The question of how GPS receivers get the time is a fascinating one and it turns out to be absolutely integral to how they determine position. That is: it is impossible to solve for position without solving for time, and vice-versa.
One key technical requirement is that all the satellites carry extremely precise clocks are synchronized *with each other*. This allows each one to send a signal to a receiver, essentially timestamped with the time the signal was sent according to the GPS timescale. A receiver can then look at the set of received signals along with their timestamps. The range from each satellite is not initially known, because we do not yet know the difference between our (receiver's) clock and the shared GPS clock. However, because we know that all the GPS clocks are synchronized with each other, we know that there's just a single time bias value to solve for, not one for each received signal. So, we can essentially ask: what clock bias would make all the measured range values converge? I drew a picture of this for a presentation I did some 20 years ago: https://www.circlemud.org/jelson/writings/localization/sld020.htm . Let's think about the problem in two dimensions first. The 3 dots in the picture are satellites. If we somehow knew the exact range to each satellite, we could draw a circle around it and know we were somewhere on that circle. If we had two circles, they'd intersect at our location. Since we don't know the range, but the range plus an unknown bias, we can add a third satellite and then solve for the bias: the key insight is that only a single bias values will make all the circles converge. In the picture, some incorrectly-computed bias is shown as the dotted circles, you can see the three dotted circles do not meet at a single point. There is just a single correct bias value, shown as the solid circles, that causes the circles to converge -- and thus we have solved for both our position (the point where the circles intersect) and the time (the bias values that caused the circles to intersect). In three dimensions, the circles are actually spheres, and you theoretically need four satellites instead of three to account for the extra dimension. Of course, because of errors, the imaginary spheres never actually intersect in one place. More and more satellites let us get better and better estimates of the true bias and true location because it lets us average away non-systematic errors. With this model in mind, you might also now see why "survey mode" works well for timing receivers. If we eliminate the position as a variable, but assume it is known, the system is even more overconstrained; we can use 3 more satellites to average away errors rather than to solve for position. In fact, if we theoretically knew our position a priori, we could determine the time with just a single satellite. Taking this argument to its extreme, if we know our position *and* the time, we need "0 satellites", i.e., we can determine the clock error on the satellite itself! And this is how the clocks in the GPS constellation are set -- a receiver that has canonical USNO time (e.g., because it's at the observatory) and a surveyed position listens for transmissions from a satellite, determines the time error, and sends back a message with a clock correction. -Jeremy N3UUO On Thu, Jul 22, 2021 at 6:01 PM Robert DiRosario <ka3...@comcast.net> wrote: > If I want to use GPS for time and frequency standards, just how solidly > does the antenna need to be mounted? > The easiest and least expensive way to mount a GPS antenna would be up > on two 10' TV mast sections, but that > would move around a bit in the wind. Maybe two or three inches. Or do > I need to do better? All of the "easy" or > "good" spots in my yard already have amateur radio antennas. > > A second question, and it may very between different GPS receivers, how > to they get the time? Do they just take one signal > with a good S/N number and correct for the distance from that satellite, > or do something more complicated with several signals? > > Thanks > Robert > _______________________________________________ > time-nuts mailing list -- time-nuts@lists.febo.com -- To unsubscribe send > an email to time-nuts-le...@lists.febo.com > To unsubscribe, go to and follow the instructions there. > _______________________________________________ time-nuts mailing list -- time-nuts@lists.febo.com -- To unsubscribe send an email to time-nuts-le...@lists.febo.com To unsubscribe, go to and follow the instructions there.