In this second of a three part series we're going to go over how GPS receivers actually measure distance. A lot of math and science goes into this stuff so sit back and get ready to strain your brain.
At any given time, let's choose midnight for this example, the satellite begins transmitting a digital pattern called a pseudo-random code. At that same time the GPS receiver begins running that same random pattern. When the satellite's signal reaches the receiver the pattern transmission will lag a little behind the receivers playing of the same pattern. The length of the delay is equal to the travel time of the signal. The receiver multiplies this time by the speed of light to measure how far the signal actually travelled. We assume the signal travelled in a straight line and this therefore is the distance from receiver to satellite.
In order for this measurement to be able to be made the receiver and the satellite both need clocks that can be synchronized to the nanosecond. In order to make this possible you need atomic clocks, not only in the receiver but in every satellite as well. Atomic clocks cost between $50,000 and $100,000. That makes them a little too expensive for everyday use.
To overcome this cost problem the GPS system has a very clever solution. Every satellite contains an expensive atomic clock but the receiver contains a regular quartz clock which the receiver itself constantly resets. The receiver looks at the incoming signals from four or more of the satellites and compensates for it's own inaccuracy. Once it calculates the correct time value this will cause all the signals that the receiver is getting from the satellites to align at a single point in space. That is the time value held by the atomic clocks in the satellites themselves. So the receiver sets it's clock to that time value and therefore has the same time value as all the satellites. Atomic clock accuracy for quartz clock prices. You can't beat that.
When you measure the distance to four satellites you can draw four spheres that all intersect at one point. Three spheres will intersect even if you're way off but four spheres will only intersect if you are exactly right. The receiver can calculate the time needed for the spheres to intersect at one point. Based on this it resets it's clock to match the atomic clocks of the satellites. The receiver does this constantly as long as it is on, which gives it the same accuracy as the atomic clocks in the satellites.
In order for this info to be of any use, the receiver also has to know where the satellites actually are. To do this, the receiver stores an almanac that tells where each satellite is at a given time. Any adjustments that need to be made because of gravitational pull are transmitted to the receivers by the department of the military.
In the last instalment of this series we'll go over problems with the system, how they can be compensated for and how to use the data itself.
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Michael Russell
Your Independent guide to Global Positioning Systems
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