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I am trying to really understand how GPS works, to be able to "explain it to my grandma" level of understanding.

One key aspect that I can't find an answer to is: how is the GPS signal transmission time, as registered by the on-board atomic clock, encoded in the GPS signal?

I would not imagine it is in the Navigation Message which has only a rate of 50bit/s which is surely not enough to achieve any type of spatial resolution.

largehadroncollider
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  • Welcome to Stack Exchange! You've added the gps tag, click it to see related questions and answers that may be helpful. – uhoh Aug 14 '22 at 05:42
  • There is no easy and short description of this theme. A book about GPS needs 7 pages and 5 complex figures. Unfortunately there is no Wikipedia entry about this theme. – Uwe Aug 14 '22 at 09:29
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    You can probably find the relevant info on Navipedia. https://gssc.esa.int/navipedia/index.php/GPS_Navigation_Message – PM 2Ring Aug 14 '22 at 10:22
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    When comparing 50bit/s to the required timing precision, you miss one important fact: It doesn't matter how long a 'beep' is - the import thing is, how precisely can you detect when it starts? – asdfex Aug 14 '22 at 16:27
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    Not an expert here (hence, not an "answer") but aren't the PRN codes and even the carrier waves synchronized to the satellite's atomic clocks? I.E., if you are decoding the signal at all, then your local clock already is ticking in sync with the satellite's clock. If that's true, then in theory you should only need to hear the "clock offset" one time, and you should be able to know the value of the satellite's clock from that point onward. – Solomon Slow Aug 15 '22 at 00:20
  • @SolomonSlow Almost right. Although you don't have a local clock that is in sync to a degree necessary for positioning. That's why you need signals from four satellites and not only three. Your clock will run at the same speed has the received one, but the time offset is unknown. – asdfex Aug 15 '22 at 07:44
  • @asdfex yeah but that doesn't really answer my question. Even if you can detect when it starts precisely, it will be the time that you detected at the receiver the start of the bit sequence. How do you know when that sequence left the GNSS satellite from your incorrect receive time? – largehadroncollider Aug 18 '22 at 11:09
  • @SolomonSlow, I think I understand your point and @ asdfe comment to your comment. You just say: okay I am synced up, now the definition of a second is univocal between receiver and GNSS satellite. I just have to calculate the offset. Very well, but then what is Tsat, signal transmission time? do you just assume this is the same a Treceived and work back from there? You need a hard figure for Tsat otherwise you can't precisely use the ephemeris in the Nav message. – largehadroncollider Aug 18 '22 at 11:19
  • It's the wrong place for discussion here, but: You can do that iteratively. First you take some approximation of the distance, get an initial guess of your position, recalculate distance and repeat. – asdfex Aug 18 '22 at 12:34

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