They left out one of the more interesting aspects of GPS calculations, which is the corrections that must be made for special & general relativistic effects.
Those corrections are not actually essential for GPS to function. In first order it's only the satellites clocks that have to be run at a slightly elevated frequency (or is it the other way round? Don't know). The actual GPS receivers don't have to mess with relativity at all.
The really interesting innovation in GPS is the way they use a priori information about each satellite's signal to "amplify" the signal by processing:
http://www.trimble.com/gps/sub_amplify.shtml
Oh boy. What a strange article. While they try to explain all intricate details, their funny use of analogies turns most things they tell either wrong or at least wildly off the mark.
A GPS receiver only receives at a single frequency (leaving out doppler for now) but correlates several pseudorandom codes in simultaneously. It needs four sattelites no to increase the accuracy, but to solve for the fourth unknown, time. Also it doesn't use a quartz clock that resets "lets say at midnight" but measures the relative state of it's correlators' counters (that's what's often called "pseudorange"). And DGPS doesn't correct for incorrectly sent out almanacs. It only corrects for unknown propagation properties of our atmosphere (rather oddly described as slowing down of electromagnetic energy). DGPS also doesn't help you with multipath reception due to reflections at skyscrapers.
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[ 3.9 ms ] story [ 20.5 ms ] threadhttp://en.wikipedia.org/wiki/Gps#Relativity
The really interesting innovation in GPS is the way they use a priori information about each satellite's signal to "amplify" the signal by processing: http://www.trimble.com/gps/sub_amplify.shtml
A GPS receiver only receives at a single frequency (leaving out doppler for now) but correlates several pseudorandom codes in simultaneously. It needs four sattelites no to increase the accuracy, but to solve for the fourth unknown, time. Also it doesn't use a quartz clock that resets "lets say at midnight" but measures the relative state of it's correlators' counters (that's what's often called "pseudorange"). And DGPS doesn't correct for incorrectly sent out almanacs. It only corrects for unknown propagation properties of our atmosphere (rather oddly described as slowing down of electromagnetic energy). DGPS also doesn't help you with multipath reception due to reflections at skyscrapers.
http://en.wikipedia.org/wiki/Wide_Area_Augmentation_System#C...