudo-random code to itself while listening for the satellite’s signal.

When the signal reaches the receiver the satellite’s pseudo-random code will be slightly delayed compared to the receiver’s playback of the pattern. This delay is due to the large distance between the satellite and receiver, as well as the signal-slowing effects of the troposphere which the signal has to pass through.

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The signal travel time is the length of the delay. The receiver merely multiplies this time by the speed of light (GPS signals are electromagnetic waves, which all travel at the speed of light) to find out the distance between the satellite and receiver.

This brings up an interesting point: how does the receiver know the exact time that the satellite started transmitting? Wouldn’t the clocks in the receiver and on the satellite need to be perfectly synchronized? The answer is, funnily enough, no. While GPS satellites have a highly accurate atomic clock onboard for timekeeping, it is unfeasible to put an atomic clock in a handheld

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To solve the problem, the receiver uses the signals from four or more GPS satellites and finds out the inaccuracy of it’s internal clock. As it has determined it’s own inaccuracy, it is able to adjust it’s clock to make it accurate – and the problem is solved.    more...

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