[time-nuts] Re: GPS antenna question

[Sanjeev Gupta]

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 <jelson at gmail.com> 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 <ka3zyx at 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
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