[time-nuts] CORS, Etc.
jfor at quik.com
Thu Sep 10 17:23:21 UTC 2009
This is from a friend:
> I have a geodetic grade Ashtech Z12 GPS receiver and antenna. You
> data with it (both L1 and L2 carrier phase) and email the data to the
> National Geodetic Survey OPUS processing system. They crunch the
> and come back with a location (it's free).
> The location is calculated by crunching the numbers against the data
> collected simultaneously at 3-9 CORS reference stations. The CORS
> network is a network of several hundred fixed high-precision GPS
> that continuously collect data and monitor and cross-check each other.
> Included in the OPUS results is an error estimate. I have done
> runs and the error estimates are usually under 4mm. However if you
> compare the spread in the actual locations generated, they are
> within 400 microns.
The writer (Mark Sims) must be located near a CORS reference station.
If he were within about 1 km of a reference station, then I would
expect his position to be determined with respect to this station
repeatably within a small fraction of 1 mm -- as appears to be
I don't know how OPUS' uncertainty estimates are derived. [BTW, it's
wrong to call them "error estimates," because this name implies that
they are estimates of the errors of the estimated values of the
position coordinates. They are not estimates of these errors. The
error of an estimate, by definition, is the difference between the
estimated value and the true value, which you probably don't know and
may never know. The error is a random variable. One _can_, however,
reasonably estimate properties or parameters of the probability
density function of this random variable. For example, based on
experience with similar determinations or measurements, you might
estimate the standard deviation of the error, or the "CEP" (Circular
Error Probable), or the like.] It is common to estimate the
covariance of a position determination by combining an a priori
covariance matrix for a very large set of parameters, e.g., the
position coordinates of the CORS reference stations, with the
covariance matrix (actually the inverse covariance) derived from a
weighted-least-squares fit to the observations just processed -- in
this case the L1 & L2 carrier phase observations by your Z12 receiver.
The 4-mm uncertainty of your position estimate may be dominated by a
priori uncertainty in the assumed coordinates of the nearby CORS
Remember that _all_ position determination is relative to some
artificial origin. There is no such thing as absolute position. The
coordinates of all of the CORS reference stations were determined by
some person(s) with respect to an origin that they chose. Most likely
this origin was not any single, identifiable point; it was some
average of many identifiable points.
The uncertainty of the determination of the position difference, or
the relative-position vector, between your antenna's phase-center and
the nearby CORS reference station antenna's phase-center may be less
than one millimeter. (The locally-horizontal coordinate components of
the vector are usually better determined than the locally-vertical
component, typically by a factor of about three.)
> I am pretty darn sure I know where I am... except that I am drifting
> across the planet at about 10 mm / year. (The location info for the
> reference stations includes a velocity vector).
That's right. It must be, because the CORS reference stations are
physical monuments planted in the ground, i.e., in the crust of the
Earth; and the crust of the Earth is not rigid. Every monument is
moving with respect to every other monument. So the coordinates of
the CORS reference stations are not constant; they have non-zero time-
derivatives. The magnitudes of these derivatives are of the order of
a few centimeters per second. Parts of the Pacific Plate are moving
with respect to parts of the North American Plate by about 8 cm/yr.
Parts of California are moving with respect to other parts of
California by about 4 cm/yr. The northeastern USA is moving with
respect to northern Europe by about 1.7 cm/yr. These positions and
velocities have been estimated by various people/groups/organizations
and are published on the Web. Many of these positions and velocities
are very well known, because determinations of the relative positions
of monuments separated by transcontinental and intercontinental
distances have been made with cm- to mm-level uncertainties for about
thirty years now.
> And let's not get into things like thermal expansion of my front
> deck and tidal deformation of
> the earth's crust...
Whether you like it or not, the Earth's crust deforms on various time-
scales. Over years to millions of years, plate tectonics move things
at more or less uniform rates of centimeters per year. Tidal strains
are quasi-periodic with mainly semidiurnal, daily, and monthly
periods, and amplitudes of the order of 10^-7. Earthquakes and other
motions associated with active faults may be episodic, may be sudden,
and may be quite large (meters to tens of meters) locally. Subsidence
occurs on various time-scales due, e.g., to extraction of fluids via
wells. Parts of the Earth's crust that were covered by the glacier
more than 10^4 years ago are still rebounding. Then there's frost.
The oceans load the crust and deform it, too.
Thinking of the Earth as rigid can lead a person into serious error,
just as thinking that there is such a thing as "ground" for
electricity at radio frequencies has led many radio engineers /
technicians / hams into serious error.
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