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I'm just finishing up a report on the mathematics of GPS, but I'm not sure how to determine how often a GPS receiver actually receives data from the satellites.

If a satellite send out its microwave signals at a frequency of 1575.42 MHz, does that mean it sends out a signal every $1/1575.42\times10^6=6.35\times10^{-10}$ seconds? Or I am I just working out the period of the wave here? If so, how would I determine how often a signal is received?

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    $\begingroup$ 1575.42 MHz is the carrier frequency. The signal is modulated onto this at a much lower frequency. L band microwave is a common comms frequency between Earth and satellites, not only GPS. This would be a much better question for Electrical Engineering SE - you're much likelier to get a good answer there. $\endgroup$ – WetSavannaAnimal May 23 '15 at 10:05
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The satellites broadcast continuously, so there is no "signal reception interval" per se. Like others wrote, the 1.57542 GHz oscillation is just a carrier-wave for additional modulations on top of it.

To directly answer the question - a receiver can chose to sample the satellite signal for example for only 8 milliseconds, or longer say 500 ms, or it can continuously receive it (this is usually called "tracking mode" and is done after acquisition of the signal in the first place). If you listen longer, you have a better chance of "seeing" the satellites and getting a better fix.

The more complicated answer is that you have to realize that the GPS system is not a typical communications medium where you send abstract pieces of information from A to B like in a normal radio transmission, in GPS there are layers of bit encodings and sub-bit / phase decodings of the modulation layers themselves, doppler-shift analysis of the modulations because the sats move etc.; a bit too complicated to describe in a reply here and I don't think it's what you're looking for either (but if you want, just ask in the comment and I'll explain).

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There is a description of GPS signals here. 1575.42 MHz is one of five carrier frequencies used (reflects the period of a carrier wave, not a message).

Several signals are transmitted by the GPS satellites. One has a message period of a millisecond, so part of your answer is 1000 times a second. Another signal is transmitted at 50 bits/sec and requires 12.5 minutes for the receiver to assemble a complete message. Yet another message is extremely long and repeats only once a week.

I think the answer to your question is

  1. not straightforward, and
  2. dependent on what type of information is to be extracted from the GPS signals
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