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How GPS receivers work (simple and advanced explanations of trilateration)

  1. Nov 19, 2012 #1
    First, the GPS receiver has to "find" at least three satellites. The more, the better.
    Then, it sends a signal to the satellites and waits for their response. It even records the time between when the receiver sent a signal and when it received the response. In a vacuum, the signals can travel at the speed of light (about 3 million meters/second). All it has to do is take the time, divide it by half to get the time it took the signal it sent to reach the satellite, and multiply it by the speed of light. For the most accurate calculation, the timing must be accurate, so the receiver figures out what time it is according to the clocks that the satellites use.
    The receiver now knows its distance to the satellites and the latitude, longitude, and elevation of each of the satellites.
    The receiver then "draws" three spheres, each one centered at a satellite and having a radius equal to its distance to the receiver. Those three spheres intersect at only one point: your current location. This is known as trilateration.

    Advanced (for math geeks): The receiver knows that its distance to a satellite can be calculated using the following equation:

    (x1-x2)2 + (y1 - y2)2 + (z1 - z2)2 = r2

    where point 1 represents the satellite, and point 2 represents the receiver, and r is the distance to the satellite
    Given the distance to three satellites and their positions, it now has three equations. The receiver then finds the point whose x, y, and z coordinates satisfy all three equations. This point represents where you are in coordinate space.
     
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  3. Nov 19, 2012 #2

    rcgldr

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  4. Nov 19, 2012 #3

    phinds

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    moonman239, what was your point in posting this? Is there a question in there somewhere or did you just need to get that off your chest?

    I note that you have completely ignored relativity effects, which means that your receiver will likely end you up in a cornfield somewhere.
     
  5. Nov 19, 2012 #4
    How does relativity affect the accuracy of the signal?
     
  6. Nov 19, 2012 #5

    rcgldr

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    Due to gravitational relativistic effects, the clocks on satellites in orbit should run faster than they would if on the surface of the earth. The relative speed of the satellites should cause their clocks to run slower. The combined effects result in their clocks running faster.

    More information can be found at this web site:

    gps_and_relativity.htm

    The wiki article on GPS mentions a correction factor:

    the P code, for U.S. military use, transmits at 10.23 million chips per second. The actual internal reference of the satellites is 10.22999999543 MHz to compensate for relativistic effects
     
    Last edited: Nov 19, 2012
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