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    Re: Manual calculation of compass variation
    From: Richard B. Langley
    Date: 2004 Oct 19, 09:58 -0300

    On Sat, 16 Oct 2004, Fred Hebard wrote:
    >That was a very informative article for this non-expert navigator, not
    >to mention a reminder of how much I don't know.
    >I was surprised that a vessel needs to be going 5-10 km/hr to get a GPS
    >track accurate to better than one degree, and am wondering what the
    >accuracy of the track is for low speeds, which might easily be
    >encountered in a sailing vessel; I suppose this information is included
    >in GPS manuals, but I don't have one.
    The GPS receiver manuals typically don't discuss heading accuracy (at least
    the one for the Garmin eTrex Vista, which I own, doesn't). But it is not too
    difficult to show, using a back-of-the-envelope propagation of error
    calculation, that the heading accuracy is roughly inversely proportional to
    the speed. The heading is determined by taking the arcsine of the ratio of the
    east component of the velocity to the speed (the magnitude of the velocity
    vector) (arcosine of north component over speed or arctangent of the ratio of
    the east and north components could also be used -- although the latter will
    have problems near 90 and 270 degrees).
    As an approxixmation (making assumptions that the east component is
    approximately equal to the total speed; i.e. the receiver is heading nearly
    due east), we end up with
    delta-A = 1/v delta-v
    that is, the error in the heading (as an azimuth) equals the error in the
    speed divided by the speed (result is in radians which can then be converted
    to degrees). A typical GPS receiver determines speed to an accuracy of about
    0.05 metres per second or 0.2 km per hour. So the heading error will be
         Speed     Heading Error
         (km/hr)     (degrees)
           100         0.1
            10         1.0
             1         10.
    And that is why for GPS receivers which include an electronic magnetic
    compass, an option is included to switch to the compass when the speed drops
    below a certain user-specified value as the compass (if properly calibrated)
    will be more accurate.
    -- Richard
     Richard B. Langley                            E-mail: lang---.ca
     Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
     Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506 453-5142
     University of New Brunswick                   Fax:      +1 506 453-4943
     Fredericton, N.B., Canada  E3B 5A3
         Fredericton?  Where's that?  See: http://www.city.fredericton.nb.ca/

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