Jeremy, thank you, especially for covering the 0-satellite case. I wish stuff like this could be on a web page or FAQ or something, where it was easily discoverable.
-- Sanjeev Gupta +65 98551208 http://www.linkedin.com/in/ghane On Fri, Jul 23, 2021 at 9:18 AM Jeremy Elson <[email protected]> wrote: > 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 <[email protected]> > 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 -- [email protected] -- To unsubscribe > send > > an email to [email protected] > > To unsubscribe, go to and follow the instructions there. > > > _______________________________________________ > time-nuts mailing list -- [email protected] -- To unsubscribe send > an email to [email protected] > To unsubscribe, go to and follow the instructions there. > _______________________________________________ time-nuts mailing list -- [email protected] -- To unsubscribe send an email to [email protected] To unsubscribe, go to and follow the instructions there.
