[time-nuts] tube GPS receivers

Magnus Danielson magnus at rubidium.dyndns.org
Sat Jun 22 20:13:28 EDT 2013


On 06/23/2013 01:52 AM, Jim Lux wrote:
> On 6/22/13 4:38 PM, Magnus Danielson wrote:
>
>>>
>>> electromechanical.. like omega receivers. rotary transformers can do
>>> very high quality trig functions, but do you actually need trig
>>> functions assuming you're just solving for X,Y,Z,T.
>>
>> Oh yes. Check IS-GPS-200F, clause 20.3.3.4.3 User Algorithm for
>> Ephemeris Determination, found on page 113 and forward. The Table 20-IV
>> contains the actual formulas. The Kepler's Equation for Eccentric
>> Anomaly is a bit annoying, since it is not in closed form, so one way or
>> another of approximation iteration is needed.
>>
>> Quite a bit of trigonometry goes on just to have each tracked satellites
>> current position estimated, such that the pseudo-range value taken for
>> the bird can be diffed out with the position. That process becomes
>> trivial if the position is known and only time is needed, given that we
>> cranked out the birds X, Y, Z and T position, which requires
>> trigonometry.
>
> Yes, but that trig can be done VERY slowly, since the cycle time is 12
> hours, which is why a resolver/rotary transformer approach seems viable.
>
> (rather, than, say, integrating the satellite state vector)

Indeed.

>>
>>> Are you allowed to externally supply the almanac, in the form of a
>>> electromechanical system. The satellites are in circular orbits and
>>> fairly stable, and with multiple satellites in the same plane.
>>
>> You could naturally cheat in several interesting ways, but you need
>> fairly accurate X, Y and Z values for the birds at any given time.
>
>
> How accurate?? Resolvers are good to about 16 bit accuracy, so I guess 1
> part in 60,000. if the orbit circumference is 163 Mm, then a resolver
> can determine the position to a few km.
> However, I don't know that that is good enough. If you need to know to 1
> chip at C/A code rates, 1 microsecond, that's a pretty small fraction of
> one 12 hour rev of 43200 seconds. But maybe not.

Hmm. You could tabulate it even. It would be quite a bit of core-memory, 
but achieveable.

Oh, and it isn't full 43200 s, it's only about 11 hours and 58 min.

>>> Actually, how bad would your time estimate be if you just assumed
>>> perfect circular orbits with no higher order corrections?
>>
>> Grabbing a modern set of data, doing the calculations with and without
>> the proper values would tell you. I would not be surprised if it where
>> way over the km off. On the other hand, the precision we talk about in
>> general already throws us off sufficiently, so who cares.
>>
>> One should realize that we talk about tens of Mm numbers in pseudo-range
>> distances.
>>
>
> So I think you probably can't get a position fix within 10km, but hey,
> what a beast it would be.

Oh yes.

With a RAIM algorithm you could use extra channels to overcome 
deficiencies in the crudeness of the calculations.

Would be neat if there would be a PLL steering of the revolving calender 
to maintain with minimum error. The T error would be a natural detector 
to use. Extra grade if individual birds got adjusted.

Cheers,
Magnus


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