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    From: Alexandre Eremenko
    Date: 2004 Oct 22, 01:34 -0500

    Of course, if you are using a computer to reduce
    the sights, there is no point in the averaging
    Well, almost no point.
    (For me, for example, computing averages of
    5 altitudes and 5 times with a pencil
    is a shorter procedure than typing them into
    computer together with GHA and Dec for each of them:-)
    Another point, is that there is no sense in making observations
    in a short time interval.
    If you reduce each sight anyway,
    it is much better to spread them in time,
    so that your position lines will intersect under some decent angles.
    I also doubt that the rigorous "least square" method
    is of any use in practical navigation.
    I think the last chapter of Chauvenet is aimed at astronomers,
    who have a lot of time, and make VERY precise observations.
    Well, again if you are using a computer, you can afford
    to "shoot the birds with a cannon".
    Here is what Russian manuals recommend.
    First reject the lines which look like obvious blunders
    (This applies only if you have more than 3 lines).
    Then you obtain a convex polygon formed by the points
    of intersections of the valid lines.
    Circumscribe an ellipse (by hand, of course!) about this
    polygon. The center of this ellipse is your best guess.
    Even in the case of two lines, they recommend to draw
    parallel lines on the distance of your estimated error
    for each observation. Then you inscribe an ellips in the
    parallelogram thus obtained. The center of the ellips is
    of course the intersection of your lines. But the size and
    shape of the ellipse gives you some good estimate of where you
    actually can be.
    I always assumed that this is all a practical navigator has to
    know about "least squares".
    But again, I am mostly talking about calculation and plotting
    "by hands".
    P.S. Celestaire has a wonderful device called datascope.
    According to their description (I don't have it) it records
    automatically the time and altitude. Now I think it is
    technically easy to upgrade it a bit: to add to this device
    a little computer with the almanach
    in it, (plus termometer-barometer, of course:-) so that
    it will just tell you your position when you press a button
    after having finished your altitude taking.
    So we will be relieved of all tasks except the observation.

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