[time-nuts] tube GPS receivers

[Bob Camp]

Hi


On Jun 22, 2013, at 8:13 PM, Magnus Danielson <magnus at rubidium.dyndns.org> wrote:

> 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,

Core and tubes??? Hmmm…..

Bob

> 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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