"Mark Sims" <hol...@hotmail.com> wrote: >> >> My Ashtech Z12 system has located my g-spot to within 4mm lat/lon >> and 27mm altitude.
I forwarded the full post to a good friend who knows a LOT about GPS and herewith is his reply: > The Z-12 is an excellent receiver and should determine lat. & lon. > within 4 mm. Height uncertainty is always greater, usually by a > factor of three. This guy's height uncertainty is anomalously large > -- greater than his lat. or lon. uncertainty by a factor of about > seven(!). The most likely reason for his large height uncertainty is > that he failed to observe satellites all the way from high elevation > angles (greater than about 70 deg) down to low elevations (certainly > below 15 deg, preferably below 10 deg, and even better, down to 5 deg). > > It is _important_ to observe down to low elevation because only at low > elevation can tropospheric thickness be distinguished from height (and > relatedly, from receiver clock synchronization offset). The signature > of height in the pseudorange phase-delay (carrier phase) observable is > proportional to the cosine of the zenith angle. The signature of > receiver clock synchronization offset is constant, so the only useful > parts of the height signature are its slope (the linear term in a > Taylor-series expansion in powers of the zenith angle) and curvature > (the quadratic term in this Taylor series). (The software that > analyzes GPS observations does not use Taylor series; it uses > trigonometry. However, for mental understanding it can be useful to > _think_ of the terms of a Taylor series.) > > The signature of tropospheric thickness is approximately proportional > to the secant of the zenith angle. (The proportionality would be > exact if the Earth were flat and the troposphere were horizontally > stratified with any vertical profile.) In a Taylor-series expansion > of the signature of tropospheric thickness as a function of zenith > angle, the constant, linear, and quadratic terms are similar to, or > are masked by, the combination of receiver clock and height. To > distinguish height from troposphere you need to see the _next_ term in > the series, the cubic term. More accurately speaking, you need to see > the pseudorange blow up as the zenith angle approaches 90 degrees and > the secant approaches infinity. The near-singularity at the horizon > is a unique signature, and by far your best handle on the > troposphere. If you pin down the troposphere by observing close to > the horizon, then your only problem is to distinguish clock-offset > from height, which is easy if you have observed from zenith angle < 20 > degrees to zenith angle > 70 deg. > > _Then_ your height uncertainty will still be three times your lat. or > lon. uncertainty because you saw the signature of latitude vary almost > from -1 to +1 when you observed satellites low in the north and low in > the south; and you saw the signature of longitude vary almost from -1 > to +1 when you observed satellites low in the east and low in the > west; but you saw the signature of height vary only from about +0.94 > ( = cos 70 deg ) to about +0.25 ( = sin 15 deg ). So your handle on > height was smaller than your handle on lat. or lon. by a factor of > about three. > > I kinda rushed through this explanation. I hope it made some sense to > you. > > If this guy cares most about clock sync., then he needs to determine > height well, so he needs to determine tropospheric thickness, so he > needs to observe down to low elevations. He may have been unable to > observe low elevations because his antenna's view of the sky was > blocked by houses and trees. If so, then he should put his antenna up > on a pole, and in the middle of a wide open space. > >> I used the OPUS-RS system to process 1.5 hours of data.... > > A GPS satellite moves through the sky by less than a radian in 1.5 > hours. In order to watch each satellite move through a wide range of > elevation or zenith angle, from culmination (max. el.) to as close to > the horizon as possible, he should observe longer than 1.5 hours. At > least three hours. Preferably six. If he's at home, or at any fixed > location, 24 hours. Why not? The receiver and the data-processing > software will handle 24 hours of observing all available satellites > with no sweat; and the data-processing s/w will be much happier with > its simultaneous solution for lat., lon., height, clock-offset, clock > rate, and troposphere. > > Observing only 1.5 hours makes sense only when the distance between > receiver-antennas is small so that the troposphere cancels well > between them, and/or if you don't care about millimeter-level position > (or picosecond-level clock) accuracy. > > In land surveying, it's customary to observe at least twice as long as > it takes to travel to a site and set up; and for longer if the > customer is paying for accuracy. > > >> using 9 baselines to national CORS reference stations... > > Excellent. That's how it's done by people who know. > >> and the rapid (1-day) orbits... > > Which is fine for rapid results and/or for short distances. For > longer distances, after you allow for travel time and time spent > writing a report, you may as well use precise (two-week) ephemerides, > and you'll want to if your customer is paying for accuracy. > >> not too shabby for 15+ year old technology. > > The only thing shabby was the height determination, as discussed above. > >> The fix should be even more accurate when the precise (two week) >> orbits are available. > > Yes, but the height will still be poorly determined, as discussed above. > [snip] > >> Doing some statistical hand waving over the fixes produced by the >> Tbolt, >> I think I can get it to find its antenna to within around 1 foot. >> So far, >> the fixes that I can get it to produce look much better than the >> standard >> self survey results. Again, it may be an exercise in futility if I >> can't >> get the Tbolt to accept and store a precise location. > > ?? > > >> A GPS guy I know comments that when you start talking down in the >> sub-meter sorts of accuracies, particularly for absolute >> measurements... > > I wish people would not imagine that GPS measurements are "absolute." > If you don't determine position with respect to reference points on > the ground by DGPS, then you are determining position with respect to > a particular combination of satellite orbital position coordinates and > clock-offset parameters that you got from real-time broadcasts or > perhaps later via the Internet from someone. Those position- > coordinate and clock-offset parameter values were determined by > someone who _assumed_ position-coordinate values for certain ground > stations. (Real-time broadcasts suffer substantially from > extrapolation; and short-time orbit-determinations usually also > involve a significant amount of extrapolation.) There ain't no such > thing as absolute position, any more than there is "absolute time." > All position and all time measurements are _relative_ to some man-made > and man-maintained "standard." If you are talking about state-of-the- > art, research-grade measurements, then it is essential to understand > the relevant standards. > > >> there's a whole raft of factors that are all of the same general >> magnitude >> that you need to take into account: tidal deformation, ionosphere, >> multipath, thermal distortion of your antenna, changes in the cable >> due to >> temperature, etc.etc.etc.> > > The factors recited in the above-quoted paragraph are _NOT_ all of the > same magnitude. Not even close. > > In principle, there is no upper limit on the magnitudes of the errors > that bad hardware, bad software, or a bad operator may commit. > However, with an Ashtech Z-12 receiver (which is a good geodetic-grade > receiver), a good geodetic-grade antenna, good geodetic-grade > software, and a knowledgeable operator, NONE of these factors is > significant at the meter level. > > Only one of them rises above the decimeter level. Proper data- > processing algorithms reduce sensitivity to half of them to below the > _millimeter_ level. Proper differencing between satellites reduces > cable effects to _way_ below the millimeter level. > > Only a totally inappropriate antenna would introduce thermal effects > above the millimeter level. Only with a bad antenna COMBINED with > inappropriate observing and inappropriate data-processing, could > multipath cause errors greater than a few millimeters. [Yes, > multipath can affect the group-delay (a.k.a. code delay) of a signal > by more than a nanosecond, equivalent to more than 30 cm or range. > However, in proper data-processing, group-delay observations are > utilized only to get a first, rough, position and clock-offset > determination or "fix." Then the software utilizes carrier-phase > observations to determine position at the few-millimeter to millimeter > to submillimeter level (depending on distance from a reference > station) and the receiver clock synchronization offset at the > picosecond level. > > Only with a single-band receiver, with inappropriate observing, and/or > with inappropriate data-processing, could the ionosphere cause errors > greater than a centimeter. > > Of all the named factors, only solid-Earth tide is a decimeter-level > effect. Straightforward modeling in software reduces its residual > effect to less than a centimeter, or less for distances under 1000 km. > [snip] ********** I've omitted his name as he is really too busy consulting to participate in much correspondance. Best, -John _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.