Hi
On Jun 22, 2013, at 8:13 PM, Magnus Danielson <[email protected]> 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 > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
