Hi Well if the chip rate is at or above 1 MHz, a wavelength is 300 meters or less. A 1 KM error is probably a bit to large.
Bob On Jun 22, 2013, at 7:52 PM, Jim Lux <[email protected]> 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) > > >> >>> 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. > > > >> >>> You'd only need trig to convert X,Y,Z into lat/lon, and for us timenuts >>> types, do you really need lat/lon? In fact, do you even need to solve >>> for earth centered coordinates? Why not work in inertial space (whether >>> your receiver happens to be moving in a circle at 1 rev/24 hrs or flying >>> in a plane at something else is sort of immaterial) >> >> Once you come to having a X, Y, Z and T, the remaining trig operations >> is trivial to what you already have done, so you might as well do them. >> >>> I envision something with a common shaft running at 1 rev/12 hours that >>> drives N rotors (one for each satellite). there's a small motor that >>> sets the offset of the rotor relative to the shaft to account for small >>> movements along the orbit plane. That, plus some other transformers >>> would give you X,Y, and Z for each satellite. >> >> You have a sick mind. What worse is, I understood what you actually meant! >> >>> 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. > > > > >> 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. _______________________________________________ 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.
