[time-nuts] [Fwd: Accurate Thunderbolt position]

J. Forster jfor at quik.com
Wed Jul 15 17:53:35 UTC 2009


"Mark Sims" <holrum at 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





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