[You may copy what I've written as long as you don't identify me. -C.] On Sep 9, 2009, at 9:31 PM, J. Forster wrote: ---------------------------- Original Message ---------------------------- Subject: Re: [time-nuts] time-nuts Digest, Vol 62, Issue 25 From: "Mark Sims" <[1]holrum@hotmail.com> Date: Wed, September 9, 2009 4:43 pm To: [2]time-nuts@febo.com ----------------------------------------------------------------------- --- I have a geodetic grade Ashtech Z12 GPS receiver and antenna. You collect data with it (both L1 and L2 carrier phase) and email ! the data to the National Geodetic Survey OPUS processing system. They crunch the numbers 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 stations that continuously collect data and monitor and cross-check each other. Included in the OPUS results is an error estimate. I have done several runs and the error estimates are usually under 4mm. However if you compare the spread in the actual locations generated, they are usually 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 repeatab! ly within a small fraction of 1 mm -- as appears to be happening. 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 reference station. 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 positi! on 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 CORS 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. References 1. mailto:holrum@hotmail.com 2. mailto:time-nuts@febo.com