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    Re: Geodetic Survey Web site
    From: Thomas Schmidt
    Date: 1997 Dec 14, 3:46 PM

    Paul Hirose wrote:
    > [...]
    > I'm skeptical about this SA eliminator program.  The developer says it
    > has .0001 minute accuracy?  Maybe it does, but I'll bet this is an
    > extreme figure, based on occupying the site for an impractical length
    > of time.  I'd like to see his test results.
    > [...]
    Yes, the problem is: you need not only a lot of fixes for averaging,
    they also must be adequately spaced in time.
    Improving a result by averaging individual measurements assumes that
    the errors in these measurements are randomly distributed so that
    they have a tendency to cancel out in the average.
    However, the errors induced by SA are varying only _slowly_, so that
    two fixes obtained within a few seconds have more or less the same
    error and nothing is gained by averaging them. The well-known rule
    about the error of the average decreasing as the square root of the
    number of the measurements averaged does not apply for these
    'correlated' measurements.
    So you have to wait a while until SA has produced a 'new' error to
    obtain a new, uncorrelated fix.
    A rough estimate:
    Let's say the average error of a fix is 50 m (as a _very_ rough number).
    That's about 0.03 min of arc. Getting down to 0.0001 means an
    improvement by a factor 300. _If_ your fixes are uncorrelated, that
    means you need 300^2 = 90000 fixes for averaging. In order to have your
    fixes uncorrelated, you have to wait say four minutes between fixes.
    That results in a total measurement duration of 90000*4 minutes or
    250 days.
    And that's assuming there are no systematic errors (like deficiencies
    in the atmospheric delay models etc. etc.)
    Any comments on this estimate?
    Anyone who would like a closer look at some averaging results
    may want to visit
    Kind regards,
      Th. Schmidt
    schmidt@hoki.ibp.fhg.de                 > This is a standard disclaimer
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